elliptic-curve 0.1.0 → 0.2.1

raw patch · 131 files changed

+11698/−4549 lines, 131 filesdep +textdep ~basedep ~galois-fielddep ~protolude

Dependencies added: text

Dependency ranges changed: base, galois-field, protolude

Files

ChangeLog.md +33/−0
README.md +22/−22
benchmarks/BinaryBenchmarks.hs +50/−0
benchmarks/EdwardsBenchmarks.hs +32/−0
benchmarks/FieldBenchmarks.hs +11/−0
benchmarks/GroupBenchmarks.hs +8/−0
benchmarks/Main.hs +6/−173
benchmarks/MontgomeryBenchmarks.hs +25/−0
benchmarks/WeierstrassBenchmarks.hs +109/−0
elliptic-curve.cabal +71/−31
generate/Generate/Binary/Curve.hs +144/−0
generate/Generate/Binary/Generate.hs +84/−0
generate/Generate/Binary/Parameters.hs +379/−0
generate/Generate/Binary/Types.hs +27/−0
generate/Generate/Curve.hs +62/−0
generate/Generate/Edwards/Curve.hs +144/−0
generate/Generate/Edwards/Generate.hs +84/−0
generate/Generate/Edwards/Parameters.hs +199/−0
generate/Generate/Edwards/Types.hs +27/−0
generate/Generate/Generate.hs +41/−0
generate/Generate/Montgomery/Curve.hs +129/−0
generate/Generate/Montgomery/Generate.hs +84/−0
generate/Generate/Montgomery/Parameters.hs +139/−0
generate/Generate/Montgomery/Types.hs +27/−0
generate/Generate/Pretty.hs +40/−0
generate/Generate/Types.hs +24/−0
generate/Generate/Weierstrass/Curve.hs +159/−0
generate/Generate/Weierstrass/Generate.hs +84/−0
generate/Generate/Weierstrass/Parameters.hs +1035/−0
generate/Generate/Weierstrass/Types.hs +27/−0
generate/Main.hs +104/−0
src/Curve.hs +78/−40
src/Curve/Binary.hs +209/−71
src/Curve/Binary/SECT113R1.hs +74/−42
src/Curve/Binary/SECT113R2.hs +74/−42
src/Curve/Binary/SECT131R1.hs +74/−42
src/Curve/Binary/SECT131R2.hs +74/−42
src/Curve/Binary/SECT163K1.hs +76/−44
src/Curve/Binary/SECT163R1.hs +74/−42
src/Curve/Binary/SECT163R2.hs +75/−43
src/Curve/Binary/SECT193R1.hs +74/−42
src/Curve/Binary/SECT193R2.hs +74/−42
src/Curve/Binary/SECT233K1.hs +76/−44
src/Curve/Binary/SECT233R1.hs +75/−43
src/Curve/Binary/SECT239K1.hs +76/−44
src/Curve/Binary/SECT283K1.hs +76/−44
src/Curve/Binary/SECT283R1.hs +75/−43
src/Curve/Binary/SECT409K1.hs +76/−44
src/Curve/Binary/SECT409R1.hs +75/−43
src/Curve/Binary/SECT571K1.hs +76/−44
src/Curve/Binary/SECT571R1.hs +75/−43
src/Curve/Edwards.hs +197/−55
src/Curve/Edwards/Curve1174.hs +77/−46
src/Curve/Edwards/Curve41417.hs +77/−46
src/Curve/Edwards/E222.hs +77/−46
src/Curve/Edwards/E382.hs +77/−46
src/Curve/Edwards/E521.hs +77/−46
src/Curve/Edwards/Ed25519.hs +77/−46
src/Curve/Edwards/Ed3363.hs +77/−46
src/Curve/Edwards/Ed448.hs +77/−46
src/Curve/Edwards/JubJub.hs +77/−46
src/Curve/Montgomery.hs +96/−74
src/Curve/Montgomery/Curve25519.hs +64/−46
src/Curve/Montgomery/Curve383187.hs +64/−46
src/Curve/Montgomery/Curve448.hs +64/−46
src/Curve/Montgomery/M221.hs +64/−46
src/Curve/Montgomery/M383.hs +64/−46
src/Curve/Montgomery/M511.hs +64/−46
src/Curve/Weierstrass.hs +343/−76
src/Curve/Weierstrass/ANSSIFRP256V1.hs +89/−45
src/Curve/Weierstrass/Anomalous.hs +89/−45
src/Curve/Weierstrass/BLS12381.hs +118/−0
src/Curve/Weierstrass/BLS12381T.hs +130/−0
src/Curve/Weierstrass/BLS12_381.hs +0/−74
src/Curve/Weierstrass/BLS12_381T.hs +0/−86
src/Curve/Weierstrass/BLS48581.hs +118/−0
src/Curve/Weierstrass/BLS48581T.hs +168/−0
src/Curve/Weierstrass/BLS48_581.hs +0/−74
src/Curve/Weierstrass/BLS48_581T.hs +0/−130
src/Curve/Weierstrass/BN224.hs +91/−47
src/Curve/Weierstrass/BN254.hs +91/−47
src/Curve/Weierstrass/BN254A.hs +91/−47
src/Curve/Weierstrass/BN254AT.hs +101/−57
src/Curve/Weierstrass/BN254B.hs +91/−47
src/Curve/Weierstrass/BN254BT.hs +101/−57
src/Curve/Weierstrass/BN254T.hs +101/−57
src/Curve/Weierstrass/BN256.hs +91/−47
src/Curve/Weierstrass/BN384.hs +91/−47
src/Curve/Weierstrass/BN462.hs +91/−47
src/Curve/Weierstrass/BN462T.hs +101/−57
src/Curve/Weierstrass/BN512.hs +91/−47
src/Curve/Weierstrass/BrainpoolP160R1.hs +89/−45
src/Curve/Weierstrass/BrainpoolP160T1.hs +89/−45
src/Curve/Weierstrass/BrainpoolP192R1.hs +89/−45
src/Curve/Weierstrass/BrainpoolP192T1.hs +89/−45
src/Curve/Weierstrass/BrainpoolP224R1.hs +89/−45
src/Curve/Weierstrass/BrainpoolP224T1.hs +89/−45
src/Curve/Weierstrass/BrainpoolP256R1.hs +89/−45
src/Curve/Weierstrass/BrainpoolP256T1.hs +89/−45
src/Curve/Weierstrass/BrainpoolP320R1.hs +89/−45
src/Curve/Weierstrass/BrainpoolP320T1.hs +89/−45
src/Curve/Weierstrass/BrainpoolP384R1.hs +89/−45
src/Curve/Weierstrass/BrainpoolP384T1.hs +90/−46
src/Curve/Weierstrass/BrainpoolP512R1.hs +89/−45
src/Curve/Weierstrass/BrainpoolP512T1.hs +89/−45
src/Curve/Weierstrass/SECP112R1.hs +89/−45
src/Curve/Weierstrass/SECP112R2.hs +89/−45
src/Curve/Weierstrass/SECP128R1.hs +89/−45
src/Curve/Weierstrass/SECP128R2.hs +89/−45
src/Curve/Weierstrass/SECP160K1.hs +91/−47
src/Curve/Weierstrass/SECP160R1.hs +89/−45
src/Curve/Weierstrass/SECP160R2.hs +89/−45
src/Curve/Weierstrass/SECP192K1.hs +91/−47
src/Curve/Weierstrass/SECP192R1.hs +89/−45
src/Curve/Weierstrass/SECP224K1.hs +91/−47
src/Curve/Weierstrass/SECP224R1.hs +89/−45
src/Curve/Weierstrass/SECP256K1.hs +91/−47
src/Curve/Weierstrass/SECP256R1.hs +89/−45
src/Curve/Weierstrass/SECP384R1.hs +89/−45
src/Curve/Weierstrass/SECP521R1.hs +89/−45
src/Group.hs +56/−0
src/Group/Field.hs +100/−0
src/Group/Field/BN254TF.hs +85/−0
tests/BinaryTests.hs +28/−20
tests/CurveTests.hs +0/−74
tests/EdwardsTests.hs +19/−11
tests/FieldTests.hs +11/−0
tests/GroupTests.hs +122/−0
tests/Main.hs +2/−1
tests/MontgomeryTests.hs +20/−13
tests/WeierstrassTests.hs +62/−53

ChangeLog.md view

@@ -1,5 +1,38 @@ # Change log for elliptic-curve +## 0.2.1++* Fix dependency issue with `galois-field`.++## 0.2.0++* Add `Arbitrary` instances for elliptic curves.+* Add `Pretty` instances for elliptic curves.+* Add `Random` instances for elliptic curves.+* Add `Group` class for elliptic curves.+* Add `Field` group under the `Group` class.+* Add `BN254TF` field group under the `Field` form.+* Add `Projective` coordinates for `Binary` curves.+* Add `Projective` coordinates for `Edwards` curves.+* Add `Jacobian` coordinates for `Weierstrass` curves.+* Add `Projective` coordinates for `Weierstrass` curves.+* Add `char` function for elliptic curves.+* Add `cof` function for elliptic curves.+* Add `disc` function for elliptic curves.+* Add `def` function for groups.+* Add `gen` function for groups.+* Add `order` function for groups.+* Add `mul` function over exponent prime fields.+* Add `mul'` function over integers.+* Add `point` function for elliptic curves.+* Add `pointX` function for elliptic curves.+* Add `fromA` function for elliptic curves.+* Add `toA` function for elliptic curves.++## 0.1.1++* Fix dependency issue with `galois-field`.+ ## 0.1.0  * Initial release.

README.md view

@@ -206,19 +206,19 @@   * [Curve25519 (Ed25519)](src/Curve/Montgomery/Curve25519.hs)   * [Curve383187](src/Curve/Montgomery/Curve383187.hs)   * [Curve448 (Goldilocks)](src/Curve/Montgomery/Curve448.hs)-  * [M-221](src/Curve/Montgomery/M221.hs)-  * [M-383](src/Curve/Montgomery/M383.hs)-  * [M-511](src/Curve/Montgomery/M511.hs)+  * [M221](src/Curve/Montgomery/M221.hs)+  * [M383](src/Curve/Montgomery/M383.hs)+  * [M511](src/Curve/Montgomery/M511.hs)  ### Weierstrass curves  * [Anomalous](src/Curve/Weierstrass/Anomalous.hs)-* [ANSSI-FRP256V1](src/Curve/Weierstrass/ANSSIFRP256V1.hs)+* [ANSSIFRP256V1](src/Curve/Weierstrass/ANSSIFRP256V1.hs) * Barreto-Lynn-Scott (BLS) curves-  * [BLS12-381](src/Curve/Weierstrass/BLS12_381.hs)-  * [BLS12-381T](src/Curve/Weierstrass/BLS12_381T.hs)-  * [BLS48-581](src/Curve/Weierstrass/BLS48_581.hs)-  * [BLS48-581T](src/Curve/Weierstrass/BLS48_581T.hs)+  * [BLS12381](src/Curve/Weierstrass/BLS12381.hs)+  * [BLS12381T](src/Curve/Weierstrass/BLS12381T.hs)+  * [BLS48581](src/Curve/Weierstrass/BLS48581.hs)+  * [BLS48581T](src/Curve/Weierstrass/BLS48581T.hs) * Barreto-Naehrig (BN) curves   * [BN224 (Fp224BN)](src/Curve/Weierstrass/BN224.hs)   * [BN254 (CurveSNARK)](src/Curve/Weierstrass/BN254.hs)@@ -233,20 +233,20 @@   * [BN462T (Fp462n2BN)](src/Curve/Weierstrass/BN462T.hs)   * [BN512 (Fp512BN)](src/Curve/Weierstrass/BN512.hs) * Brainpool curves-  * [Brainpool-P160R1](src/Curve/Weierstrass/BrainpoolP160R1.hs)-  * [Brainpool-P160T1](src/Curve/Weierstrass/BrainpoolP160T1.hs)-  * [Brainpool-P192R1](src/Curve/Weierstrass/BrainpoolP192R1.hs)-  * [Brainpool-P192T1](src/Curve/Weierstrass/BrainpoolP192T1.hs)-  * [Brainpool-P224R1](src/Curve/Weierstrass/BrainpoolP224R1.hs)-  * [Brainpool-P224T1](src/Curve/Weierstrass/BrainpoolP224T1.hs)-  * [Brainpool-P256R1](src/Curve/Weierstrass/BrainpoolP256R1.hs)-  * [Brainpool-P256T1](src/Curve/Weierstrass/BrainpoolP256T1.hs)-  * [Brainpool-P320R1](src/Curve/Weierstrass/BrainpoolP320R1.hs)-  * [Brainpool-P320T1](src/Curve/Weierstrass/BrainpoolP320T1.hs)-  * [Brainpool-P384R1](src/Curve/Weierstrass/BrainpoolP384R1.hs)-  * [Brainpool-P384T1](src/Curve/Weierstrass/BrainpoolP384T1.hs)-  * [Brainpool-P512R1](src/Curve/Weierstrass/BrainpoolP512R1.hs)-  * [Brainpool-P512T1](src/Curve/Weierstrass/BrainpoolP512T1.hs)+  * [BrainpoolP160R1](src/Curve/Weierstrass/BrainpoolP160R1.hs)+  * [BrainpoolP160T1](src/Curve/Weierstrass/BrainpoolP160T1.hs)+  * [BrainpoolP192R1](src/Curve/Weierstrass/BrainpoolP192R1.hs)+  * [BrainpoolP192T1](src/Curve/Weierstrass/BrainpoolP192T1.hs)+  * [BrainpoolP224R1](src/Curve/Weierstrass/BrainpoolP224R1.hs)+  * [BrainpoolP224T1](src/Curve/Weierstrass/BrainpoolP224T1.hs)+  * [BrainpoolP256R1](src/Curve/Weierstrass/BrainpoolP256R1.hs)+  * [BrainpoolP256T1](src/Curve/Weierstrass/BrainpoolP256T1.hs)+  * [BrainpoolP320R1](src/Curve/Weierstrass/BrainpoolP320R1.hs)+  * [BrainpoolP320T1](src/Curve/Weierstrass/BrainpoolP320T1.hs)+  * [BrainpoolP384R1](src/Curve/Weierstrass/BrainpoolP384R1.hs)+  * [BrainpoolP384T1](src/Curve/Weierstrass/BrainpoolP384T1.hs)+  * [BrainpoolP512R1](src/Curve/Weierstrass/BrainpoolP512R1.hs)+  * [BrainpoolP512T1](src/Curve/Weierstrass/BrainpoolP512T1.hs) * SECP (NIST) curves   * [SECP112R1](src/Curve/Weierstrass/SECP112R1.hs)   * [SECP112R2](src/Curve/Weierstrass/SECP112R2.hs)

+ benchmarks/BinaryBenchmarks.hs view

@@ -0,0 +1,50 @@+module BinaryBenchmarks where++import Criterion.Main+import qualified Curve.Binary.SECT113R1 as SECT113R1+import qualified Curve.Binary.SECT113R2 as SECT113R2+import qualified Curve.Binary.SECT131R1 as SECT131R1+import qualified Curve.Binary.SECT131R2 as SECT131R2+import qualified Curve.Binary.SECT163K1 as SECT163K1+import qualified Curve.Binary.SECT163R1 as SECT163R1+import qualified Curve.Binary.SECT163R2 as SECT163R2+import qualified Curve.Binary.SECT193R1 as SECT193R1+import qualified Curve.Binary.SECT193R2 as SECT193R2+import qualified Curve.Binary.SECT233K1 as SECT233K1+import qualified Curve.Binary.SECT233R1 as SECT233R1+import qualified Curve.Binary.SECT239K1 as SECT239K1+import qualified Curve.Binary.SECT283K1 as SECT283K1+import qualified Curve.Binary.SECT283R1 as SECT283R1+import qualified Curve.Binary.SECT409K1 as SECT409K1+import qualified Curve.Binary.SECT409R1 as SECT409R1+import qualified Curve.Binary.SECT571K1 as SECT571K1+import qualified Curve.Binary.SECT571R1 as SECT571R1++import GroupBenchmarks++benchmarkBinary :: Benchmark+benchmarkBinary = bgroup "Binary"+  [ benchmarkBinary' "SECT113R1" SECT113R1.gA SECT113R1.gP+  , benchmarkBinary' "SECT113R2" SECT113R2.gA SECT113R2.gP+  , benchmarkBinary' "SECT131R1" SECT131R1.gA SECT131R1.gP+  , benchmarkBinary' "SECT131R2" SECT131R2.gA SECT131R2.gP+  , benchmarkBinary' "SECT163K1" SECT163K1.gA SECT163K1.gP+  , benchmarkBinary' "SECT163R1" SECT163R1.gA SECT163R1.gP+  , benchmarkBinary' "SECT163R2" SECT163R2.gA SECT163R2.gP+  , benchmarkBinary' "SECT193R1" SECT193R1.gA SECT193R1.gP+  , benchmarkBinary' "SECT193R2" SECT193R2.gA SECT193R2.gP+  , benchmarkBinary' "SECT233K1" SECT233K1.gA SECT233K1.gP+  , benchmarkBinary' "SECT233R1" SECT233R1.gA SECT233R1.gP+  , benchmarkBinary' "SECT239K1" SECT239K1.gA SECT239K1.gP+  , benchmarkBinary' "SECT283K1" SECT283K1.gA SECT283K1.gP+  , benchmarkBinary' "SECT283R1" SECT283R1.gA SECT283R1.gP+  , benchmarkBinary' "SECT409K1" SECT409K1.gA SECT409K1.gP+  , benchmarkBinary' "SECT409R1" SECT409R1.gA SECT409R1.gP+  , benchmarkBinary' "SECT571K1" SECT571K1.gA SECT571K1.gP+  , benchmarkBinary' "SECT571R1" SECT571R1.gA SECT571R1.gP+  ]+  where+    benchmarkBinary' curve affine projective = bgroup curve+      [ benchmark "Affine" affine+      , benchmark "Projective" projective+      ]

+ benchmarks/EdwardsBenchmarks.hs view

@@ -0,0 +1,32 @@+module EdwardsBenchmarks where++import Criterion.Main+import qualified Curve.Edwards.Curve1174  as Curve1174+import qualified Curve.Edwards.Curve41417 as Curve41417+import qualified Curve.Edwards.E222       as E222+import qualified Curve.Edwards.E382       as E382+import qualified Curve.Edwards.E521       as E521+import qualified Curve.Edwards.Ed448      as Ed448+import qualified Curve.Edwards.Ed3363     as Ed3363+import qualified Curve.Edwards.Ed25519    as Ed25519+import qualified Curve.Edwards.JubJub     as JubJub++import GroupBenchmarks++benchmarkEdwards :: Benchmark+benchmarkEdwards = bgroup "Edwards"+  [ benchmarkEdwards'  "Curve1174"  Curve1174.gA  Curve1174.gP+  , benchmarkEdwards' "Curve41417" Curve41417.gA Curve41417.gP+  , benchmarkEdwards'       "E222"       E222.gA       E222.gP+  , benchmarkEdwards'       "E382"       E382.gA       E382.gP+  , benchmarkEdwards'       "E521"       E521.gA       E521.gP+  , benchmarkEdwards'      "Ed448"      Ed448.gA      Ed448.gP+  , benchmarkEdwards'     "Ed3363"     Ed3363.gA     Ed3363.gP+  , benchmarkEdwards'    "Ed25519"    Ed25519.gA    Ed25519.gP+  , benchmarkEdwards'     "JubJub"     JubJub.gA     JubJub.gP+  ]+  where+    benchmarkEdwards' curve affine projective = bgroup curve+      [ benchmark "Affine" affine+      , benchmark "Projective" projective+      ]

+ benchmarks/FieldBenchmarks.hs view

@@ -0,0 +1,11 @@+module FieldBenchmarks where++import Criterion.Main+import qualified Group.Field.BN254TF as BN254TF++import GroupBenchmarks++benchmarkField :: Benchmark+benchmarkField = bgroup "Field"+  [ benchmark "BN254TF" BN254TF._g+  ]

+ benchmarks/GroupBenchmarks.hs view

@@ -0,0 +1,8 @@+module GroupBenchmarks where++import Criterion.Main+import GHC.Base+import Group++benchmark :: Group g => String -> g -> Benchmark+benchmark = (. whnf (flip mul' 3)) . bench

benchmarks/Main.hs view

@@ -3,180 +3,13 @@ import Protolude  import Criterion.Main-import Curve-import qualified Curve.Binary.SECT113R1            as SECT113R1-import qualified Curve.Binary.SECT113R2            as SECT113R2-import qualified Curve.Binary.SECT131R1            as SECT131R1-import qualified Curve.Binary.SECT131R2            as SECT131R2-import qualified Curve.Binary.SECT163K1            as SECT163K1-import qualified Curve.Binary.SECT163R1            as SECT163R1-import qualified Curve.Binary.SECT163R2            as SECT163R2-import qualified Curve.Binary.SECT193R1            as SECT193R1-import qualified Curve.Binary.SECT193R2            as SECT193R2-import qualified Curve.Binary.SECT233K1            as SECT233K1-import qualified Curve.Binary.SECT233R1            as SECT233R1-import qualified Curve.Binary.SECT239K1            as SECT239K1-import qualified Curve.Binary.SECT283K1            as SECT283K1-import qualified Curve.Binary.SECT283R1            as SECT283R1-import qualified Curve.Binary.SECT409K1            as SECT409K1-import qualified Curve.Binary.SECT409R1            as SECT409R1-import qualified Curve.Binary.SECT571K1            as SECT571K1-import qualified Curve.Binary.SECT571R1            as SECT571R1-import qualified Curve.Edwards.Curve1174           as Curve1174-import qualified Curve.Edwards.Curve41417          as Curve41417-import qualified Curve.Edwards.E222                as E222-import qualified Curve.Edwards.E382                as E382-import qualified Curve.Edwards.E521                as E521-import qualified Curve.Edwards.Ed448               as Ed448-import qualified Curve.Edwards.Ed3363              as Ed3363-import qualified Curve.Edwards.Ed25519             as Ed25519-import qualified Curve.Edwards.JubJub              as JubJub-import qualified Curve.Montgomery.Curve448         as Curve448-import qualified Curve.Montgomery.Curve25519       as Curve25519-import qualified Curve.Montgomery.Curve383187      as Curve383187-import qualified Curve.Montgomery.M221             as M221-import qualified Curve.Montgomery.M383             as M383-import qualified Curve.Montgomery.M511             as M511-import qualified Curve.Weierstrass.Anomalous       as Anomalous-import qualified Curve.Weierstrass.ANSSIFRP256V1   as ANSSIFRP256V1-import qualified Curve.Weierstrass.BLS12_381       as BLS12_381-import qualified Curve.Weierstrass.BLS12_381T      as BLS12_381T-import qualified Curve.Weierstrass.BLS48_581       as BLS48_581-import qualified Curve.Weierstrass.BLS48_581T      as BLS48_581T-import qualified Curve.Weierstrass.BN224           as BN224-import qualified Curve.Weierstrass.BN254           as BN254-import qualified Curve.Weierstrass.BN254T          as BN254T-import qualified Curve.Weierstrass.BN254A          as BN254A-import qualified Curve.Weierstrass.BN254AT         as BN254AT-import qualified Curve.Weierstrass.BN254B          as BN254B-import qualified Curve.Weierstrass.BN254BT         as BN254BT-import qualified Curve.Weierstrass.BN256           as BN256-import qualified Curve.Weierstrass.BN384           as BN384-import qualified Curve.Weierstrass.BN462           as BN462-import qualified Curve.Weierstrass.BN462T          as BN462T-import qualified Curve.Weierstrass.BN512           as BN512-import qualified Curve.Weierstrass.BrainpoolP160R1 as BrainpoolP160R1-import qualified Curve.Weierstrass.BrainpoolP160T1 as BrainpoolP160T1-import qualified Curve.Weierstrass.BrainpoolP192R1 as BrainpoolP192R1-import qualified Curve.Weierstrass.BrainpoolP192T1 as BrainpoolP192T1-import qualified Curve.Weierstrass.BrainpoolP224R1 as BrainpoolP224R1-import qualified Curve.Weierstrass.BrainpoolP224T1 as BrainpoolP224T1-import qualified Curve.Weierstrass.BrainpoolP256R1 as BrainpoolP256R1-import qualified Curve.Weierstrass.BrainpoolP256T1 as BrainpoolP256T1-import qualified Curve.Weierstrass.BrainpoolP320R1 as BrainpoolP320R1-import qualified Curve.Weierstrass.BrainpoolP320T1 as BrainpoolP320T1-import qualified Curve.Weierstrass.BrainpoolP384R1 as BrainpoolP384R1-import qualified Curve.Weierstrass.BrainpoolP384T1 as BrainpoolP384T1-import qualified Curve.Weierstrass.BrainpoolP512R1 as BrainpoolP512R1-import qualified Curve.Weierstrass.BrainpoolP512T1 as BrainpoolP512T1-import qualified Curve.Weierstrass.SECP112R1       as SECP112R1-import qualified Curve.Weierstrass.SECP112R2       as SECP112R2-import qualified Curve.Weierstrass.SECP128R1       as SECP128R1-import qualified Curve.Weierstrass.SECP128R2       as SECP128R2-import qualified Curve.Weierstrass.SECP160K1       as SECP160K1-import qualified Curve.Weierstrass.SECP160R1       as SECP160R1-import qualified Curve.Weierstrass.SECP160R2       as SECP160R2-import qualified Curve.Weierstrass.SECP192K1       as SECP192K1-import qualified Curve.Weierstrass.SECP192R1       as SECP192R1-import qualified Curve.Weierstrass.SECP224K1       as SECP224K1-import qualified Curve.Weierstrass.SECP224R1       as SECP224R1-import qualified Curve.Weierstrass.SECP256K1       as SECP256K1-import qualified Curve.Weierstrass.SECP256R1       as SECP256R1-import qualified Curve.Weierstrass.SECP384R1       as SECP384R1-import qualified Curve.Weierstrass.SECP521R1       as SECP521R1-import GHC.Base -benchmark :: forall r c k . Curve r c k => String -> Point r c k -> Benchmark-benchmark = (. whnf (mul (6 :: Int))) . bench+import BinaryBenchmarks+import EdwardsBenchmarks+import MontgomeryBenchmarks+import WeierstrassBenchmarks+import FieldBenchmarks  main :: IO () main = defaultMain-  [ bgroup "Binary"-    [ benchmark        "SECT113R1"       SECT113R1._g-    , benchmark        "SECT113R2"       SECT113R2._g-    , benchmark        "SECT131R1"       SECT131R1._g-    , benchmark        "SECT131R2"       SECT131R2._g-    , benchmark        "SECT163K1"       SECT163K1._g-    , benchmark        "SECT163R1"       SECT163R1._g-    , benchmark        "SECT163R2"       SECT163R2._g-    , benchmark        "SECT193R1"       SECT193R1._g-    , benchmark        "SECT193R2"       SECT193R2._g-    , benchmark        "SECT233K1"       SECT233K1._g-    , benchmark        "SECT233R1"       SECT233R1._g-    , benchmark        "SECT239K1"       SECT239K1._g-    , benchmark        "SECT283K1"       SECT283K1._g-    , benchmark        "SECT283R1"       SECT283R1._g-    , benchmark        "SECT409K1"       SECT409K1._g-    , benchmark        "SECT409R1"       SECT409R1._g-    , benchmark        "SECT571K1"       SECT571K1._g-    , benchmark        "SECT571R1"       SECT571R1._g-    ]-  , bgroup "Edwards"-    [ benchmark        "Curve1174"       Curve1174._g-    , benchmark       "Curve41417"      Curve41417._g-    , benchmark            "E-222"            E222._g-    , benchmark            "E-382"            E382._g-    , benchmark            "E-521"            E521._g-    , benchmark            "Ed448"           Ed448._g-    , benchmark           "Ed3363"          Ed3363._g-    , benchmark          "Ed25519"         Ed25519._g-    , benchmark           "JubJub"          JubJub._g-    ]-  , bgroup "Montgomery"-    [ benchmark         "Curve448"        Curve448._g-    , benchmark       "Curve25519"      Curve25519._g-    , benchmark      "Curve383187"     Curve383187._g-    , benchmark            "M-221"            M221._g-    , benchmark            "M-383"            M383._g-    , benchmark            "M-511"            M511._g-    ]-  , bgroup "Weierstrass"-    [ benchmark        "Anomalous"       Anomalous._g-    , benchmark   "ANSSI-FRP256V1"   ANSSIFRP256V1._g-    , benchmark        "BLS12-381"       BLS12_381._g-    , benchmark       "BLS12-381T"      BLS12_381T._g-    , benchmark        "BLS48-581"       BLS48_581._g-    , benchmark       "BLS48-581T"      BLS48_581T._g-    , benchmark            "BN224"           BN224._g-    , benchmark            "BN254"           BN254._g-    , benchmark           "BN254T"          BN254T._g-    , benchmark           "BN254A"          BN254A._g-    , benchmark          "BN254AT"         BN254AT._g-    , benchmark           "BN254B"          BN254B._g-    , benchmark          "BN254BT"         BN254BT._g-    , benchmark            "BN256"           BN256._g-    , benchmark            "BN384"           BN384._g-    , benchmark            "BN462"           BN462._g-    , benchmark           "BN462T"          BN462T._g-    , benchmark            "BN512"           BN512._g-    , benchmark "Brainpool-P160R1" BrainpoolP160R1._g-    , benchmark "Brainpool-P160T1" BrainpoolP160T1._g-    , benchmark "Brainpool-P192R1" BrainpoolP192R1._g-    , benchmark "Brainpool-P192T1" BrainpoolP192T1._g-    , benchmark "Brainpool-P224R1" BrainpoolP224R1._g-    , benchmark "Brainpool-P224T1" BrainpoolP224T1._g-    , benchmark "Brainpool-P256R1" BrainpoolP256R1._g-    , benchmark "Brainpool-P256T1" BrainpoolP256T1._g-    , benchmark "Brainpool-P320R1" BrainpoolP320R1._g-    , benchmark "Brainpool-P320T1" BrainpoolP320T1._g-    , benchmark "Brainpool-P384R1" BrainpoolP384R1._g-    , benchmark "Brainpool-P384T1" BrainpoolP384T1._g-    , benchmark "Brainpool-P512R1" BrainpoolP512R1._g-    , benchmark "Brainpool-P512T1" BrainpoolP512T1._g-    , benchmark        "SECP112R1"       SECP112R1._g-    , benchmark        "SECP112R2"       SECP112R2._g-    , benchmark        "SECP128R1"       SECP128R1._g-    , benchmark        "SECP128R2"       SECP128R2._g-    , benchmark        "SECP160K1"       SECP160K1._g-    , benchmark        "SECP160R1"       SECP160R1._g-    , benchmark        "SECP160R2"       SECP160R2._g-    , benchmark        "SECP192K1"       SECP192K1._g-    , benchmark        "SECP192R1"       SECP192R1._g-    , benchmark        "SECP224K1"       SECP224K1._g-    , benchmark        "SECP224R1"       SECP224R1._g-    , benchmark        "SECP256K1"       SECP256K1._g-    , benchmark        "SECP256R1"       SECP256R1._g-    , benchmark        "SECP384R1"       SECP384R1._g-    , benchmark        "SECP521R1"       SECP521R1._g-    ]-  ]+  [benchmarkBinary, benchmarkEdwards, benchmarkMontgomery, benchmarkWeierstrass, benchmarkField]

+ benchmarks/MontgomeryBenchmarks.hs view

@@ -0,0 +1,25 @@+module MontgomeryBenchmarks where++import Criterion.Main+import qualified Curve.Montgomery.Curve448    as Curve448+import qualified Curve.Montgomery.Curve25519  as Curve25519+import qualified Curve.Montgomery.Curve383187 as Curve383187+import qualified Curve.Montgomery.M221        as M221+import qualified Curve.Montgomery.M383        as M383+import qualified Curve.Montgomery.M511        as M511++import GroupBenchmarks++benchmarkMontgomery :: Benchmark+benchmarkMontgomery = bgroup "Montgomery"+  [ benchmarkMontgomery'    "Curve448"    Curve448.gA+  , benchmarkMontgomery'  "Curve25519"  Curve25519.gA+  , benchmarkMontgomery' "Curve383187" Curve383187.gA+  , benchmarkMontgomery'        "M221"        M221.gA+  , benchmarkMontgomery'        "M383"        M383.gA+  , benchmarkMontgomery'        "M511"        M511.gA+  ]+  where+    benchmarkMontgomery' curve affine = bgroup curve+      [ benchmark "Affine" affine+      ]

+ benchmarks/WeierstrassBenchmarks.hs view

@@ -0,0 +1,109 @@+module WeierstrassBenchmarks where++import Criterion.Main+import qualified Curve.Weierstrass.Anomalous       as Anomalous+import qualified Curve.Weierstrass.ANSSIFRP256V1   as ANSSIFRP256V1+import qualified Curve.Weierstrass.BLS12381        as BLS12381+import qualified Curve.Weierstrass.BLS12381T       as BLS12381T+import qualified Curve.Weierstrass.BLS48581        as BLS48581+import qualified Curve.Weierstrass.BLS48581T       as BLS48581T+import qualified Curve.Weierstrass.BN224           as BN224+import qualified Curve.Weierstrass.BN254           as BN254+import qualified Curve.Weierstrass.BN254T          as BN254T+import qualified Curve.Weierstrass.BN254A          as BN254A+import qualified Curve.Weierstrass.BN254AT         as BN254AT+import qualified Curve.Weierstrass.BN254B          as BN254B+import qualified Curve.Weierstrass.BN254BT         as BN254BT+import qualified Curve.Weierstrass.BN256           as BN256+import qualified Curve.Weierstrass.BN384           as BN384+import qualified Curve.Weierstrass.BN462           as BN462+import qualified Curve.Weierstrass.BN462T          as BN462T+import qualified Curve.Weierstrass.BN512           as BN512+import qualified Curve.Weierstrass.BrainpoolP160R1 as BrainpoolP160R1+import qualified Curve.Weierstrass.BrainpoolP160T1 as BrainpoolP160T1+import qualified Curve.Weierstrass.BrainpoolP192R1 as BrainpoolP192R1+import qualified Curve.Weierstrass.BrainpoolP192T1 as BrainpoolP192T1+import qualified Curve.Weierstrass.BrainpoolP224R1 as BrainpoolP224R1+import qualified Curve.Weierstrass.BrainpoolP224T1 as BrainpoolP224T1+import qualified Curve.Weierstrass.BrainpoolP256R1 as BrainpoolP256R1+import qualified Curve.Weierstrass.BrainpoolP256T1 as BrainpoolP256T1+import qualified Curve.Weierstrass.BrainpoolP320R1 as BrainpoolP320R1+import qualified Curve.Weierstrass.BrainpoolP320T1 as BrainpoolP320T1+import qualified Curve.Weierstrass.BrainpoolP384R1 as BrainpoolP384R1+import qualified Curve.Weierstrass.BrainpoolP384T1 as BrainpoolP384T1+import qualified Curve.Weierstrass.BrainpoolP512R1 as BrainpoolP512R1+import qualified Curve.Weierstrass.BrainpoolP512T1 as BrainpoolP512T1+import qualified Curve.Weierstrass.SECP112R1       as SECP112R1+import qualified Curve.Weierstrass.SECP112R2       as SECP112R2+import qualified Curve.Weierstrass.SECP128R1       as SECP128R1+import qualified Curve.Weierstrass.SECP128R2       as SECP128R2+import qualified Curve.Weierstrass.SECP160K1       as SECP160K1+import qualified Curve.Weierstrass.SECP160R1       as SECP160R1+import qualified Curve.Weierstrass.SECP160R2       as SECP160R2+import qualified Curve.Weierstrass.SECP192K1       as SECP192K1+import qualified Curve.Weierstrass.SECP192R1       as SECP192R1+import qualified Curve.Weierstrass.SECP224K1       as SECP224K1+import qualified Curve.Weierstrass.SECP224R1       as SECP224R1+import qualified Curve.Weierstrass.SECP256K1       as SECP256K1+import qualified Curve.Weierstrass.SECP256R1       as SECP256R1+import qualified Curve.Weierstrass.SECP384R1       as SECP384R1+import qualified Curve.Weierstrass.SECP521R1       as SECP521R1++import GroupBenchmarks++benchmarkWeierstrass :: Benchmark+benchmarkWeierstrass = bgroup "Weierstrass"+  [ benchmarkWeierstrass'       "Anomalous"       Anomalous.gA       Anomalous.gJ       Anomalous.gP+  , benchmarkWeierstrass'   "ANSSIFRP256V1"   ANSSIFRP256V1.gA   ANSSIFRP256V1.gJ   ANSSIFRP256V1.gP+  , benchmarkWeierstrass'        "BLS12381"        BLS12381.gA        BLS12381.gJ        BLS12381.gP+  , benchmarkWeierstrass'       "BLS12381T"       BLS12381T.gA       BLS12381T.gJ       BLS12381T.gP+  , benchmarkWeierstrass'        "BLS48581"        BLS48581.gA        BLS48581.gJ        BLS48581.gP+  , benchmarkWeierstrass'       "BLS48581T"       BLS48581T.gA       BLS48581T.gJ       BLS48581T.gP+  , benchmarkWeierstrass'           "BN224"           BN224.gA           BN224.gJ           BN224.gP+  , benchmarkWeierstrass'           "BN254"           BN254.gA           BN254.gJ           BN254.gP+  , benchmarkWeierstrass'          "BN254T"          BN254T.gA          BN254T.gJ          BN254T.gP+  , benchmarkWeierstrass'          "BN254A"          BN254A.gA          BN254A.gJ          BN254A.gP+  , benchmarkWeierstrass'         "BN254AT"         BN254AT.gA         BN254AT.gJ         BN254AT.gP+  , benchmarkWeierstrass'          "BN254B"          BN254B.gA          BN254B.gJ          BN254B.gP+  , benchmarkWeierstrass'         "BN254BT"         BN254BT.gA         BN254BT.gJ         BN254BT.gP+  , benchmarkWeierstrass'           "BN256"           BN256.gA           BN256.gJ           BN256.gP+  , benchmarkWeierstrass'           "BN384"           BN384.gA           BN384.gJ           BN384.gP+  , benchmarkWeierstrass'           "BN462"           BN462.gA           BN462.gJ           BN462.gP+  , benchmarkWeierstrass'          "BN462T"          BN462T.gA          BN462T.gJ          BN462T.gP+  , benchmarkWeierstrass'           "BN512"           BN512.gA           BN512.gJ           BN512.gP+  , benchmarkWeierstrass' "BrainpoolP160R1" BrainpoolP160R1.gA BrainpoolP160R1.gJ BrainpoolP160R1.gP+  , benchmarkWeierstrass' "BrainpoolP160T1" BrainpoolP160T1.gA BrainpoolP160T1.gJ BrainpoolP160T1.gP+  , benchmarkWeierstrass' "BrainpoolP192R1" BrainpoolP192R1.gA BrainpoolP192R1.gJ BrainpoolP192R1.gP+  , benchmarkWeierstrass' "BrainpoolP192T1" BrainpoolP192T1.gA BrainpoolP192T1.gJ BrainpoolP192T1.gP+  , benchmarkWeierstrass' "BrainpoolP224R1" BrainpoolP224R1.gA BrainpoolP224R1.gJ BrainpoolP224R1.gP+  , benchmarkWeierstrass' "BrainpoolP224T1" BrainpoolP224T1.gA BrainpoolP224T1.gJ BrainpoolP224T1.gP+  , benchmarkWeierstrass' "BrainpoolP256R1" BrainpoolP256R1.gA BrainpoolP256R1.gJ BrainpoolP256R1.gP+  , benchmarkWeierstrass' "BrainpoolP256T1" BrainpoolP256T1.gA BrainpoolP256T1.gJ BrainpoolP256T1.gP+  , benchmarkWeierstrass' "BrainpoolP320R1" BrainpoolP320R1.gA BrainpoolP320R1.gJ BrainpoolP320R1.gP+  , benchmarkWeierstrass' "BrainpoolP320T1" BrainpoolP320T1.gA BrainpoolP320T1.gJ BrainpoolP320T1.gP+  , benchmarkWeierstrass' "BrainpoolP384R1" BrainpoolP384R1.gA BrainpoolP384R1.gJ BrainpoolP384R1.gP+  , benchmarkWeierstrass' "BrainpoolP384T1" BrainpoolP384T1.gA BrainpoolP384T1.gJ BrainpoolP384T1.gP+  , benchmarkWeierstrass' "BrainpoolP512R1" BrainpoolP512R1.gA BrainpoolP512R1.gJ BrainpoolP512R1.gP+  , benchmarkWeierstrass' "BrainpoolP512T1" BrainpoolP512T1.gA BrainpoolP512T1.gJ BrainpoolP512T1.gP+  , benchmarkWeierstrass'       "SECP112R1"       SECP112R1.gA       SECP112R1.gJ       SECP112R1.gP+  , benchmarkWeierstrass'       "SECP112R2"       SECP112R2.gA       SECP112R2.gJ       SECP112R2.gP+  , benchmarkWeierstrass'       "SECP128R1"       SECP128R1.gA       SECP128R1.gJ       SECP128R1.gP+  , benchmarkWeierstrass'       "SECP128R2"       SECP128R2.gA       SECP128R2.gJ       SECP128R2.gP+  , benchmarkWeierstrass'       "SECP160K1"       SECP160K1.gA       SECP160K1.gJ       SECP160K1.gP+  , benchmarkWeierstrass'       "SECP160R1"       SECP160R1.gA       SECP160R1.gJ       SECP160R1.gP+  , benchmarkWeierstrass'       "SECP160R2"       SECP160R2.gA       SECP160R2.gJ       SECP160R2.gP+  , benchmarkWeierstrass'       "SECP192K1"       SECP192K1.gA       SECP192K1.gJ       SECP192K1.gP+  , benchmarkWeierstrass'       "SECP192R1"       SECP192R1.gA       SECP192R1.gJ       SECP192R1.gP+  , benchmarkWeierstrass'       "SECP224K1"       SECP224K1.gA       SECP224K1.gJ       SECP224K1.gP+  , benchmarkWeierstrass'       "SECP224R1"       SECP224R1.gA       SECP224R1.gJ       SECP224R1.gP+  , benchmarkWeierstrass'       "SECP256K1"       SECP256K1.gA       SECP256K1.gJ       SECP256K1.gP+  , benchmarkWeierstrass'       "SECP256R1"       SECP256R1.gA       SECP256R1.gJ       SECP256R1.gP+  , benchmarkWeierstrass'       "SECP384R1"       SECP384R1.gA       SECP384R1.gJ       SECP384R1.gP+  , benchmarkWeierstrass'       "SECP521R1"       SECP521R1.gA       SECP521R1.gJ       SECP521R1.gP+  ]+  where+    benchmarkWeierstrass' curve affine jacobian projective = bgroup curve+      [ benchmark "Affine" affine+      , benchmark "Jacobian" jacobian+      , benchmark "Projective" projective+      ]

elliptic-curve.cabal view

@@ -4,10 +4,10 @@ -- -- see: https://github.com/sol/hpack ----- hash: bdbd38917d50ccd9f993f22110c962321da59072497a327bb80a0309791e767b+-- hash: 664a809970025f3cc9258b03d8eaed1d4a44189ed18d2cda5ffb313eb866a2ce  name:           elliptic-curve-version:        0.1.0+version:        0.2.1 synopsis:       Elliptic curve library description:    An extensible library of elliptic curves used in cryptography research category:       Cryptography@@ -67,10 +67,10 @@       Curve.Weierstrass       Curve.Weierstrass.Anomalous       Curve.Weierstrass.ANSSIFRP256V1-      Curve.Weierstrass.BLS12_381-      Curve.Weierstrass.BLS12_381T-      Curve.Weierstrass.BLS48_581-      Curve.Weierstrass.BLS48_581T+      Curve.Weierstrass.BLS12381+      Curve.Weierstrass.BLS12381T+      Curve.Weierstrass.BLS48581+      Curve.Weierstrass.BLS48581T       Curve.Weierstrass.BN224       Curve.Weierstrass.BN254       Curve.Weierstrass.BN254T@@ -112,18 +112,43 @@       Curve.Weierstrass.BrainpoolP384T1       Curve.Weierstrass.BrainpoolP512R1       Curve.Weierstrass.BrainpoolP512T1+      Group+      Group.Field+      Group.Field.BN254TF   other-modules:-      Paths_elliptic_curve+      Generate.Binary.Curve+      Generate.Binary.Generate+      Generate.Binary.Parameters+      Generate.Binary.Types+      Generate.Curve+      Generate.Edwards.Curve+      Generate.Edwards.Generate+      Generate.Edwards.Parameters+      Generate.Edwards.Types+      Generate.Generate+      Generate.Montgomery.Curve+      Generate.Montgomery.Generate+      Generate.Montgomery.Parameters+      Generate.Montgomery.Types+      Generate.Pretty+      Generate.Types+      Generate.Weierstrass.Curve+      Generate.Weierstrass.Generate+      Generate.Weierstrass.Parameters+      Generate.Weierstrass.Types+      Main   hs-source-dirs:       src-  default-extensions: LambdaCase RecordWildCards OverloadedStrings NoImplicitPrelude FlexibleInstances FlexibleContexts ScopedTypeVariables RankNTypes DataKinds DeriveAnyClass DeriveGeneric MultiParamTypeClasses TypeFamilyDependencies UndecidableInstances-  ghc-options: -O2 -Wall -fno-warn-orphans+      generate+  default-extensions: LambdaCase RecordWildCards OverloadedStrings NoImplicitPrelude FlexibleInstances FlexibleContexts ScopedTypeVariables RankNTypes DataKinds DeriveAnyClass DeriveFunctor DeriveGeneric MultiParamTypeClasses PatternSynonyms PolyKinds TypeFamilyDependencies+  ghc-options: -Wall   build-depends:       MonadRandom-    , base >=4.7 && <5-    , galois-field-    , protolude >=0.2+    , base >=4.10 && <5+    , galois-field >=0.4 && <0.5+    , protolude     , tasty-quickcheck+    , text     , wl-pprint-text   default-language: Haskell2010 @@ -132,8 +157,9 @@   main-is: Main.hs   other-modules:       BinaryTests-      CurveTests       EdwardsTests+      FieldTests+      GroupTests       MontgomeryTests       WeierstrassTests       Curve@@ -176,10 +202,10 @@       Curve.Weierstrass       Curve.Weierstrass.Anomalous       Curve.Weierstrass.ANSSIFRP256V1-      Curve.Weierstrass.BLS12_381-      Curve.Weierstrass.BLS12_381T-      Curve.Weierstrass.BLS48_581-      Curve.Weierstrass.BLS48_581T+      Curve.Weierstrass.BLS12381+      Curve.Weierstrass.BLS12381T+      Curve.Weierstrass.BLS48581+      Curve.Weierstrass.BLS48581T       Curve.Weierstrass.BN224       Curve.Weierstrass.BN254       Curve.Weierstrass.BN254A@@ -221,21 +247,25 @@       Curve.Weierstrass.SECP256R1       Curve.Weierstrass.SECP384R1       Curve.Weierstrass.SECP521R1+      Group+      Group.Field+      Group.Field.BN254TF       Paths_elliptic_curve   hs-source-dirs:       tests       src-  default-extensions: LambdaCase RecordWildCards OverloadedStrings NoImplicitPrelude FlexibleInstances FlexibleContexts ScopedTypeVariables RankNTypes DataKinds DeriveAnyClass DeriveGeneric MultiParamTypeClasses TypeFamilyDependencies UndecidableInstances-  ghc-options: -O2 -Wall -main-is Main+  default-extensions: LambdaCase RecordWildCards OverloadedStrings NoImplicitPrelude FlexibleInstances FlexibleContexts ScopedTypeVariables RankNTypes DataKinds DeriveAnyClass DeriveFunctor DeriveGeneric MultiParamTypeClasses PatternSynonyms PolyKinds TypeFamilyDependencies+  ghc-options: -Wall -main-is Main   build-depends:       MonadRandom     , arithmoi-    , base >=4.7 && <5-    , galois-field-    , protolude >=0.2+    , base >=4.10 && <5+    , galois-field >=0.4 && <0.5+    , protolude     , tasty     , tasty-hunit     , tasty-quickcheck+    , text     , wl-pprint-text   default-language: Haskell2010 @@ -243,6 +273,12 @@   type: exitcode-stdio-1.0   main-is: Main.hs   other-modules:+      BinaryBenchmarks+      EdwardsBenchmarks+      FieldBenchmarks+      GroupBenchmarks+      MontgomeryBenchmarks+      WeierstrassBenchmarks       Curve       Curve.Binary       Curve.Binary.SECT113R1@@ -283,10 +319,10 @@       Curve.Weierstrass       Curve.Weierstrass.Anomalous       Curve.Weierstrass.ANSSIFRP256V1-      Curve.Weierstrass.BLS12_381-      Curve.Weierstrass.BLS12_381T-      Curve.Weierstrass.BLS48_581-      Curve.Weierstrass.BLS48_581T+      Curve.Weierstrass.BLS12381+      Curve.Weierstrass.BLS12381T+      Curve.Weierstrass.BLS48581+      Curve.Weierstrass.BLS48581T       Curve.Weierstrass.BN224       Curve.Weierstrass.BN254       Curve.Weierstrass.BN254A@@ -328,18 +364,22 @@       Curve.Weierstrass.SECP256R1       Curve.Weierstrass.SECP384R1       Curve.Weierstrass.SECP521R1+      Group+      Group.Field+      Group.Field.BN254TF       Paths_elliptic_curve   hs-source-dirs:       benchmarks       src-  default-extensions: LambdaCase RecordWildCards OverloadedStrings NoImplicitPrelude FlexibleInstances FlexibleContexts ScopedTypeVariables RankNTypes DataKinds DeriveAnyClass DeriveGeneric MultiParamTypeClasses TypeFamilyDependencies UndecidableInstances-  ghc-options: -O2 -Wall -main-is Main+  default-extensions: LambdaCase RecordWildCards OverloadedStrings NoImplicitPrelude FlexibleInstances FlexibleContexts ScopedTypeVariables RankNTypes DataKinds DeriveAnyClass DeriveFunctor DeriveGeneric MultiParamTypeClasses PatternSynonyms PolyKinds TypeFamilyDependencies+  ghc-options: -Wall -main-is Main   build-depends:       MonadRandom-    , base >=4.7 && <5+    , base >=4.10 && <5     , criterion-    , galois-field-    , protolude >=0.2+    , galois-field >=0.4 && <0.5+    , protolude     , tasty-quickcheck+    , text     , wl-pprint-text   default-language: Haskell2010

+ generate/Generate/Binary/Curve.hs view

@@ -0,0 +1,144 @@+module Generate.Binary.Curve+  ( prettyCurve+  ) where++import Protolude++import Text.PrettyPrint.Leijen.Text++import Generate.Binary.Types+import Generate.Curve+import Generate.Pretty++-------------------------------------------------------------------------------+-- Curve+-------------------------------------------------------------------------------++prettyImports :: Types -> Doc+prettyImports Types{..}+  =    "module Curve.Binary." <> pretty curve+  <$$> indent 2+    (    "( module Curve.Binary"+    <$$> ", module Curve.Binary." <> pretty curve+    <$$> ") where"+    )+  <>   prettyBreak+  <$$> prettyImport field+  <>   prettyBreak+  <$$> "import Curve.Binary"+  <$$> maybe mempty pretty imports++prettyTypes :: Types -> Doc+prettyTypes Types{..}+  =    prettySection "Types"+  <$$> prettyDocumentation curve'+  <$$> "data" <+> pretty curve+  <>   prettyBreak+  <$$> prettyDocumentation ("Field of points of" <+> curve')+  <$$> prettyType field+  <>   prettyBreak+  <$$> prettyDocumentation ("Field of coefficients of" <+> curve')+  <$$> prettyType field'+  <>   prettyBreak+  <$$> prettyDocumentation (curve' <+> "is a binary curve")+  <$$> "instance Curve 'Binary c" <+> pretty curve <+> prettyField field+  <+>  "Fr => BCurve c" <+> pretty curve <+> prettyField field <+> "Fr where"+  <$$> indent 2+    (    "a_ = const _a"+    <$$> prettyInline "a_"+    <$$> "b_ = const _b"+    <$$> prettyInline "b_"+    <$$> "h_ = const _h"+    <$$> prettyInline "h_"+    <$$> "p_ = const _p"+    <$$> prettyInline "p_"+    <$$> "r_ = const _r"+    <$$> prettyInline "r_"+    <$$> "x_ = const _x"+    <$$> prettyInline "x_"+    <$$> "y_ = const _y"+    <$$> prettyInline "y_"+    )+  <>   prettyBreak+  <$$> prettyDocumentation ("Affine" <+> curve' <+> "point")+  <$$> "type PA = BAPoint" <+> pretty curve <+> prettyField field <+> "Fr"+  <>   prettyBreak+  <$$> prettyDocumentation ("Affine" <+> curve' <+> "is a binary affine curve")+  <$$> "instance BACurve" <+> pretty curve <+> prettyField field <+> "Fr where"+  <$$> indent 2+    (    "gA_ = gA"+    <$$> prettyInline "gA_"+    )+  <>   prettyBreak+  <$$> prettyDocumentation ("Projective" <+> pretty curve <+> "point")+  <$$> "type PP = BPPoint" <+> pretty curve <+> prettyField field <+> "Fr"+  <>   prettyBreak+  <$$> prettyDocumentation ("Projective" <+> curve' <+> "is a binary projective curve")+  <$$> "instance BPCurve" <+> pretty curve <+> prettyField field <+> "Fr where"+  <$$> indent 2+    (    "gP_ = gP"+    <$$> prettyInline "gP_"+    )+  where+    curve' :: Doc+    curve' = pretty curve <+> "curve"++prettyParameters :: Types -> Parameters -> Doc+prettyParameters Types{..} Parameters{..}+  =    prettySection "Parameters"+  <$$> prettyDocumentation ("Coefficient @A@ of" <+> curve')+  <$$> "_a ::" <+> prettyField field+  <$$> "_a =" <+> prettyElement a+  <$$> prettyInline "_a"+  <>   prettyBreak+  <$$> prettyDocumentation ("Coefficient @B@ of" <+> curve')+  <$$> "_b ::" <+> prettyField field+  <$$> "_b =" <+> prettyElement b+  <$$> prettyInline "_b"+  <>   prettyBreak+  <$$> prettyDocumentation ("Cofactor of" <+> curve')+  <$$> "_h :: Integer"+  <$$> "_h =" <+> prettyInteger h+  <$$> prettyInline "_h"+  <>   prettyBreak+  <$$> prettyDocumentation ("Polynomial of" <+> curve')+  <$$> "_p :: Integer"+  <$$> "_p =" <+> prettyInteger p+  <$$> prettyInline "_p"+  <>   prettyBreak+  <$$> prettyDocumentation ("Order of" <+> curve')+  <$$> "_r :: Integer"+  <$$> "_r =" <+> prettyInteger r+  <$$> prettyInline "_r"+  <>   prettyBreak+  <$$> prettyDocumentation ("Coordinate @X@ of" <+> curve')+  <$$> "_x ::" <+> prettyField field+  <$$> "_x =" <+> prettyElement x+  <$$> prettyInline "_x"+  <>   prettyBreak+  <$$> prettyDocumentation ("Coordinate @Y@ of" <+> curve')+  <$$> "_y ::" <+> prettyField field+  <$$> "_y =" <+> prettyElement y+  <$$> prettyInline "_y"+  <>   prettyBreak+  <$$> prettyDocumentation ("Generator of affine" <+> curve')+  <$$> "gA :: PA"+  <$$> "gA = A _x _y"+  <$$> prettyInline "gA"+  <>   prettyBreak+  <$$> prettyDocumentation ("Generator of projective" <+> curve')+  <$$> "gP :: PP"+  <$$> "gP = P _x _y 1"+  <$$> prettyInline "gP"+  where+    curve' :: Doc+    curve' = pretty curve <+> "curve"++prettyCurve :: Curve -> Doc+prettyCurve (Curve types parameters)+  =    prettyImports types+  <>   prettyBreak+  <$$> prettyTypes types+  <>   prettyBreak+  <$$> prettyParameters types parameters+  <>   prettyBreak

+ generate/Generate/Binary/Generate.hs view

@@ -0,0 +1,84 @@+module Generate.Binary.Generate+  ( prettyGenerate+  ) where++import Protolude++import Data.Text (toLower)+import Text.PrettyPrint.Leijen.Text++import Generate.Binary.Types+import Generate.Generate+import Generate.Pretty++-------------------------------------------------------------------------------+-- Generate+-------------------------------------------------------------------------------++prettyImports :: Doc+prettyImports+  =    "module Generate.Binary.Parameters"+  <$$> indent 2+    (    "( curves"+    <$$> ") where"+    )+  <>   prettyBreak+  <$$> "import Protolude"+  <>   prettyBreak+  <$$> "import Generate.Binary.Types"++prettyCurves :: [Curve] -> Doc+prettyCurves curves+  =    prettySection "Curves"+  <$$> "curves :: [Curve]"+  <$$> "curves ="+  <$$> indent 2+    (    "[ "+    <>   hcat (punctuate "\n, " (map prettyCurves' curves))+    <$$> "]"+    )+  where+    prettyCurves' :: Curve -> Doc+    prettyCurves' = pretty . toLower . curve . types++prettyParameters :: [Curve] -> Doc+prettyParameters curves+  =    prettySection "Parameters"+  <$$> vcat (punctuate prettyBreak (map prettyParameters' curves))+  where+    prettyParameters' :: Curve -> Doc+    prettyParameters' (Curve Types{..} Parameters{..})+      =    pretty (toLower curve) <+> ":: Curve"+      <$$> pretty (toLower curve) <+> "= Curve"+      <$$> indent 2+        (    "{ types = Types"+        <$$> indent 2+          (    "{ curve   =" <+> prettyText curve+          <$$> ", field   =" <+> prettyField field+          <$$> ", field'  =" <+> prettyField field'+          <$$> ", imports = "+          <>   maybe "Nothing" ((<>) "Just " . prettyText) imports+          <$$> "}"+          )+        <$$> ", parameters = Parameters"+        <$$> indent 2+          (    "{ a =" <+> prettyElement a+          <$$> ", b =" <+> prettyElement b+          <$$> ", h =" <+> prettyInteger h+          <$$> ", p =" <+> prettyInteger p+          <$$> ", r =" <+> prettyInteger r+          <$$> ", x =" <+> prettyElement x+          <$$> ", y =" <+> prettyElement y+          <$$> "}"+          )+        <$$> "}"+        )++prettyGenerate :: [Curve] -> Doc+prettyGenerate curves+  =    prettyImports+  <>   prettyBreak+  <$$> prettyCurves curves+  <>   prettyBreak+  <$$> prettyParameters curves+  <>   prettyBreak

+ generate/Generate/Binary/Parameters.hs view

@@ -0,0 +1,379 @@+module Generate.Binary.Parameters+  ( curves+  ) where++import Protolude++import Generate.Binary.Types++-------------------------------------------------------------------------------+-- Curves+-------------------------------------------------------------------------------++curves :: [Curve]+curves =+  [ sect113r1+  , sect113r2+  , sect131r1+  , sect131r2+  , sect163k1+  , sect163r1+  , sect163r2+  , sect193r1+  , sect193r2+  , sect233k1+  , sect233r1+  , sect239k1+  , sect283k1+  , sect283r1+  , sect409k1+  , sect409r1+  , sect571k1+  , sect571r1+  ]++-------------------------------------------------------------------------------+-- Parameters+-------------------------------------------------------------------------------++sect113r1 :: Curve+sect113r1 = Curve+  { types = Types+    { curve   = "SECT113R1"+    , field   = BinaryField "F2m" 0x20000000000000000000000000201+    , field'  = PrimeField "Fr" 0x100000000000000d9ccec8a39e56f+    , imports = Nothing+    }+  , parameters = Parameters+    { a = BF 0x3088250ca6e7c7fe649ce85820f7+    , b = BF 0xe8bee4d3e2260744188be0e9c723+    , h = 0x2+    , p = 0x20000000000000000000000000201+    , r = 0x100000000000000d9ccec8a39e56f+    , x = BF 0x9d73616f35f4ab1407d73562c10f+    , y = BF 0xa52830277958ee84d1315ed31886+    }+  }++sect113r2 :: Curve+sect113r2 = Curve+  { types = Types+    { curve   = "SECT113R2"+    , field   = BinaryField "F2m" 0x20000000000000000000000000201+    , field'  = PrimeField "Fr" 0x10000000000000108789b2496af93+    , imports = Nothing+    }+  , parameters = Parameters+    { a = BF 0x689918dbec7e5a0dd6dfc0aa55c7+    , b = BF 0x95e9a9ec9b297bd4bf36e059184f+    , h = 0x2+    , p = 0x20000000000000000000000000201+    , r = 0x10000000000000108789b2496af93+    , x = BF 0x1a57a6a7b26ca5ef52fcdb8164797+    , y = BF 0xb3adc94ed1fe674c06e695baba1d+    }+  }++sect131r1 :: Curve+sect131r1 = Curve+  { types = Types+    { curve   = "SECT131R1"+    , field   = BinaryField "F2m" 0x80000000000000000000000000000010d+    , field'  = PrimeField "Fr" 0x400000000000000023123953a9464b54d+    , imports = Nothing+    }+  , parameters = Parameters+    { a = BF 0x7a11b09a76b562144418ff3ff8c2570b8+    , b = BF 0x217c05610884b63b9c6c7291678f9d341+    , h = 0x2+    , p = 0x80000000000000000000000000000010d+    , r = 0x400000000000000023123953a9464b54d+    , x = BF 0x81baf91fdf9833c40f9c181343638399+    , y = BF 0x78c6e7ea38c001f73c8134b1b4ef9e150+    }+  }++sect131r2 :: Curve+sect131r2 = Curve+  { types = Types+    { curve   = "SECT131R2"+    , field   = BinaryField "F2m" 0x80000000000000000000000000000010d+    , field'  = PrimeField "Fr" 0x400000000000000016954a233049ba98f+    , imports = Nothing+    }+  , parameters = Parameters+    { a = BF 0x3e5a88919d7cafcbf415f07c2176573b2+    , b = BF 0x4b8266a46c55657ac734ce38f018f2192+    , h = 0x2+    , p = 0x80000000000000000000000000000010d+    , r = 0x400000000000000016954a233049ba98f+    , x = BF 0x356dcd8f2f95031ad652d23951bb366a8+    , y = BF 0x648f06d867940a5366d9e265de9eb240f+    }+  }++sect163k1 :: Curve+sect163k1 = Curve+  { types = Types+    { curve   = "SECT163K1"+    , field   = BinaryField "F2m" 0x800000000000000000000000000000000000000c9+    , field'  = PrimeField "Fr" 0x4000000000000000000020108a2e0cc0d99f8a5ef+    , imports = Nothing+    }+  , parameters = Parameters+    { a = BF 0x1+    , b = BF 0x1+    , h = 0x2+    , p = 0x800000000000000000000000000000000000000c9+    , r = 0x4000000000000000000020108a2e0cc0d99f8a5ef+    , x = BF 0x2fe13c0537bbc11acaa07d793de4e6d5e5c94eee8+    , y = BF 0x289070fb05d38ff58321f2e800536d538ccdaa3d9+    }+  }++sect163r1 :: Curve+sect163r1 = Curve+  { types = Types+    { curve   = "SECT163R1"+    , field   = BinaryField "F2m" 0x800000000000000000000000000000000000000c9+    , field'  = PrimeField "Fr" 0x3ffffffffffffffffffff48aab689c29ca710279b+    , imports = Nothing+    }+  , parameters = Parameters+    { a = BF 0x7b6882caaefa84f9554ff8428bd88e246d2782ae2+    , b = BF 0x713612dcddcb40aab946bda29ca91f73af958afd9+    , h = 0x2+    , p = 0x800000000000000000000000000000000000000c9+    , r = 0x3ffffffffffffffffffff48aab689c29ca710279b+    , x = BF 0x369979697ab43897789566789567f787a7876a654+    , y = BF 0x435edb42efafb2989d51fefce3c80988f41ff883+    }+  }++sect163r2 :: Curve+sect163r2 = Curve+  { types = Types+    { curve   = "SECT163R2"+    , field   = BinaryField "F2m" 0x800000000000000000000000000000000000000c9+    , field'  = PrimeField "Fr" 0x40000000000000000000292fe77e70c12a4234c33+    , imports = Nothing+    }+  , parameters = Parameters+    { a = BF 0x1+    , b = BF 0x20a601907b8c953ca1481eb10512f78744a3205fd+    , h = 0x2+    , p = 0x800000000000000000000000000000000000000c9+    , r = 0x40000000000000000000292fe77e70c12a4234c33+    , x = BF 0x3f0eba16286a2d57ea0991168d4994637e8343e36+    , y = BF 0xd51fbc6c71a0094fa2cdd545b11c5c0c797324f1+    }+  }++sect193r1 :: Curve+sect193r1 = Curve+  { types = Types+    { curve   = "SECT193R1"+    , field   = BinaryField "F2m" 0x2000000000000000000000000000000000000000000008001+    , field'  = PrimeField "Fr" 0x1000000000000000000000000c7f34a778f443acc920eba49+    , imports = Nothing+    }+  , parameters = Parameters+    { a = BF 0x17858feb7a98975169e171f77b4087de098ac8a911df7b01+    , b = BF 0xfdfb49bfe6c3a89facadaa7a1e5bbc7cc1c2e5d831478814+    , h = 0x2+    , p = 0x2000000000000000000000000000000000000000000008001+    , r = 0x1000000000000000000000000c7f34a778f443acc920eba49+    , x = BF 0x1f481bc5f0ff84a74ad6cdf6fdef4bf6179625372d8c0c5e1+    , y = BF 0x25e399f2903712ccf3ea9e3a1ad17fb0b3201b6af7ce1b05+    }+  }++sect193r2 :: Curve+sect193r2 = Curve+  { types = Types+    { curve   = "SECT193R2"+    , field   = BinaryField "F2m" 0x2000000000000000000000000000000000000000000008001+    , field'  = PrimeField "Fr" 0x10000000000000000000000015aab561b005413ccd4ee99d5+    , imports = Nothing+    }+  , parameters = Parameters+    { a = BF 0x163f35a5137c2ce3ea6ed8667190b0bc43ecd69977702709b+    , b = BF 0xc9bb9e8927d4d64c377e2ab2856a5b16e3efb7f61d4316ae+    , h = 0x2+    , p = 0x2000000000000000000000000000000000000000000008001+    , r = 0x10000000000000000000000015aab561b005413ccd4ee99d5+    , x = BF 0xd9b67d192e0367c803f39e1a7e82ca14a651350aae617e8f+    , y = BF 0x1ce94335607c304ac29e7defbd9ca01f596f927224cdecf6c+    }+  }++sect233k1 :: Curve+sect233k1 = Curve+  { types = Types+    { curve   = "SECT233K1"+    , field   = BinaryField "F2m" 0x20000000000000000000000000000000000000004000000000000000001+    , field'  = PrimeField "Fr" 0x8000000000000000000000000000069d5bb915bcd46efb1ad5f173abdf+    , imports = Nothing+    }+  , parameters = Parameters+    { a = BF 0x0+    , b = BF 0x1+    , h = 0x4+    , p = 0x20000000000000000000000000000000000000004000000000000000001+    , r = 0x8000000000000000000000000000069d5bb915bcd46efb1ad5f173abdf+    , x = BF 0x17232ba853a7e731af129f22ff4149563a419c26bf50a4c9d6eefad6126+    , y = BF 0x1db537dece819b7f70f555a67c427a8cd9bf18aeb9b56e0c11056fae6a3+    }+  }++sect233r1 :: Curve+sect233r1 = Curve+  { types = Types+    { curve   = "SECT233R1"+    , field   = BinaryField "F2m" 0x20000000000000000000000000000000000000004000000000000000001+    , field'  = PrimeField "Fr" 0x1000000000000000000000000000013e974e72f8a6922031d2603cfe0d7+    , imports = Nothing+    }+  , parameters = Parameters+    { a = BF 0x1+    , b = BF 0x66647ede6c332c7f8c0923bb58213b333b20e9ce4281fe115f7d8f90ad+    , h = 0x2+    , p = 0x20000000000000000000000000000000000000004000000000000000001+    , r = 0x1000000000000000000000000000013e974e72f8a6922031d2603cfe0d7+    , x = BF 0xfac9dfcbac8313bb2139f1bb755fef65bc391f8b36f8f8eb7371fd558b+    , y = BF 0x1006a08a41903350678e58528bebf8a0beff867a7ca36716f7e01f81052+    }+  }++sect239k1 :: Curve+sect239k1 = Curve+  { types = Types+    { curve   = "SECT239K1"+    , field   = BinaryField "F2m" 0x800000000000000000004000000000000000000000000000000000000001+    , field'  = PrimeField "Fr" 0x2000000000000000000000000000005a79fec67cb6e91f1c1da800e478a5+    , imports = Nothing+    }+  , parameters = Parameters+    { a = BF 0x0+    , b = BF 0x1+    , h = 0x4+    , p = 0x800000000000000000004000000000000000000000000000000000000001+    , r = 0x2000000000000000000000000000005a79fec67cb6e91f1c1da800e478a5+    , x = BF 0x29a0b6a887a983e9730988a68727a8b2d126c44cc2cc7b2a6555193035dc+    , y = BF 0x76310804f12e549bdb011c103089e73510acb275fc312a5dc6b76553f0ca+    }+  }++sect283k1 :: Curve+sect283k1 = Curve+  { types = Types+    { curve   = "SECT283K1"+    , field   = BinaryField "F2m" 0x800000000000000000000000000000000000000000000000000000000000000000010a1+    , field'  = PrimeField "Fr" 0x1ffffffffffffffffffffffffffffffffffe9ae2ed07577265dff7f94451e061e163c61+    , imports = Nothing+    }+  , parameters = Parameters+    { a = BF 0x0+    , b = BF 0x1+    , h = 0x4+    , p = 0x800000000000000000000000000000000000000000000000000000000000000000010a1+    , r = 0x1ffffffffffffffffffffffffffffffffffe9ae2ed07577265dff7f94451e061e163c61+    , x = BF 0x503213f78ca44883f1a3b8162f188e553cd265f23c1567a16876913b0c2ac2458492836+    , y = BF 0x1ccda380f1c9e318d90f95d07e5426fe87e45c0e8184698e45962364e34116177dd2259+    }+  }++sect283r1 :: Curve+sect283r1 = Curve+  { types = Types+    { curve   = "SECT283R1"+    , field   = BinaryField "F2m" 0x800000000000000000000000000000000000000000000000000000000000000000010a1+    , field'  = PrimeField "Fr" 0x3ffffffffffffffffffffffffffffffffffef90399660fc938a90165b042a7cefadb307+    , imports = Nothing+    }+  , parameters = Parameters+    { a = BF 0x1+    , b = BF 0x27b680ac8b8596da5a4af8a19a0303fca97fd7645309fa2a581485af6263e313b79a2f5+    , h = 0x2+    , p = 0x800000000000000000000000000000000000000000000000000000000000000000010a1+    , r = 0x3ffffffffffffffffffffffffffffffffffef90399660fc938a90165b042a7cefadb307+    , x = BF 0x5f939258db7dd90e1934f8c70b0dfec2eed25b8557eac9c80e2e198f8cdbecd86b12053+    , y = BF 0x3676854fe24141cb98fe6d4b20d02b4516ff702350eddb0826779c813f0df45be8112f4+    }+  }++sect409k1 :: Curve+sect409k1 = Curve+  { types = Types+    { curve   = "SECT409K1"+    , field   = BinaryField "F2m" 0x2000000000000000000000000000000000000000000000000000000000000000000000000000000008000000000000000000001+    , field'  = PrimeField "Fr" 0x7ffffffffffffffffffffffffffffffffffffffffffffffffffe5f83b2d4ea20400ec4557d5ed3e3e7ca5b4b5c83b8e01e5fcf+    , imports = Nothing+    }+  , parameters = Parameters+    { a = BF 0x0+    , b = BF 0x1+    , h = 0x4+    , p = 0x2000000000000000000000000000000000000000000000000000000000000000000000000000000008000000000000000000001+    , r = 0x7ffffffffffffffffffffffffffffffffffffffffffffffffffe5f83b2d4ea20400ec4557d5ed3e3e7ca5b4b5c83b8e01e5fcf+    , x = BF 0x60f05f658f49c1ad3ab1890f7184210efd0987e307c84c27accfb8f9f67cc2c460189eb5aaaa62ee222eb1b35540cfe9023746+    , y = BF 0x1e369050b7c4e42acba1dacbf04299c3460782f918ea427e6325165e9ea10e3da5f6c42e9c55215aa9ca27a5863ec48d8e0286b+    }+  }++sect409r1 :: Curve+sect409r1 = Curve+  { types = Types+    { curve   = "SECT409R1"+    , field   = BinaryField "F2m" 0x2000000000000000000000000000000000000000000000000000000000000000000000000000000008000000000000000000001+    , field'  = PrimeField "Fr" 0x10000000000000000000000000000000000000000000000000001e2aad6a612f33307be5fa47c3c9e052f838164cd37d9a21173+    , imports = Nothing+    }+  , parameters = Parameters+    { a = BF 0x1+    , b = BF 0x21a5c2c8ee9feb5c4b9a753b7b476b7fd6422ef1f3dd674761fa99d6ac27c8a9a197b272822f6cd57a55aa4f50ae317b13545f+    , h = 0x2+    , p = 0x2000000000000000000000000000000000000000000000000000000000000000000000000000000008000000000000000000001+    , r = 0x10000000000000000000000000000000000000000000000000001e2aad6a612f33307be5fa47c3c9e052f838164cd37d9a21173+    , x = BF 0x15d4860d088ddb3496b0c6064756260441cde4af1771d4db01ffe5b34e59703dc255a868a1180515603aeab60794e54bb7996a7+    , y = BF 0x61b1cfab6be5f32bbfa78324ed106a7636b9c5a7bd198d0158aa4f5488d08f38514f1fdf4b4f40d2181b3681c364ba0273c706+    }+  }++sect571k1 :: Curve+sect571k1 = Curve+  { types = Types+    { curve   = "SECT571K1"+    , field   = BinaryField "F2m" 0x80000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000425+    , field'  = PrimeField "Fr" 0x20000000000000000000000000000000000000000000000000000000000000000000000131850e1f19a63e4b391a8db917f4138b630d84be5d639381e91deb45cfe778f637c1001+    , imports = Nothing+    }+  , parameters = Parameters+    { a = BF 0x0+    , b = BF 0x1+    , h = 0x4+    , p = 0x80000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000425+    , r = 0x20000000000000000000000000000000000000000000000000000000000000000000000131850e1f19a63e4b391a8db917f4138b630d84be5d639381e91deb45cfe778f637c1001+    , x = BF 0x26eb7a859923fbc82189631f8103fe4ac9ca2970012d5d46024804801841ca44370958493b205e647da304db4ceb08cbbd1ba39494776fb988b47174dca88c7e2945283a01c8972+    , y = BF 0x349dc807f4fbf374f4aeade3bca95314dd58cec9f307a54ffc61efc006d8a2c9d4979c0ac44aea74fbebbb9f772aedcb620b01a7ba7af1b320430c8591984f601cd4c143ef1c7a3+    }+  }++sect571r1 :: Curve+sect571r1 = Curve+  { types = Types+    { curve   = "SECT571R1"+    , field   = BinaryField "F2m" 0x80000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000425+    , field'  = PrimeField "Fr" 0x3ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffe661ce18ff55987308059b186823851ec7dd9ca1161de93d5174d66e8382e9bb2fe84e47+    , imports = Nothing+    }+  , parameters = Parameters+    { a = BF 0x1+    , b = BF 0x2f40e7e2221f295de297117b7f3d62f5c6a97ffcb8ceff1cd6ba8ce4a9a18ad84ffabbd8efa59332be7ad6756a66e294afd185a78ff12aa520e4de739baca0c7ffeff7f2955727a+    , h = 0x2+    , p = 0x80000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000425+    , r = 0x3ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffe661ce18ff55987308059b186823851ec7dd9ca1161de93d5174d66e8382e9bb2fe84e47+    , x = BF 0x303001d34b856296c16c0d40d3cd7750a93d1d2955fa80aa5f40fc8db7b2abdbde53950f4c0d293cdd711a35b67fb1499ae60038614f1394abfa3b4c850d927e1e7769c8eec2d19+    , y = BF 0x37bf27342da639b6dccfffeb73d69d78c6c27a6009cbbca1980f8533921e8a684423e43bab08a576291af8f461bb2a8b3531d2f0485c19b16e2f1516e23dd3c1a4827af1b8ac15b+    }+  }

+ generate/Generate/Binary/Types.hs view

@@ -0,0 +1,27 @@+module Generate.Binary.Types+  ( module Generate.Binary.Types+  , module Generate.Types+  ) where++import Protolude++import Generate.Types++-------------------------------------------------------------------------------+-- Types+-------------------------------------------------------------------------------++data Curve = Curve+  { types      :: Types+  , parameters :: Parameters+  }++data Parameters = Parameters+  { a :: Element+  , b :: Element+  , h :: Integer+  , p :: Integer+  , r :: Integer+  , x :: Element+  , y :: Element+  }

+ generate/Generate/Curve.hs view

@@ -0,0 +1,62 @@+module Generate.Curve+  ( module Generate.Curve+  ) where++import Protolude++import Text.PrettyPrint.Leijen.Text++import Generate.Pretty+import Generate.Types++-------------------------------------------------------------------------------+-- Pretty+-------------------------------------------------------------------------------++prettyElement :: Element -> Doc+prettyElement (BF n)+  = prettyInteger n+prettyElement (EF ns)+  = "toField" <+> align+    (    (if null ns then "[" else "[ ")+    <>   hcat (punctuate "\n, " (map prettyElement ns))+    <$$> "]"+    )+prettyElement (PF n)+  = prettyInteger n++prettyField :: Field -> Doc+prettyField (BinaryField f2m _)+  = pretty f2m+prettyField (ExtensionField fq' _ _ _ _)+  = pretty fq'+prettyField (PrimeField fq _)+  = pretty fq++prettyImport :: Field -> Doc+prettyImport k+  =    "import Protolude"+  <>   prettyBreak+  <$$> k'+  <$$> "import PrimeField"+  where+    k' = case k of+      BinaryField _ _          -> "import BinaryField"+      ExtensionField _ _ _ _ _ -> "import ExtensionField"+      _                        -> mempty++prettyType :: Field -> Doc+prettyType (BinaryField f2m q)+  = "type" <+> pretty f2m <+> "= BinaryField" <+> prettyInteger q+prettyType (ExtensionField fq' fq q s k)+  =    prettyType' k+  <$$> "data" <+> pretty q+  <$$> "instance IrreducibleMonic" <+> pretty fq <+> pretty q <+> "where"+  <$$> "  split _ =" <+> pretty s+  <$$> "type" <+> pretty fq' <+> "= ExtensionField" <+> pretty fq <+> pretty q+  where+    prettyType' :: Maybe Field -> Doc+    prettyType' (Just f) = prettyType f+    prettyType' _        = mempty+prettyType (PrimeField fq q)+  = "type" <+> pretty fq <+> "= PrimeField" <+> prettyInteger q

+ generate/Generate/Edwards/Curve.hs view

@@ -0,0 +1,144 @@+module Generate.Edwards.Curve+  ( prettyCurve+  ) where++import Protolude++import Text.PrettyPrint.Leijen.Text++import Generate.Curve+import Generate.Edwards.Types+import Generate.Pretty++-------------------------------------------------------------------------------+-- Curve+-------------------------------------------------------------------------------++prettyImports :: Types -> Doc+prettyImports Types{..}+  =    "module Curve.Edwards." <> pretty curve+  <$$> indent 2+    (    "( module Curve.Edwards"+    <$$> ", module Curve.Edwards." <> pretty curve+    <$$> ") where"+    )+  <>   prettyBreak+  <$$> prettyImport field+  <>   prettyBreak+  <$$> "import Curve.Edwards"+  <$$> maybe mempty pretty imports++prettyTypes :: Types -> Doc+prettyTypes Types{..}+  =    prettySection "Types"+  <$$> prettyDocumentation curve'+  <$$> "data" <+> pretty curve+  <>   prettyBreak+  <$$> prettyDocumentation ("Field of points of" <+> curve')+  <$$> prettyType field+  <>   prettyBreak+  <$$> prettyDocumentation ("Field of coefficients of" <+> curve')+  <$$> prettyType field'+  <>   prettyBreak+  <$$> prettyDocumentation (curve' <+> "is an Edwards curve")+  <$$> "instance Curve 'Edwards c" <+> pretty curve <+> prettyField field+  <+>  "Fr => ECurve c" <+> pretty curve <+> prettyField field <+> "Fr where"+  <$$> indent 2+    (    "a_ = const _a"+    <$$> prettyInline "a_"+    <$$> "d_ = const _d"+    <$$> prettyInline "d_"+    <$$> "h_ = const _h"+    <$$> prettyInline "h_"+    <$$> "q_ = const _q"+    <$$> prettyInline "q_"+    <$$> "r_ = const _r"+    <$$> prettyInline "r_"+    <$$> "x_ = const _x"+    <$$> prettyInline "x_"+    <$$> "y_ = const _y"+    <$$> prettyInline "y_"+    )+  <>   prettyBreak+  <$$> prettyDocumentation ("Affine" <+> curve' <+> "point")+  <$$> "type PA = EAPoint" <+> pretty curve <+> prettyField field <+> "Fr"+  <>   prettyBreak+  <$$> prettyDocumentation ("Affine" <+> curve' <+> "is an Edwards affine curve")+  <$$> "instance EACurve" <+> pretty curve <+> prettyField field <+> "Fr where"+  <$$> indent 2+    (    "gA_ = gA"+    <$$> prettyInline "gA_"+    )+  <>   prettyBreak+  <$$> prettyDocumentation ("Projective" <+> pretty curve <+> "point")+  <$$> "type PP = EPPoint" <+> pretty curve <+> prettyField field <+> "Fr"+  <>   prettyBreak+  <$$> prettyDocumentation ("Projective" <+> curve' <+> "is an Edwards projective curve")+  <$$> "instance EPCurve" <+> pretty curve <+> prettyField field <+> "Fr where"+  <$$> indent 2+    (    "gP_ = gP"+    <$$> prettyInline "gP_"+    )+  where+    curve' :: Doc+    curve' = pretty curve <+> "curve"++prettyParameters :: Types -> Parameters -> Doc+prettyParameters Types{..} Parameters{..}+  =    prettySection "Parameters"+  <$$> prettyDocumentation ("Coefficient @A@ of" <+> curve')+  <$$> "_a ::" <+> prettyField field+  <$$> "_a =" <+> prettyElement a+  <$$> prettyInline "_a"+  <>   prettyBreak+  <$$> prettyDocumentation ("Coefficient @D@ of" <+> curve')+  <$$> "_d ::" <+> prettyField field+  <$$> "_d =" <+> prettyElement d+  <$$> prettyInline "_d"+  <>   prettyBreak+  <$$> prettyDocumentation ("Cofactor of" <+> curve')+  <$$> "_h :: Integer"+  <$$> "_h =" <+> prettyInteger h+  <$$> prettyInline "_h"+  <>   prettyBreak+  <$$> prettyDocumentation ("Characteristic of" <+> curve')+  <$$> "_q :: Integer"+  <$$> "_q =" <+> prettyInteger q+  <$$> prettyInline "_q"+  <>   prettyBreak+  <$$> prettyDocumentation ("Order of" <+> curve')+  <$$> "_r :: Integer"+  <$$> "_r =" <+> prettyInteger r+  <$$> prettyInline "_r"+  <>   prettyBreak+  <$$> prettyDocumentation ("Coordinate @X@ of" <+> curve')+  <$$> "_x ::" <+> prettyField field+  <$$> "_x =" <+> prettyElement x+  <$$> prettyInline "_x"+  <>   prettyBreak+  <$$> prettyDocumentation ("Coordinate @Y@ of" <+> curve')+  <$$> "_y ::" <+> prettyField field+  <$$> "_y =" <+> prettyElement y+  <$$> prettyInline "_y"+  <>   prettyBreak+  <$$> prettyDocumentation ("Generator of affine" <+> curve')+  <$$> "gA :: PA"+  <$$> "gA = A _x _y"+  <$$> prettyInline "gA"+  <>   prettyBreak+  <$$> prettyDocumentation ("Generator of projective" <+> curve')+  <$$> "gP :: PP"+  <$$> "gP = P _x _y 1"+  <$$> prettyInline "gP"+  where+    curve' :: Doc+    curve' = pretty curve <+> "curve"++prettyCurve :: Curve -> Doc+prettyCurve (Curve types parameters)+  =    prettyImports types+  <>   prettyBreak+  <$$> prettyTypes types+  <>   prettyBreak+  <$$> prettyParameters types parameters+  <>   prettyBreak

+ generate/Generate/Edwards/Generate.hs view

@@ -0,0 +1,84 @@+module Generate.Edwards.Generate+  ( prettyGenerate+  ) where++import Protolude++import Data.Text (toLower)+import Text.PrettyPrint.Leijen.Text++import Generate.Edwards.Types+import Generate.Generate+import Generate.Pretty++-------------------------------------------------------------------------------+-- Generate+-------------------------------------------------------------------------------++prettyImports :: Doc+prettyImports+  =    "module Generate.Edwards.Parameters"+  <$$> indent 2+    (    "( curves"+    <$$> ") where"+    )+  <>   prettyBreak+  <$$> "import Protolude"+  <>   prettyBreak+  <$$> "import Generate.Edwards.Types"++prettyCurves :: [Curve] -> Doc+prettyCurves curves+  =    prettySection "Curves"+  <$$> "curves :: [Curve]"+  <$$> "curves ="+  <$$> indent 2+    (    "[ "+    <>   hcat (punctuate "\n, " (map prettyCurves' curves))+    <$$> "]"+    )+  where+    prettyCurves' :: Curve -> Doc+    prettyCurves' = pretty . toLower . curve . types++prettyParameters :: [Curve] -> Doc+prettyParameters curves+  =    prettySection "Parameters"+  <$$> vcat (punctuate prettyBreak (map prettyParameters' curves))+  where+    prettyParameters' :: Curve -> Doc+    prettyParameters' (Curve Types{..} Parameters{..})+      =    pretty (toLower curve) <+> ":: Curve"+      <$$> pretty (toLower curve) <+> "= Curve"+      <$$> indent 2+        (    "{ types = Types"+        <$$> indent 2+          (    "{ curve   =" <+> prettyText curve+          <$$> ", field   =" <+> prettyField field+          <$$> ", field'  =" <+> prettyField field'+          <$$> ", imports = "+          <>   maybe "Nothing" ((<>) "Just " . prettyText) imports+          <$$> "}"+          )+        <$$> ", parameters = Parameters"+        <$$> indent 2+          (    "{ a =" <+> prettyElement a+          <$$> ", d =" <+> prettyElement d+          <$$> ", h =" <+> prettyInteger h+          <$$> ", q =" <+> prettyInteger q+          <$$> ", r =" <+> prettyInteger r+          <$$> ", x =" <+> prettyElement x+          <$$> ", y =" <+> prettyElement y+          <$$> "}"+          )+        <$$> "}"+        )++prettyGenerate :: [Curve] -> Doc+prettyGenerate curves+  =    prettyImports+  <>   prettyBreak+  <$$> prettyCurves curves+  <>   prettyBreak+  <$$> prettyParameters curves+  <>   prettyBreak

+ generate/Generate/Edwards/Parameters.hs view

@@ -0,0 +1,199 @@+module Generate.Edwards.Parameters+  ( curves+  ) where++import Protolude++import Generate.Edwards.Types++-------------------------------------------------------------------------------+-- Curves+-------------------------------------------------------------------------------++curves :: [Curve]+curves =+  [ curve1174+  , curve41417+  , e222+  , e382+  , e521+  , ed448+  , ed3363+  , ed25519+  , jubjub+  ]++-------------------------------------------------------------------------------+-- Parameters+-------------------------------------------------------------------------------++curve1174 :: Curve+curve1174 = Curve+  { types = Types+    { curve   = "Curve1174"+    , field   = PrimeField "Fq" 0x7fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff7+    , field'  = PrimeField "Fr" 0x1fffffffffffffffffffffffffffffff77965c4dfd307348944d45fd166c971+    , imports = Nothing+    }+  , parameters = Parameters+    { a = PF 0x1+    , d = PF 0x7fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffb61+    , h = 0x4+    , q = 0x7fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff7+    , r = 0x1fffffffffffffffffffffffffffffff77965c4dfd307348944d45fd166c971+    , x = PF 0x37fbb0cea308c479343aee7c029a190c021d96a492ecd6516123f27bce29eda+    , y = PF 0x6b72f82d47fb7cc6656841169840e0c4fe2dee2af3f976ba4ccb1bf9b46360e+    }+  }++curve41417 :: Curve+curve41417 = Curve+  { types = Types+    { curve   = "Curve41417"+    , field   = PrimeField "Fq" 0x3fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffef+    , field'  = PrimeField "Fr" 0x7ffffffffffffffffffffffffffffffffffffffffffffffffffeb3cc92414cf706022b36f1c0338ad63cf181b0e71a5e106af79+    , imports = Nothing+    }+  , parameters = Parameters+    { a = PF 0x1+    , d = PF 0xe21+    , h = 0x8+    , q = 0x3fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffef+    , r = 0x7ffffffffffffffffffffffffffffffffffffffffffffffffffeb3cc92414cf706022b36f1c0338ad63cf181b0e71a5e106af79+    , x = PF 0x1a334905141443300218c0631c326e5fcd46369f44c03ec7f57ff35498a4ab4d6d6ba111301a73faa8537c64c4fd3812f3cbc595+    , y = PF 0x22+    }+  }++e222 :: Curve+e222 = Curve+  { types = Types+    { curve   = "E222"+    , field   = PrimeField "Fq" 0x3fffffffffffffffffffffffffffffffffffffffffffffffffffff8b+    , field'  = PrimeField "Fr" 0xffffffffffffffffffffffffffff70cbc95e932f802f31423598cbf+    , imports = Nothing+    }+  , parameters = Parameters+    { a = PF 0x1+    , d = PF 0x27166+    , h = 0x4+    , q = 0x3fffffffffffffffffffffffffffffffffffffffffffffffffffff8b+    , r = 0xffffffffffffffffffffffffffff70cbc95e932f802f31423598cbf+    , x = PF 0x19b12bb156a389e55c9768c303316d07c23adab3736eb2bc3eb54e51+    , y = PF 0x1c+    }+  }++e382 :: Curve+e382 = Curve+  { types = Types+    { curve   = "E382"+    , field   = PrimeField "Fq" 0x3fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff97+    , field'  = PrimeField "Fr" 0xfffffffffffffffffffffffffffffffffffffffffffffffd5fb21f21e95eee17c5e69281b102d2773e27e13fd3c9719+    , imports = Nothing+    }+  , parameters = Parameters+    { a = PF 0x1+    , d = PF 0x3ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffef8e1+    , h = 0x4+    , q = 0x3fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff97+    , r = 0xfffffffffffffffffffffffffffffffffffffffffffffffd5fb21f21e95eee17c5e69281b102d2773e27e13fd3c9719+    , x = PF 0x196f8dd0eab20391e5f05be96e8d20ae68f840032b0b64352923bab85364841193517dbce8105398ebc0cc9470f79603+    , y = PF 0x11+    }+  }++e521 :: Curve+e521 = Curve+  { types = Types+    { curve   = "E521"+    , field   = PrimeField "Fq" 0x1ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff+    , field'  = PrimeField "Fr" 0x7ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffd15b6c64746fc85f736b8af5e7ec53f04fbd8c4569a8f1f4540ea2435f5180d6b+    , imports = Nothing+    }+  , parameters = Parameters+    { a = PF 0x1+    , d = PF 0x1fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffa4331+    , h = 0x4+    , q = 0x1ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff+    , r = 0x7ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffd15b6c64746fc85f736b8af5e7ec53f04fbd8c4569a8f1f4540ea2435f5180d6b+    , x = PF 0x752cb45c48648b189df90cb2296b2878a3bfd9f42fc6c818ec8bf3c9c0c6203913f6ecc5ccc72434b1ae949d568fc99c6059d0fb13364838aa302a940a2f19ba6c+    , y = PF 0xc+    }+  }++ed448 :: Curve+ed448 = Curve+  { types = Types+    { curve   = "Ed448"+    , field   = PrimeField "Fq" 0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffeffffffffffffffffffffffffffffffffffffffffffffffffffffffff+    , field'  = PrimeField "Fr" 0x3fffffffffffffffffffffffffffffffffffffffffffffffffffffff7cca23e9c44edb49aed63690216cc2728dc58f552378c292ab5844f3+    , imports = Nothing+    }+  , parameters = Parameters+    { a = PF 0x1+    , d = PF 0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffeffffffffffffffffffffffffffffffffffffffffffffffffffff6756+    , h = 0x4+    , q = 0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffeffffffffffffffffffffffffffffffffffffffffffffffffffffffff+    , r = 0x3fffffffffffffffffffffffffffffffffffffffffffffffffffffff7cca23e9c44edb49aed63690216cc2728dc58f552378c292ab5844f3+    , x = PF 0x297ea0ea2692ff1b4faff46098453a6a26adf733245f065c3c59d0709cecfa96147eaaf3932d94c63d96c170033f4ba0c7f0de840aed939f+    , y = PF 0x13+    }+  }++ed3363 :: Curve+ed3363 = Curve+  { types = Types+    { curve   = "Ed3363"+    , field   = PrimeField "Fq" 0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffd+    , field'  = PrimeField "Fr" 0x200000000000000000000000000000000000000000071415fa9850c0bd6b87f93baa7b2f95973e9fa805+    , imports = Nothing+    }+  , parameters = Parameters+    { a = PF 0x1+    , d = PF 0x2b67+    , h = 0x8+    , q = 0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffd+    , r = 0x200000000000000000000000000000000000000000071415fa9850c0bd6b87f93baa7b2f95973e9fa805+    , x = PF 0xc+    , y = PF 0xc0dc616b56502e18e1c161d007853d1b14b46c3811c7ef435b6db5d5650ca0365db12bec68505fe8632+    }+  }++ed25519 :: Curve+ed25519 = Curve+  { types = Types+    { curve   = "Ed25519"+    , field   = PrimeField "Fq" 0x7fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffed+    , field'  = PrimeField "Fr" 0x1000000000000000000000000000000014def9dea2f79cd65812631a5cf5d3ed+    , imports = Nothing+    }+  , parameters = Parameters+    { a = PF 0x7fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffec+    , d = PF 0x52036cee2b6ffe738cc740797779e89800700a4d4141d8ab75eb4dca135978a3+    , h = 0x8+    , q = 0x7fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffed+    , r = 0x1000000000000000000000000000000014def9dea2f79cd65812631a5cf5d3ed+    , x = PF 0x216936d3cd6e53fec0a4e231fdd6dc5c692cc7609525a7b2c9562d608f25d51a+    , y = PF 0x6666666666666666666666666666666666666666666666666666666666666658+    }+  }++jubjub :: Curve+jubjub = Curve+  { types = Types+    { curve   = "JubJub"+    , field   = PrimeField "Fq" 0x73eda753299d7d483339d80809a1d80553bda402fffe5bfeffffffff00000001+    , field'  = PrimeField "Fr" 0xe7db4ea6533afa906673b0101343b00a6682093ccc81082d0970e5ed6f72cb7+    , imports = Nothing+    }+  , parameters = Parameters+    { a = PF 0x73eda753299d7d483339d80809a1d80553bda402fffe5bfeffffffff00000000+    , d = PF 0x2a9318e74bfa2b48f5fd9207e6bd7fd4292d7f6d37579d2601065fd6d6343eb1+    , h = 0x8+    , q = 0x73eda753299d7d483339d80809a1d80553bda402fffe5bfeffffffff00000001+    , r = 0xe7db4ea6533afa906673b0101343b00a6682093ccc81082d0970e5ed6f72cb7+    , x = PF 0x5183972af8eff38ca624b4df00384882000c546bf2f39ede7f4ecf1a74f976c4+    , y = PF 0x3b43f8472ca2fc2c9e8fcc5abd9dc308096c8707ffa6833b146bad709349702e+    }+  }

+ generate/Generate/Edwards/Types.hs view

@@ -0,0 +1,27 @@+module Generate.Edwards.Types+  ( module Generate.Edwards.Types+  , module Generate.Types+  ) where++import Protolude++import Generate.Types++-------------------------------------------------------------------------------+-- Types+-------------------------------------------------------------------------------++data Curve = Curve+  { types      :: Types+  , parameters :: Parameters+  }++data Parameters = Parameters+  { a :: Element+  , d :: Element+  , h :: Integer+  , q :: Integer+  , r :: Integer+  , x :: Element+  , y :: Element+  }

+ generate/Generate/Generate.hs view

@@ -0,0 +1,41 @@+module Generate.Generate+  ( module Generate.Generate+  ) where++import Protolude++import Text.PrettyPrint.Leijen.Text++import Generate.Pretty+import Generate.Types++-------------------------------------------------------------------------------+-- Pretty+-------------------------------------------------------------------------------++prettyElement :: Element -> Doc+prettyElement (BF n)+  = "BF" <+> prettyInteger n+prettyElement (EF ns)+  = "EF" <+> align+    (    (if null ns then "[" else "[ ")+    <>   hcat (punctuate "\n, " (map prettyElement ns))+    <$$> "]"+    )+prettyElement (PF n)+  = "PF" <+> prettyInteger n++prettyField :: Field -> Doc+prettyField (BinaryField fp p)+  = "BinaryField" <+> prettyText fp <+> prettyInteger p+prettyField (ExtensionField fq fp p s k)+  = align+    (   "ExtensionField" <+> prettyText fq <+> prettyText fp+    <+> prettyText p <+> prettyText s <+> prettyField' k+    )+  where+    prettyField' :: Maybe Field -> Doc+    prettyField' (Just f) = "(Just" <$$> "(" <+> align (prettyField f) <$$> "))"+    prettyField' _        = "Nothing"+prettyField (PrimeField f2m p)+  = "PrimeField" <+> prettyText f2m <+> prettyInteger p

+ generate/Generate/Montgomery/Curve.hs view

@@ -0,0 +1,129 @@+module Generate.Montgomery.Curve+  ( prettyCurve+  ) where++import Protolude++import Text.PrettyPrint.Leijen.Text++import Generate.Curve+import Generate.Montgomery.Types+import Generate.Pretty++-------------------------------------------------------------------------------+-- Curve+-------------------------------------------------------------------------------++prettyImports :: Types -> Doc+prettyImports Types{..}+  =    "module Curve.Montgomery." <> pretty curve+  <$$> indent 2+    (    "( module Curve.Montgomery"+    <$$> ", module Curve.Montgomery." <> pretty curve+    <$$> ") where"+    )+  <>   prettyBreak+  <$$> prettyImport field+  <>   prettyBreak+  <$$> "import Curve.Montgomery"+  <$$> maybe mempty pretty imports++prettyTypes :: Types -> Doc+prettyTypes Types{..}+  =    prettySection "Types"+  <$$> prettyDocumentation curve'+  <$$> "data" <+> pretty curve+  <>   prettyBreak+  <$$> prettyDocumentation ("Field of points of" <+> curve')+  <$$> prettyType field+  <>   prettyBreak+  <$$> prettyDocumentation ("Field of coefficients of" <+> curve')+  <$$> prettyType field'+  <>   prettyBreak+  <$$> prettyDocumentation (curve' <+> "is a Montgomery curve")+  <$$> "instance Curve 'Montgomery c" <+> pretty curve <+> prettyField field+  <+>  "Fr => MCurve c" <+> pretty curve <+> prettyField field <+> "Fr where"+  <$$> indent 2+    (    "a_ = const _a"+    <$$> prettyInline "a_"+    <$$> "b_ = const _b"+    <$$> prettyInline "b_"+    <$$> "h_ = const _h"+    <$$> prettyInline "h_"+    <$$> "q_ = const _q"+    <$$> prettyInline "q_"+    <$$> "r_ = const _r"+    <$$> prettyInline "r_"+    <$$> "x_ = const _x"+    <$$> prettyInline "x_"+    <$$> "y_ = const _y"+    <$$> prettyInline "y_"+    )+  <>   prettyBreak+  <$$> prettyDocumentation ("Affine" <+> curve' <+> "point")+  <$$> "type PA = MAPoint" <+> pretty curve <+> prettyField field <+> "Fr"+  <>   prettyBreak+  <$$> prettyDocumentation ("Affine" <+> curve' <+> "is a Montgomery affine curve")+  <$$> "instance MACurve" <+> pretty curve <+> prettyField field <+> "Fr where"+  <$$> indent 2+    (    "gA_ = gA"+    <$$> prettyInline "gA_"+    )+  where+    curve' :: Doc+    curve' = pretty curve <+> "curve"++prettyParameters :: Types -> Parameters -> Doc+prettyParameters Types{..} Parameters{..}+  =    prettySection "Parameters"+  <$$> prettyDocumentation ("Coefficient @A@ of" <+> curve')+  <$$> "_a ::" <+> prettyField field+  <$$> "_a =" <+> prettyElement a+  <$$> prettyInline "_a"+  <>   prettyBreak+  <$$> prettyDocumentation ("Coefficient @B@ of" <+> curve')+  <$$> "_b ::" <+> prettyField field+  <$$> "_b =" <+> prettyElement b+  <$$> prettyInline "_b"+  <>   prettyBreak+  <$$> prettyDocumentation ("Cofactor of" <+> curve')+  <$$> "_h :: Integer"+  <$$> "_h =" <+> prettyInteger h+  <$$> prettyInline "_h"+  <>   prettyBreak+  <$$> prettyDocumentation ("Characteristic of" <+> curve')+  <$$> "_q :: Integer"+  <$$> "_q =" <+> prettyInteger q+  <$$> prettyInline "_q"+  <>   prettyBreak+  <$$> prettyDocumentation ("Order of" <+> curve')+  <$$> "_r :: Integer"+  <$$> "_r =" <+> prettyInteger r+  <$$> prettyInline "_r"+  <>   prettyBreak+  <$$> prettyDocumentation ("Coordinate @X@ of" <+> curve')+  <$$> "_x ::" <+> prettyField field+  <$$> "_x =" <+> prettyElement x+  <$$> prettyInline "_x"+  <>   prettyBreak+  <$$> prettyDocumentation ("Coordinate @Y@ of" <+> curve')+  <$$> "_y ::" <+> prettyField field+  <$$> "_y =" <+> prettyElement y+  <$$> prettyInline "_y"+  <>   prettyBreak+  <$$> prettyDocumentation ("Generator of affine" <+> curve')+  <$$> "gA :: PA"+  <$$> "gA = A _x _y"+  <$$> prettyInline "gA"+  where+    curve' :: Doc+    curve' = pretty curve <+> "curve"++prettyCurve :: Curve -> Doc+prettyCurve (Curve types parameters)+  =    prettyImports types+  <>   prettyBreak+  <$$> prettyTypes types+  <>   prettyBreak+  <$$> prettyParameters types parameters+  <>   prettyBreak

+ generate/Generate/Montgomery/Generate.hs view

@@ -0,0 +1,84 @@+module Generate.Montgomery.Generate+  ( prettyGenerate+  ) where++import Protolude++import Data.Text (toLower)+import Text.PrettyPrint.Leijen.Text++import Generate.Generate+import Generate.Montgomery.Types+import Generate.Pretty++-------------------------------------------------------------------------------+-- Generate+-------------------------------------------------------------------------------++prettyImports :: Doc+prettyImports+  =    "module Generate.Montgomery.Parameters"+  <$$> indent 2+    (    "( curves"+    <$$> ") where"+    )+  <>   prettyBreak+  <$$> "import Protolude"+  <>   prettyBreak+  <$$> "import Generate.Montgomery.Types"++prettyCurves :: [Curve] -> Doc+prettyCurves curves+  =    prettySection "Curves"+  <$$> "curves :: [Curve]"+  <$$> "curves ="+  <$$> indent 2+    (    "[ "+    <>   hcat (punctuate "\n, " (map prettyCurves' curves))+    <$$> "]"+    )+  where+    prettyCurves' :: Curve -> Doc+    prettyCurves' = pretty . toLower . curve . types++prettyParameters :: [Curve] -> Doc+prettyParameters curves+  =    prettySection "Parameters"+  <$$> vcat (punctuate prettyBreak (map prettyParameters' curves))+  where+    prettyParameters' :: Curve -> Doc+    prettyParameters' (Curve Types{..} Parameters{..})+      =    pretty (toLower curve) <+> ":: Curve"+      <$$> pretty (toLower curve) <+> "= Curve"+      <$$> indent 2+        (    "{ types = Types"+        <$$> indent 2+          (    "{ curve   =" <+> prettyText curve+          <$$> ", field   =" <+> prettyField field+          <$$> ", field'  =" <+> prettyField field'+          <$$> ", imports = "+          <>   maybe "Nothing" ((<>) "Just " . prettyText) imports+          <$$> "}"+          )+        <$$> ", parameters = Parameters"+        <$$> indent 2+          (    "{ a =" <+> prettyElement a+          <$$> ", b =" <+> prettyElement b+          <$$> ", h =" <+> prettyInteger h+          <$$> ", q =" <+> prettyInteger q+          <$$> ", r =" <+> prettyInteger r+          <$$> ", x =" <+> prettyElement x+          <$$> ", y =" <+> prettyElement y+          <$$> "}"+          )+        <$$> "}"+        )++prettyGenerate :: [Curve] -> Doc+prettyGenerate curves+  =    prettyImports+  <>   prettyBreak+  <$$> prettyCurves curves+  <>   prettyBreak+  <$$> prettyParameters curves+  <>   prettyBreak

+ generate/Generate/Montgomery/Parameters.hs view

@@ -0,0 +1,139 @@+module Generate.Montgomery.Parameters+  ( curves+  ) where++import Protolude++import Generate.Montgomery.Types++-------------------------------------------------------------------------------+-- Curves+-------------------------------------------------------------------------------++curves :: [Curve]+curves =+  [ curve448+  , curve25519+  , curve383187+  , m221+  , m383+  , m511+  ]++-------------------------------------------------------------------------------+-- Parameters+-------------------------------------------------------------------------------++curve448 :: Curve+curve448 = Curve+  { types = Types+    { curve   = "Curve448"+    , field   = PrimeField "Fq" 0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffeffffffffffffffffffffffffffffffffffffffffffffffffffffffff+    , field'  = PrimeField "Fr" 0x3fffffffffffffffffffffffffffffffffffffffffffffffffffffff7cca23e9c44edb49aed63690216cc2728dc58f552378c292ab5844f3+    , imports = Nothing+    }+  , parameters = Parameters+    { a = PF 0x262a6+    , b = PF 0x1+    , h = 0x4+    , q = 0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffeffffffffffffffffffffffffffffffffffffffffffffffffffffffff+    , r = 0x3fffffffffffffffffffffffffffffffffffffffffffffffffffffff7cca23e9c44edb49aed63690216cc2728dc58f552378c292ab5844f3+    , x = PF 0x5+    , y = PF 0x7d235d1295f5b1f66c98ab6e58326fcecbae5d34f55545d060f75dc28df3f6edb8027e2346430d211312c4b150677af76fd7223d457b5b1a+    }+  }++curve25519 :: Curve+curve25519 = Curve+  { types = Types+    { curve   = "Curve25519"+    , field   = PrimeField "Fq" 0x7fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffed+    , field'  = PrimeField "Fr" 0x1000000000000000000000000000000014def9dea2f79cd65812631a5cf5d3ed+    , imports = Nothing+    }+  , parameters = Parameters+    { a = PF 0x76d06+    , b = PF 0x1+    , h = 0x8+    , q = 0x7fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffed+    , r = 0x1000000000000000000000000000000014def9dea2f79cd65812631a5cf5d3ed+    , x = PF 0x9+    , y = PF 0x20ae19a1b8a086b4e01edd2c7748d14c923d4d7e6d7c61b229e9c5a27eced3d9+    }+  }++curve383187 :: Curve+curve383187 = Curve+  { types = Types+    { curve   = "Curve383187"+    , field   = PrimeField "Fq" 0x7fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff45+    , field'  = PrimeField "Fr" 0x1000000000000000000000000000000000000000000000000e85a85287a1488acd41ae84b2b7030446f72088b00a0e21+    , imports = Nothing+    }+  , parameters = Parameters+    { a = PF 0x38251+    , b = PF 0x1+    , h = 0x8+    , q = 0x7fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff45+    , r = 0x1000000000000000000000000000000000000000000000000e85a85287a1488acd41ae84b2b7030446f72088b00a0e21+    , x = PF 0x5+    , y = PF 0x1eebe07dc1871896732b12d5504a32370471965c7a11f2c89865f855ab3cbd7c224e3620c31af3370788457dd5ce46df+    }+  }++m221 :: Curve+m221 = Curve+  { types = Types+    { curve   = "M221"+    , field   = PrimeField "Fq" 0x1ffffffffffffffffffffffffffffffffffffffffffffffffffffffd+    , field'  = PrimeField "Fr" 0x40000000000000000000000000015a08ed730e8a2f77f005042605b+    , imports = Nothing+    }+  , parameters = Parameters+    { a = PF 0x1c93a+    , b = PF 0x1+    , h = 0x8+    , q = 0x1ffffffffffffffffffffffffffffffffffffffffffffffffffffffd+    , r = 0x40000000000000000000000000015a08ed730e8a2f77f005042605b+    , x = PF 0x4+    , y = PF 0xf7acdd2a4939571d1cef14eca37c228e61dbff10707dc6c08c5056d+    }+  }++m383 :: Curve+m383 = Curve+  { types = Types+    { curve   = "M383"+    , field   = PrimeField "Fq" 0x7fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff45+    , field'  = PrimeField "Fr" 0x10000000000000000000000000000000000000000000000006c79673ac36ba6e7a32576f7b1b249e46bbc225be9071d7+    , imports = Nothing+    }+  , parameters = Parameters+    { a = PF 0x1f82fe+    , b = PF 0x1+    , h = 0x8+    , q = 0x7fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff45+    , r = 0x10000000000000000000000000000000000000000000000006c79673ac36ba6e7a32576f7b1b249e46bbc225be9071d7+    , x = PF 0xc+    , y = PF 0x1ec7ed04aaf834af310e304b2da0f328e7c165f0e8988abd3992861290f617aa1f1b2e7d0b6e332e969991b62555e77e+    }+  }++m511 :: Curve+m511 = Curve+  { types = Types+    { curve   = "M511"+    , field   = PrimeField "Fq" 0x7fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff45+    , field'  = PrimeField "Fr" 0x100000000000000000000000000000000000000000000000000000000000000017b5feff30c7f5677ab2aeebd13779a2ac125042a6aa10bfa54c15bab76baf1b+    , imports = Nothing+    }+  , parameters = Parameters+    { a = PF 0x81806+    , b = PF 0x1+    , h = 0x8+    , q = 0x7fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff45+    , r = 0x100000000000000000000000000000000000000000000000000000000000000017b5feff30c7f5677ab2aeebd13779a2ac125042a6aa10bfa54c15bab76baf1b+    , x = PF 0x5+    , y = PF 0x2fbdc0ad8530803d28fdbad354bb488d32399ac1cf8f6e01ee3f96389b90c809422b9429e8a43dbf49308ac4455940abe9f1dbca542093a895e30a64af056fa5+    }+  }

+ generate/Generate/Montgomery/Types.hs view

@@ -0,0 +1,27 @@+module Generate.Montgomery.Types+  ( module Generate.Montgomery.Types+  , module Generate.Types+  ) where++import Protolude++import Generate.Types++-------------------------------------------------------------------------------+-- Types+-------------------------------------------------------------------------------++data Curve = Curve+  { types      :: Types+  , parameters :: Parameters+  }++data Parameters = Parameters+  { a :: Element+  , b :: Element+  , h :: Integer+  , q :: Integer+  , r :: Integer+  , x :: Element+  , y :: Element+  }

+ generate/Generate/Pretty.hs view

@@ -0,0 +1,40 @@+module Generate.Pretty+  ( module Generate.Pretty+  ) where++import Protolude++import Numeric (showHex)+import Text.PrettyPrint.Leijen.Text++-------------------------------------------------------------------------------+-- Pretty+-------------------------------------------------------------------------------++prettyBreak :: Doc+prettyBreak+  = linebreak++prettyDocumentation :: Doc -> Doc+prettyDocumentation+  = enclose "-- | " dot++prettyInline :: Doc -> Doc+prettyInline+  = braces . enclose "-# INLINABLE " " #-"++prettyInteger :: Integer -> Doc+prettyInteger+  = (<>) "0x" . pretty . flip showHex ""++prettyLine :: Doc+prettyLine+  = pretty (replicate 79 '-')++prettySection :: Doc -> Doc+prettySection+  = enclose (prettyLine <$$> "-- ") (prettyBreak <> prettyLine <> prettyBreak)++prettyText :: Text -> Doc+prettyText+  = dquotes . pretty

+ generate/Generate/Types.hs view

@@ -0,0 +1,24 @@+module Generate.Types+  ( module Generate.Types+  ) where++import Protolude++-------------------------------------------------------------------------------+-- Types+-------------------------------------------------------------------------------++data Element = BF Integer+             | EF [Element]+             | PF Integer++data Field = BinaryField Text Integer+           | ExtensionField Text Text Text Text (Maybe Field)+           | PrimeField Text Integer++data Types = Types+  { curve   :: Text+  , field   :: Field+  , field'  :: Field+  , imports :: Maybe Text+  }

+ generate/Generate/Weierstrass/Curve.hs view

@@ -0,0 +1,159 @@+module Generate.Weierstrass.Curve+  ( prettyCurve+  ) where++import Protolude++import Text.PrettyPrint.Leijen.Text++import Generate.Curve+import Generate.Pretty+import Generate.Weierstrass.Types++-------------------------------------------------------------------------------+-- Curve+-------------------------------------------------------------------------------++prettyImports :: Types -> Doc+prettyImports Types{..}+  =    "module Curve.Weierstrass." <> pretty curve+  <$$> indent 2+    (    "( module Curve.Weierstrass"+    <$$> ", module Curve.Weierstrass." <> pretty curve+    <$$> ") where"+    )+  <>   prettyBreak+  <$$> prettyImport field+  <>   prettyBreak+  <$$> "import Curve.Weierstrass"+  <$$> maybe mempty pretty imports++prettyTypes :: Types -> Doc+prettyTypes Types{..}+  =    prettySection "Types"+  <$$> prettyDocumentation curve'+  <$$> "data" <+> pretty curve+  <>   prettyBreak+  <$$> prettyDocumentation ("Field of points of" <+> curve')+  <$$> prettyType field+  <>   prettyBreak+  <$$> prettyDocumentation ("Field of coefficients of" <+> curve')+  <$$> prettyType field'+  <>   prettyBreak+  <$$> prettyDocumentation (curve' <+> "is a Weierstrass curve")+  <$$> "instance Curve 'Weierstrass c" <+> pretty curve <+> prettyField field+  <+>  "Fr => WCurve c" <+> pretty curve <+> prettyField field <+> "Fr where"+  <$$> indent 2+    (    "a_ = const _a"+    <$$> prettyInline "a_"+    <$$> "b_ = const _b"+    <$$> prettyInline "b_"+    <$$> "h_ = const _h"+    <$$> prettyInline "h_"+    <$$> "q_ = const _q"+    <$$> prettyInline "q_"+    <$$> "r_ = const _r"+    <$$> prettyInline "r_"+    <$$> "x_ = const _x"+    <$$> prettyInline "x_"+    <$$> "y_ = const _y"+    <$$> prettyInline "y_"+    )+  <>   prettyBreak+  <$$> prettyDocumentation ("Affine" <+> curve' <+> "point")+  <$$> "type PA = WAPoint" <+> pretty curve <+> prettyField field <+> "Fr"+  <>   prettyBreak+  <$$> prettyDocumentation ("Affine" <+> curve' <+> "is a Weierstrass affine curve")+  <$$> "instance WACurve" <+> pretty curve <+> prettyField field <+> "Fr where"+  <$$> indent 2+    (    "gA_ = gA"+    <$$> prettyInline "gA_"+    )+  <>   prettyBreak+  <$$> prettyDocumentation ("Jacobian" <+> pretty curve <+> "point")+  <$$> "type PJ = WJPoint" <+> pretty curve <+> prettyField field <+> "Fr"+  <>   prettyBreak+  <$$> prettyDocumentation ("Jacobian" <+> curve' <+> "is a Weierstrass Jacobian curve")+  <$$> "instance WJCurve" <+> pretty curve <+> prettyField field <+> "Fr where"+  <$$> indent 2+    (    "gJ_ = gJ"+    <$$> prettyInline "gJ_"+    )+  <>   prettyBreak+  <$$> prettyDocumentation ("Projective" <+> pretty curve <+> "point")+  <$$> "type PP = WPPoint" <+> pretty curve <+> prettyField field <+> "Fr"+  <>   prettyBreak+  <$$> prettyDocumentation ("Projective" <+> curve' <+> "is a Weierstrass projective curve")+  <$$> "instance WPCurve" <+> pretty curve <+> prettyField field <+> "Fr where"+  <$$> indent 2+    (    "gP_ = gP"+    <$$> prettyInline "gP_"+    )+  where+    curve' :: Doc+    curve' = pretty curve <+> "curve"++prettyParameters :: Types -> Parameters -> Doc+prettyParameters Types{..} Parameters{..}+  =    prettySection "Parameters"+  <$$> prettyDocumentation ("Coefficient @A@ of" <+> curve')+  <$$> "_a ::" <+> prettyField field+  <$$> "_a =" <+> prettyElement a+  <$$> prettyInline "_a"+  <>   prettyBreak+  <$$> prettyDocumentation ("Coefficient @B@ of" <+> curve')+  <$$> "_b ::" <+> prettyField field+  <$$> "_b =" <+> prettyElement b+  <$$> prettyInline "_b"+  <>   prettyBreak+  <$$> prettyDocumentation ("Cofactor of" <+> curve')+  <$$> "_h :: Integer"+  <$$> "_h =" <+> prettyInteger h+  <$$> prettyInline "_h"+  <>   prettyBreak+  <$$> prettyDocumentation ("Characteristic of" <+> curve')+  <$$> "_q :: Integer"+  <$$> "_q =" <+> prettyInteger q+  <$$> prettyInline "_q"+  <>   prettyBreak+  <$$> prettyDocumentation ("Order of" <+> curve')+  <$$> "_r :: Integer"+  <$$> "_r =" <+> prettyInteger r+  <$$> prettyInline "_r"+  <>   prettyBreak+  <$$> prettyDocumentation ("Coordinate @X@ of" <+> curve')+  <$$> "_x ::" <+> prettyField field+  <$$> "_x =" <+> prettyElement x+  <$$> prettyInline "_x"+  <>   prettyBreak+  <$$> prettyDocumentation ("Coordinate @Y@ of" <+> curve')+  <$$> "_y ::" <+> prettyField field+  <$$> "_y =" <+> prettyElement y+  <$$> prettyInline "_y"+  <>   prettyBreak+  <$$> prettyDocumentation ("Generator of affine" <+> curve')+  <$$> "gA :: PA"+  <$$> "gA = A _x _y"+  <$$> prettyInline "gA"+  <>   prettyBreak+  <$$> prettyDocumentation ("Generator of Jacobian" <+> curve')+  <$$> "gJ :: PJ"+  <$$> "gJ = J _x _y 1"+  <$$> prettyInline "gJ"+  <>   prettyBreak+  <$$> prettyDocumentation ("Generator of projective" <+> curve')+  <$$> "gP :: PP"+  <$$> "gP = P _x _y 1"+  <$$> prettyInline "gP"+  where+    curve' :: Doc+    curve' = pretty curve <+> "curve"++prettyCurve :: Curve -> Doc+prettyCurve (Curve types parameters)+  =    prettyImports types+  <>   prettyBreak+  <$$> prettyTypes types+  <>   prettyBreak+  <$$> prettyParameters types parameters+  <>   prettyBreak

+ generate/Generate/Weierstrass/Generate.hs view

@@ -0,0 +1,84 @@+module Generate.Weierstrass.Generate+  ( prettyGenerate+  ) where++import Protolude++import Data.Text (toLower)+import Text.PrettyPrint.Leijen.Text++import Generate.Generate+import Generate.Pretty+import Generate.Weierstrass.Types++-------------------------------------------------------------------------------+-- Generate+-------------------------------------------------------------------------------++prettyImports :: Doc+prettyImports+  =    "module Generate.Weierstrass.Parameters"+  <$$> indent 2+    (    "( curves"+    <$$> ") where"+    )+  <>   prettyBreak+  <$$> "import Protolude"+  <>   prettyBreak+  <$$> "import Generate.Weierstrass.Types"++prettyCurves :: [Curve] -> Doc+prettyCurves curves+  =    prettySection "Curves"+  <$$> "curves :: [Curve]"+  <$$> "curves ="+  <$$> indent 2+    (    "[ "+    <>   hcat (punctuate "\n, " (map prettyCurves' curves))+    <$$> "]"+    )+  where+    prettyCurves' :: Curve -> Doc+    prettyCurves' = pretty . toLower . curve . types++prettyParameters :: [Curve] -> Doc+prettyParameters curves+  =    prettySection "Parameters"+  <$$> vcat (punctuate prettyBreak (map prettyParameters' curves))+  where+    prettyParameters' :: Curve -> Doc+    prettyParameters' (Curve Types{..} Parameters{..})+      =    pretty (toLower curve) <+> ":: Curve"+      <$$> pretty (toLower curve) <+> "= Curve"+      <$$> indent 2+        (    "{ types = Types"+        <$$> indent 2+          (    "{ curve   =" <+> prettyText curve+          <$$> ", field   =" <+> prettyField field+          <$$> ", field'  =" <+> prettyField field'+          <$$> ", imports = "+          <>   maybe "Nothing" ((<>) "Just " . prettyText) imports+          <$$> "}"+          )+        <$$> ", parameters = Parameters"+        <$$> indent 2+          (    "{ a =" <+> prettyElement a+          <$$> ", b =" <+> prettyElement b+          <$$> ", h =" <+> prettyInteger h+          <$$> ", q =" <+> prettyInteger q+          <$$> ", r =" <+> prettyInteger r+          <$$> ", x =" <+> prettyElement x+          <$$> ", y =" <+> prettyElement y+          <$$> "}"+          )+        <$$> "}"+        )++prettyGenerate :: [Curve] -> Doc+prettyGenerate curves+  =    prettyImports+  <>   prettyBreak+  <$$> prettyCurves curves+  <>   prettyBreak+  <$$> prettyParameters curves+  <>   prettyBreak

+ generate/Generate/Weierstrass/Parameters.hs view

@@ -0,0 +1,1035 @@+module Generate.Weierstrass.Parameters+  ( curves+  ) where++import Protolude++import Generate.Weierstrass.Types++-------------------------------------------------------------------------------+-- Curves+-------------------------------------------------------------------------------++curves :: [Curve]+curves =+  [ anomalous+  , anssifrp256v1+  , bls12381+  , bls12381t+  , bls48581+  , bls48581t+  , bn224+  , bn254+  , bn254t+  , bn254a+  , bn254at+  , bn254b+  , bn254bt+  , bn256+  , bn384+  , bn462+  , bn462t+  , bn512+  , brainpoolp160r1+  , brainpoolp160t1+  , brainpoolp192r1+  , brainpoolp192t1+  , brainpoolp224r1+  , brainpoolp224t1+  , brainpoolp256r1+  , brainpoolp256t1+  , brainpoolp320r1+  , brainpoolp320t1+  , brainpoolp384r1+  , brainpoolp384t1+  , brainpoolp512r1+  , brainpoolp512t1+  , secp112r1+  , secp112r2+  , secp128r1+  , secp128r2+  , secp160k1+  , secp160r1+  , secp160r2+  , secp192k1+  , secp192r1+  , secp224k1+  , secp224r1+  , secp256k1+  , secp256r1+  , secp384r1+  , secp521r1+  ]++-------------------------------------------------------------------------------+-- Parameters+-------------------------------------------------------------------------------++anomalous :: Curve+anomalous = Curve+  { types = Types+    { curve   = "Anomalous"+    , field   = PrimeField "Fq" 0xb0000000000000000000000953000000000000000000001f9d7+    , field'  = PrimeField "Fr" 0xb0000000000000000000000953000000000000000000001f9d7+    , imports = Nothing+    }+  , parameters = Parameters+    { a = PF 0x98d0fac687d6343eb1a1f595283eb1a1f58d0fac687d635f5e4+    , b = PF 0x4a1f58d0fac687d6343eb1a5e2d6343eb1a1f58d0fac688ab3f+    , h = 0x1+    , q = 0xb0000000000000000000000953000000000000000000001f9d7+    , r = 0xb0000000000000000000000953000000000000000000001f9d7+    , x = PF 0x101efb35fd1963c4871a2d17edaafa7e249807f58f8705126c6+    , y = PF 0x22389a3954375834304ba1d509a97de6c07148ea7f5951b20e7+    }+  }++anssifrp256v1 :: Curve+anssifrp256v1 = Curve+  { types = Types+    { curve   = "ANSSIFRP256V1"+    , field   = PrimeField "Fq" 0xf1fd178c0b3ad58f10126de8ce42435b3961adbcabc8ca6de8fcf353d86e9c03+    , field'  = PrimeField "Fr" 0xf1fd178c0b3ad58f10126de8ce42435b53dc67e140d2bf941ffdd459c6d655e1+    , imports = Nothing+    }+  , parameters = Parameters+    { a = PF 0xf1fd178c0b3ad58f10126de8ce42435b3961adbcabc8ca6de8fcf353d86e9c00+    , b = PF 0xee353fca5428a9300d4aba754a44c00fdfec0c9ae4b1a1803075ed967b7bb73f+    , h = 0x1+    , q = 0xf1fd178c0b3ad58f10126de8ce42435b3961adbcabc8ca6de8fcf353d86e9c03+    , r = 0xf1fd178c0b3ad58f10126de8ce42435b53dc67e140d2bf941ffdd459c6d655e1+    , x = PF 0xb6b3d4c356c139eb31183d4749d423958c27d2dcaf98b70164c97a2dd98f5cff+    , y = PF 0x6142e0f7c8b204911f9271f0f3ecef8c2701c307e8e4c9e183115a1554062cfb+    }+  }++bls12381 :: Curve+bls12381 = Curve+  { types = Types+    { curve   = "BLS12381"+    , field   = PrimeField "Fq" 0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabfffeb153ffffb9feffffffffaaab+    , field'  = PrimeField "Fr" 0x73eda753299d7d483339d80809a1d80553bda402fffe5bfeffffffff00000001+    , imports = Nothing+    }+  , parameters = Parameters+    { a = PF 0x0+    , b = PF 0x4+    , h = 0x396c8c005555e1568c00aaab0000aaab+    , q = 0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabfffeb153ffffb9feffffffffaaab+    , r = 0x73eda753299d7d483339d80809a1d80553bda402fffe5bfeffffffff00000001+    , x = PF 0x17f1d3a73197d7942695638c4fa9ac0fc3688c4f9774b905a14e3a3f171bac586c55e83ff97a1aeffb3af00adb22c6bb+    , y = PF 0x8b3f481e3aaa0f1a09e30ed741d8ae4fcf5e095d5d00af600db18cb2c04b3edd03cc744a2888ae40caa232946c5e7e1+    }+  }++bls12381t :: Curve+bls12381t = Curve+  { types = Types+    { curve   = "BLS12381T"+    , field   = ExtensionField "Fq2" "Fq" "PolynomialU" "X2 + 1" Nothing+    , field'  = PrimeField "Fr" 0x73eda753299d7d483339d80809a1d80553bda402fffe5bfeffffffff00000001+    , imports = Just "import Curve.Weierstrass.BLS12381 (Fq)"+    }+  , parameters = Parameters+    { a = EF [+             ]+    , b = EF [ PF 0x4+             , PF 0x4+             ]+    , h = 0x5d543a95414e7f1091d50792876a202cd91de4547085abaa68a205b2e5a7ddfa628f1cb4d9e82ef21537e293a6691ae1616ec6e786f0c70cf1c38e31c7238e5+    , q = 0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabfffeb153ffffb9feffffffffaaab+    , r = 0x73eda753299d7d483339d80809a1d80553bda402fffe5bfeffffffff00000001+    , x = EF [ PF 0x24aa2b2f08f0a91260805272dc51051c6e47ad4fa403b02b4510b647ae3d1770bac0326a805bbefd48056c8c121bdb8+             , PF 0x13e02b6052719f607dacd3a088274f65596bd0d09920b61ab5da61bbdc7f5049334cf11213945d57e5ac7d055d042b7e+             ]+    , y = EF [ PF 0xce5d527727d6e118cc9cdc6da2e351aadfd9baa8cbdd3a76d429a695160d12c923ac9cc3baca289e193548608b82801+             , PF 0x606c4a02ea734cc32acd2b02bc28b99cb3e287e85a763af267492ab572e99ab3f370d275cec1da1aaa9075ff05f79be+             ]+    }+  }++bls48581 :: Curve+bls48581 = Curve+  { types = Types+    { curve   = "BLS48581"+    , field   = PrimeField "Fq" 0x1280f73ff3476f313824e31d47012a0056e84f8d122131bb3be6c0f1f3975444a48ae43af6e082acd9cd30394f4736daf68367a5513170ee0a578fdf721a4a48ac3edc154e6565912b+    , field'  = PrimeField "Fr" 0x2386f8a925e2885e233a9ccc1615c0d6c635387a3f0b3cbe003fad6bc972c2e6e741969d34c4c92016a85c7cd0562303c4ccbe599467c24da118a5fe6fcd671c01+    , imports = Nothing+    }+  , parameters = Parameters+    { a = PF 0x0+    , b = PF 0x1+    , h = 0x85555841aaaec4ac+    , q = 0x1280f73ff3476f313824e31d47012a0056e84f8d122131bb3be6c0f1f3975444a48ae43af6e082acd9cd30394f4736daf68367a5513170ee0a578fdf721a4a48ac3edc154e6565912b+    , r = 0x2386f8a925e2885e233a9ccc1615c0d6c635387a3f0b3cbe003fad6bc972c2e6e741969d34c4c92016a85c7cd0562303c4ccbe599467c24da118a5fe6fcd671c01+    , x = PF 0x2af59b7ac340f2baf2b73df1e93f860de3f257e0e86868cf61abdbaedffb9f7544550546a9df6f9645847665d859236ebdbc57db368b11786cb74da5d3a1e6d8c3bce8732315af640+    , y = PF 0xcefda44f6531f91f86b3a2d1fb398a488a553c9efeb8a52e991279dd41b720ef7bb7beffb98aee53e80f678584c3ef22f487f77c2876d1b2e35f37aef7b926b576dbb5de3e2587a70+    }+  }++bls48581t :: Curve+bls48581t = Curve+  { types = Types+    { curve   = "BLS48581T"+    , field   = ExtensionField "Fq8" "Fq4" "PolynomialW" "X2 + Y X" (Just+                ( ExtensionField "Fq4" "Fq2" "PolynomialV" "X2 + 1 + Y X" (Just+                  ( ExtensionField "Fq2" "Fq" "PolynomialU" "X2 + 1" Nothing+                  ))+                ))+    , field'  = PrimeField "Fr" 0x2386f8a925e2885e233a9ccc1615c0d6c635387a3f0b3cbe003fad6bc972c2e6e741969d34c4c92016a85c7cd0562303c4ccbe599467c24da118a5fe6fcd671c01+    , imports = Just "import Curve.Weierstrass.BLS48581 (Fq)"+    }+  , parameters = Parameters+    { a = EF [+             ]+    , b = EF [ EF [+                  ]+             , EF [ EF [+                       ]+                  , EF [ PF 0x9407b9ff9a3b7989c12718ea38095002b7427c6891098dd9df36078f9cbaa225245721d7b7041566ce6981ca7a39b6d7b41b3d2a898b877052bc7efb90d2524561f6e0aa732b2c895+                       , PF 0x9407b9ff9a3b7989c12718ea38095002b7427c6891098dd9df36078f9cbaa225245721d7b7041566ce6981ca7a39b6d7b41b3d2a898b877052bc7efb90d2524561f6e0aa732b2c896+                       ]+                  ]+             ]+    , h = 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    , q = 0x1280f73ff3476f313824e31d47012a0056e84f8d122131bb3be6c0f1f3975444a48ae43af6e082acd9cd30394f4736daf68367a5513170ee0a578fdf721a4a48ac3edc154e6565912b+    , r = 0x2386f8a925e2885e233a9ccc1615c0d6c635387a3f0b3cbe003fad6bc972c2e6e741969d34c4c92016a85c7cd0562303c4ccbe599467c24da118a5fe6fcd671c01+    , x = EF [ EF [ EF [ PF 0x5d615d9a7871e4a38237fa45a2775debabbefc70344dbccb7de64db3a2ef156c46ff79baad1a8c42281a63ca0612f400503004d80491f510317b79766322154dec34fd0b4ace8bfab+                       , PF 0x7c4973ece2258512069b0e86abc07e8b22bb6d980e1623e9526f6da12307f4e1c3943a00abfedf16214a76affa62504f0c3c7630d979630ffd75556a01afa143f1669b36676b47c57+                       ]+                  , EF [ PF 0x1fccc70198f1334e1b2ea1853ad83bc73a8a6ca9ae237ca7a6d6957ccbab5ab6860161c1dbd19242ffae766f0d2a6d55f028cbdfbb879d5fea8ef4cded6b3f0b46488156ca55a3e6a+                       , PF 0xbe2218c25ceb6185c78d8012954d4bfe8f5985ac62f3e5821b7b92a393f8be0cc218a95f63e1c776e6ec143b1b279b9468c31c5257c200ca52310b8cb4e80bc3f09a7033cbb7feafe+                       ]+                  ]+             , EF [ EF [ PF 0x38b91c600b35913a3c598e4caa9dd63007c675d0b1642b5675ff0e7c5805386699981f9e48199d5ac10b2ef492ae589274fad55fc1889aa80c65b5f746c9d4cbb739c3a1c53f8cce5+                       , PF 0xc96c7797eb0738603f1311e4ecda088f7b8f35dcef0977a3d1a58677bb037418181df63835d28997eb57b40b9c0b15dd7595a9f177612f097fc7960910fce3370f2004d914a3c093a+                       ]+                  , EF [ PF 0xb9b7951c6061ee3f0197a498908aee660dea41b39d13852b6db908ba2c0b7a449cef11f293b13ced0fd0caa5efcf3432aad1cbe4324c22d63334b5b0e205c3354e41607e60750e057+                       , PF 0x827d5c22fb2bdec5282624c4f4aaa2b1e5d7a9defaf47b5211cf741719728a7f9f8cfca93f29cff364a7190b7e2b0d4585479bd6aebf9fc44e56af2fc9e97c3f84e19da00fbc6ae34+                       ]+                  ]+             ]+    , y = EF [ EF [ EF [ PF 0xeb53356c375b5dfa497216452f3024b918b4238059a577e6f3b39ebfc435faab0906235afa27748d90f7336d8ae5163c1599abf77eea6d659045012ab12c0ff323edd3fe4d2d7971+                       , PF 0x284dc75979e0ff144da6531815fcadc2b75a422ba325e6fba01d72964732fcbf3afb096b243b1f192c5c3d1892ab24e1dd212fa097d760e2e588b423525ffc7b111471db936cd5665+                       ]+                  , EF [ PF 0xb36a201dd008523e421efb70367669ef2c2fc5030216d5b119d3a480d370514475f7d5c99d0e90411515536ca3295e5e2f0c1d35d51a652269cbc7c46fc3b8fde68332a526a2a8474+                       , PF 0xaec25a4621edc0688223fbbd478762b1c2cded3360dcee23dd8b0e710e122d2742c89b224333fa40dced2817742770ba10d67bda503ee5e578fb3d8b8a1e5337316213da92841589d+                       ]+                  ]+             , EF [ EF [ PF 0xd209d5a223a9c46916503fa5a88325a2554dc541b43dd93b5a959805f1129857ed85c77fa238cdce8a1e2ca4e512b64f59f430135945d137b08857fdddfcf7a43f47831f982e50137+                       , PF 0x7d0d03745736b7a513d339d5ad537b90421ad66eb16722b589d82e2055ab7504fa83420e8c270841f6824f47c180d139e3aafc198caa72b679da59ed8226cf3a594eedc58cf90bee4+                       ]+                  , EF [ PF 0x896767811be65ea25c2d05dfdd17af8a006f364fc0841b064155f14e4c819a6df98f425ae3a2864f22c1fab8c74b2618b5bb40fa639f53dccc9e884017d9aa62b3d41faeafeb23986+                       , PF 0x35e2524ff89029d393a5c07e84f981b5e068f1406be8e50c87549b6ef8eca9a9533a3f8e69c31e97e1ad0333ec719205417300d8c4ab33f748e5ac66e84069c55d667ffcb732718b6+                       ]+                  ]+             ]+    }+  }++bn224 :: Curve+bn224 = Curve+  { types = Types+    { curve   = "BN224"+    , field   = PrimeField "Fq" 0xfffffffffff107288ec29e602c4520db42180823bb907d1287127833+    , field'  = PrimeField "Fr" 0xfffffffffff107288ec29e602c4420db4218082b36c2accff76c58ed+    , imports = Nothing+    }+  , parameters = Parameters+    { a = PF 0x0+    , b = PF 0x3+    , h = 0x1+    , q = 0xfffffffffff107288ec29e602c4520db42180823bb907d1287127833+    , r = 0xfffffffffff107288ec29e602c4420db4218082b36c2accff76c58ed+    , x = PF 0x1+    , y = PF 0x2+    }+  }++bn254 :: Curve+bn254 = Curve+  { types = Types+    { curve   = "BN254"+    , field   = PrimeField "Fq" 0x30644e72e131a029b85045b68181585d97816a916871ca8d3c208c16d87cfd47+    , field'  = PrimeField "Fr" 0x30644e72e131a029b85045b68181585d2833e84879b9709143e1f593f0000001+    , imports = Nothing+    }+  , parameters = Parameters+    { a = PF 0x0+    , b = PF 0x3+    , h = 0x1+    , q = 0x30644e72e131a029b85045b68181585d97816a916871ca8d3c208c16d87cfd47+    , r = 0x30644e72e131a029b85045b68181585d2833e84879b9709143e1f593f0000001+    , x = PF 0x1+    , y = PF 0x2+    }+  }++bn254t :: Curve+bn254t = Curve+  { types = Types+    { curve   = "BN254T"+    , field   = ExtensionField "Fq2" "Fq" "PolynomialU" "X2 + 1" Nothing+    , field'  = PrimeField "Fr" 0x30644e72e131a029b85045b68181585d2833e84879b9709143e1f593f0000001+    , imports = Just "import Curve.Weierstrass.BN254 (Fq)"+    }+  , parameters = Parameters+    { a = EF [+             ]+    , b = EF [ PF 0x2b149d40ceb8aaae81be18991be06ac3b5b4c5e559dbefa33267e6dc24a138e5+             , PF 0x9713b03af0fed4cd2cafadeed8fdf4a74fa084e52d1852e4a2bd0685c315d2+             ]+    , h = 0x30644e72e131a029b85045b68181585e06ceecda572a2489345f2299c0f9fa8d+    , q = 0x30644e72e131a029b85045b68181585d97816a916871ca8d3c208c16d87cfd47+    , r = 0x30644e72e131a029b85045b68181585d2833e84879b9709143e1f593f0000001+    , x = EF [ PF 0x1800deef121f1e76426a00665e5c4479674322d4f75edadd46debd5cd992f6ed+             , PF 0x198e9393920d483a7260bfb731fb5d25f1aa493335a9e71297e485b7aef312c2+             ]+    , y = EF [ PF 0x12c85ea5db8c6deb4aab71808dcb408fe3d1e7690c43d37b4ce6cc0166fa7daa+             , PF 0x90689d0585ff075ec9e99ad690c3395bc4b313370b38ef355acdadcd122975b+             ]+    }+  }++bn254a :: Curve+bn254a = Curve+  { types = Types+    { curve   = "BN254A"+    , field   = PrimeField "Fq" 0x2370fb049d410fbe4e761a9886e502417d023f40180000017e80600000000001+    , field'  = PrimeField "Fr" 0x2370fb049d410fbe4e761a9886e502411dc1af70120000017e80600000000001+    , imports = Nothing+    }+  , parameters = Parameters+    { a = PF 0x0+    , b = PF 0x5+    , h = 0x1+    , q = 0x2370fb049d410fbe4e761a9886e502417d023f40180000017e80600000000001+    , r = 0x2370fb049d410fbe4e761a9886e502411dc1af70120000017e80600000000001+    , x = PF 0x1+    , y = PF 0xd45589b158faaf6ab0e4ad38d998e9982e7ff63964ee1460342a592677cccb0+    }+  }++bn254at :: Curve+bn254at = Curve+  { types = Types+    { curve   = "BN254AT"+    , field   = ExtensionField "Fq2" "Fq" "PolynomialU" "X2 + 5" Nothing+    , field'  = PrimeField "Fr" 0x2370fb049d410fbe4e761a9886e502411dc1af70120000017e80600000000001+    , imports = Just "import Curve.Weierstrass.BN254A (Fq)"+    }+  , parameters = Parameters+    { a = EF [+             ]+    , b = EF [ PF 0x0+             , PF 0x2370fb049d410fbe4e761a9886e502417d023f40180000017e80600000000000+             ]+    , h = 0x2370fb049d410fbe4e761a9886e50241dc42cf101e0000017e80600000000001+    , q = 0x2370fb049d410fbe4e761a9886e502417d023f40180000017e80600000000001+    , r = 0x2370fb049d410fbe4e761a9886e502411dc1af70120000017e80600000000001+    , x = EF [ PF 0x19b0bea4afe4c330da93cc3533da38a9f430b471c6f8a536e81962ed967909b5+             , PF 0xa1cf585585a61c6e9880b1f2a5c539f7d906fff238fa6341e1de1a2e45c3f72+             ]+    , y = EF [ PF 0x17abd366ebbd65333e49c711a80a0cf6d24adf1b9b3990eedcc91731384d2627+             , PF 0xee97d6de9902a27d00e952232a78700863bc9aa9be960c32f5bf9fd0a32d345+             ]+    }+  }++bn254b :: Curve+bn254b = Curve+  { types = Types+    { curve   = "BN254B"+    , field   = PrimeField "Fq" 0x2523648240000001ba344d80000000086121000000000013a700000000000013+    , field'  = PrimeField "Fr" 0x2523648240000001ba344d8000000007ff9f800000000010a10000000000000d+    , imports = Nothing+    }+  , parameters = Parameters+    { a = PF 0x0+    , b = PF 0x2+    , h = 0x1+    , q = 0x2523648240000001ba344d80000000086121000000000013a700000000000013+    , r = 0x2523648240000001ba344d8000000007ff9f800000000010a10000000000000d+    , x = PF 0x2523648240000001ba344d80000000086121000000000013a700000000000012+    , y = PF 0x1+    }+  }++bn254bt :: Curve+bn254bt = Curve+  { types = Types+    { curve   = "BN254BT"+    , field   = ExtensionField "Fq2" "Fq" "PolynomialU" "X2 + 1" Nothing+    , field'  = PrimeField "Fr" 0x2523648240000001ba344d8000000007ff9f800000000010a10000000000000d+    , imports = Just "import Curve.Weierstrass.BN254B (Fq)"+    }+  , parameters = Parameters+    { a = EF [+             ]+    , b = EF [ PF 0x1+             , PF 0x2523648240000001ba344d80000000086121000000000013a700000000000012+             ]+    , h = 0x2523648240000001ba344d8000000008c2a2800000000016ad00000000000019+    , q = 0x2523648240000001ba344d80000000086121000000000013a700000000000013+    , r = 0x2523648240000001ba344d8000000007ff9f800000000010a10000000000000d+    , x = EF [ PF 0x61a10bb519eb62feb8d8c7e8c61edb6a4648bbb4898bf0d91ee4224c803fb2b+             , PF 0x516aaf9ba737833310aa78c5982aa5b1f4d746bae3784b70d8c34c1e7d54cf3+             ]+    , y = EF [ PF 0x21897a06baf93439a90e096698c822329bd0ae6bdbe09bd19f0e07891cd2b9a+             , PF 0xebb2b0e7c8b15268f6d4456f5f38d37b09006ffd739c9578a2d1aec6b3ace9b+             ]+    }+  }++bn256 :: Curve+bn256 = Curve+  { types = Types+    { curve   = "BN256"+    , field   = PrimeField "Fq" 0xfffffffffffcf0cd46e5f25eee71a49f0cdc65fb12980a82d3292ddbaed33013+    , field'  = PrimeField "Fr" 0xfffffffffffcf0cd46e5f25eee71a49e0cdc65fb1299921af62d536cd10b500d+    , imports = Nothing+    }+  , parameters = Parameters+    { a = PF 0x0+    , b = PF 0x3+    , h = 0x1+    , q = 0xfffffffffffcf0cd46e5f25eee71a49f0cdc65fb12980a82d3292ddbaed33013+    , r = 0xfffffffffffcf0cd46e5f25eee71a49e0cdc65fb1299921af62d536cd10b500d+    , x = PF 0x1+    , y = PF 0x2+    }+  }++bn384 :: Curve+bn384 = Curve+  { types = Types+    { curve   = "BN384"+    , field   = PrimeField "Fq" 0xfffffffffffffffffff2a96823d5920d2a127e3f6fbca024c8fbe29531892c79534f9d306328261550a7cabd7cccd10b+    , field'  = PrimeField "Fr" 0xfffffffffffffffffff2a96823d5920d2a127e3f6fbca023c8fbe29531892c795356487d8ac63e4f4db17384341a5775+    , imports = Nothing+    }+  , parameters = Parameters+    { a = PF 0x0+    , b = PF 0x3+    , h = 0x1+    , q = 0xfffffffffffffffffff2a96823d5920d2a127e3f6fbca024c8fbe29531892c79534f9d306328261550a7cabd7cccd10b+    , r = 0xfffffffffffffffffff2a96823d5920d2a127e3f6fbca023c8fbe29531892c795356487d8ac63e4f4db17384341a5775+    , x = PF 0x1+    , y = PF 0x2+    }+  }++bn462 :: Curve+bn462 = Curve+  { types = Types+    { curve   = "BN462"+    , field   = PrimeField "Fq" 0x240480360120023ffffffffff6ff0cf6b7d9bfca0000000000d812908f41c8020ffffffffff6ff66fc6ff687f640000000002401b00840138013+    , field'  = PrimeField "Fr" 0x240480360120023ffffffffff6ff0cf6b7d9bfca0000000000d812908ee1c201f7fffffffff6ff66fc7bf717f7c0000000002401b007e010800d+    , imports = Nothing+    }+  , parameters = Parameters+    { a = PF 0x0+    , b = PF 0x5+    , h = 0x1+    , q = 0x240480360120023ffffffffff6ff0cf6b7d9bfca0000000000d812908f41c8020ffffffffff6ff66fc6ff687f640000000002401b00840138013+    , r = 0x240480360120023ffffffffff6ff0cf6b7d9bfca0000000000d812908ee1c201f7fffffffff6ff66fc7bf717f7c0000000002401b007e010800d+    , x = PF 0x21a6d67ef250191fadba34a0a30160b9ac9264b6f95f63b3edbec3cf4b2e689db1bbb4e69a416a0b1e79239c0372e5cd70113c98d91f36b6980d+    , y = PF 0x118ea0460f7f7abb82b33676a7432a490eeda842cccfa7d788c659650426e6af77df11b8ae40eb80f475432c66600622ecaa8a5734d36fb03de+    }+  }++bn462t :: Curve+bn462t = Curve+  { types = Types+    { curve   = "BN462T"+    , field   = ExtensionField "Fq2" "Fq" "PolynomialU" "X2 + 1" Nothing+    , field'  = PrimeField "Fr" 0x240480360120023ffffffffff6ff0cf6b7d9bfca0000000000d812908ee1c201f7fffffffff6ff66fc7bf717f7c0000000002401b007e010800d+    , imports = Just "import Curve.Weierstrass.BN462 (Fq)"+    }+  , parameters = Parameters+    { a = EF [+             ]+    , b = EF [ PF 0x2+             , PF 0x240480360120023ffffffffff6ff0cf6b7d9bfca0000000000d812908f41c8020ffffffffff6ff66fc6ff687f640000000002401b00840138012+             ]+    , h = 0x240480360120023ffffffffff6ff0cf6b7d9bfca0000000000d812908fa1ce0227fffffffff6ff66fc63f5f7f4c0000000002401b008a0168019+    , q = 0x240480360120023ffffffffff6ff0cf6b7d9bfca0000000000d812908f41c8020ffffffffff6ff66fc6ff687f640000000002401b00840138013+    , r = 0x240480360120023ffffffffff6ff0cf6b7d9bfca0000000000d812908ee1c201f7fffffffff6ff66fc7bf717f7c0000000002401b007e010800d+    , x = EF [ PF 0x257ccc85b58dda0dfb38e3a8cbdc5482e0337e7c1cd96ed61c913820408208f9ad2699bad92e0032ae1f0aa6a8b48807695468e3d934ae1e4df+             , PF 0x1d2e4343e8599102af8edca849566ba3c98e2a354730cbed9176884058b18134dd86bae555b783718f50af8b59bf7e850e9b73108ba6aa8cd283+             ]+    , y = EF [ PF 0xa0650439da22c1979517427a20809eca035634706e23c3fa7a6bb42fe810f1399a1f41c9ddae32e03695a140e7b11d7c3376e5b68df0db7154e+             , PF 0x73ef0cbd438cbe0172c8ae37306324d44d5e6b0c69ac57b393f1ab370fd725cc647692444a04ef87387aa68d53743493b9eba14cc552ca2a93a+             ]+    }+  }++bn512 :: Curve+bn512 = Curve+  { types = Types+    { curve   = "BN512"+    , field   = PrimeField "Fq" 0xfffffffffffffffffffffffffff9ec7f01c60ba1d8cb5307c0bbe3c111b0ef455146cf1eacbe98b8e48c65deab236fe1916a55ce5f4c6467b4eb280922adef33+    , field'  = PrimeField "Fr" 0xfffffffffffffffffffffffffff9ec7f01c60ba1d8cb5307c0bbe3c111b0ef445146cf1eacbe98b8e48c65deab2679a34a10313e04f9a2b406a64a5f519a09ed+    , imports = Nothing+    }+  , parameters = Parameters+    { a = PF 0x0+    , b = PF 0x3+    , h = 0x1+    , q = 0xfffffffffffffffffffffffffff9ec7f01c60ba1d8cb5307c0bbe3c111b0ef455146cf1eacbe98b8e48c65deab236fe1916a55ce5f4c6467b4eb280922adef33+    , r = 0xfffffffffffffffffffffffffff9ec7f01c60ba1d8cb5307c0bbe3c111b0ef445146cf1eacbe98b8e48c65deab2679a34a10313e04f9a2b406a64a5f519a09ed+    , x = PF 0x1+    , y = PF 0x2+    }+  }++brainpoolp160r1 :: Curve+brainpoolp160r1 = Curve+  { types = Types+    { curve   = "BrainpoolP160R1"+    , field   = PrimeField "Fq" 0xe95e4a5f737059dc60dfc7ad95b3d8139515620f+    , field'  = PrimeField "Fr" 0xe95e4a5f737059dc60df5991d45029409e60fc09+    , imports = Nothing+    }+  , parameters = Parameters+    { a = PF 0x340e7be2a280eb74e2be61bada745d97e8f7c300+    , b = PF 0x1e589a8595423412134faa2dbdec95c8d8675e58+    , h = 0x1+    , q = 0xe95e4a5f737059dc60dfc7ad95b3d8139515620f+    , r = 0xe95e4a5f737059dc60df5991d45029409e60fc09+    , x = PF 0xbed5af16ea3f6a4f62938c4631eb5af7bdbcdbc3+    , y = PF 0x1667cb477a1a8ec338f94741669c976316da6321+    }+  }++brainpoolp160t1 :: Curve+brainpoolp160t1 = Curve+  { types = Types+    { curve   = "BrainpoolP160T1"+    , field   = PrimeField "Fq" 0xe95e4a5f737059dc60dfc7ad95b3d8139515620f+    , field'  = PrimeField "Fr" 0xe95e4a5f737059dc60df5991d45029409e60fc09+    , imports = Nothing+    }+  , parameters = Parameters+    { a = PF 0xe95e4a5f737059dc60dfc7ad95b3d8139515620c+    , b = PF 0x7a556b6dae535b7b51ed2c4d7daa7a0b5c55f380+    , h = 0x1+    , q = 0xe95e4a5f737059dc60dfc7ad95b3d8139515620f+    , r = 0xe95e4a5f737059dc60df5991d45029409e60fc09+    , x = PF 0xb199b13b9b34efc1397e64baeb05acc265ff2378+    , y = PF 0xadd6718b7c7c1961f0991b842443772152c9e0ad+    }+  }++brainpoolp192r1 :: Curve+brainpoolp192r1 = Curve+  { types = Types+    { curve   = "BrainpoolP192R1"+    , field   = PrimeField "Fq" 0xc302f41d932a36cda7a3463093d18db78fce476de1a86297+    , field'  = PrimeField "Fr" 0xc302f41d932a36cda7a3462f9e9e916b5be8f1029ac4acc1+    , imports = Nothing+    }+  , parameters = Parameters+    { a = PF 0x6a91174076b1e0e19c39c031fe8685c1cae040e5c69a28ef+    , b = PF 0x469a28ef7c28cca3dc721d044f4496bcca7ef4146fbf25c9+    , h = 0x1+    , q = 0xc302f41d932a36cda7a3463093d18db78fce476de1a86297+    , r = 0xc302f41d932a36cda7a3462f9e9e916b5be8f1029ac4acc1+    , x = PF 0xc0a0647eaab6a48753b033c56cb0f0900a2f5c4853375fd6+    , y = PF 0x14b690866abd5bb88b5f4828c1490002e6773fa2fa299b8f+    }+  }++brainpoolp192t1 :: Curve+brainpoolp192t1 = Curve+  { types = Types+    { curve   = "BrainpoolP192T1"+    , field   = PrimeField "Fq" 0xc302f41d932a36cda7a3463093d18db78fce476de1a86297+    , field'  = PrimeField "Fr" 0xc302f41d932a36cda7a3462f9e9e916b5be8f1029ac4acc1+    , imports = Nothing+    }+  , parameters = Parameters+    { a = PF 0xc302f41d932a36cda7a3463093d18db78fce476de1a86294+    , b = PF 0x13d56ffaec78681e68f9deb43b35bec2fb68542e27897b79+    , h = 0x1+    , q = 0xc302f41d932a36cda7a3463093d18db78fce476de1a86297+    , r = 0xc302f41d932a36cda7a3462f9e9e916b5be8f1029ac4acc1+    , x = PF 0x3ae9e58c82f63c30282e1fe7bbf43fa72c446af6f4618129+    , y = PF 0x97e2c5667c2223a902ab5ca449d0084b7e5b3de7ccc01c9+    }+  }++brainpoolp224r1 :: Curve+brainpoolp224r1 = Curve+  { types = Types+    { curve   = "BrainpoolP224R1"+    , field   = PrimeField "Fq" 0xd7c134aa264366862a18302575d1d787b09f075797da89f57ec8c0ff+    , field'  = PrimeField "Fr" 0xd7c134aa264366862a18302575d0fb98d116bc4b6ddebca3a5a7939f+    , imports = Nothing+    }+  , parameters = Parameters+    { a = PF 0x68a5e62ca9ce6c1c299803a6c1530b514e182ad8b0042a59cad29f43+    , b = PF 0x2580f63ccfe44138870713b1a92369e33e2135d266dbb372386c400b+    , h = 0x1+    , q = 0xd7c134aa264366862a18302575d1d787b09f075797da89f57ec8c0ff+    , r = 0xd7c134aa264366862a18302575d0fb98d116bc4b6ddebca3a5a7939f+    , x = PF 0xd9029ad2c7e5cf4340823b2a87dc68c9e4ce3174c1e6efdee12c07d+    , y = PF 0x58aa56f772c0726f24c6b89e4ecdac24354b9e99caa3f6d3761402cd+    }+  }++brainpoolp224t1 :: Curve+brainpoolp224t1 = Curve+  { types = Types+    { curve   = "BrainpoolP224T1"+    , field   = PrimeField "Fq" 0xd7c134aa264366862a18302575d1d787b09f075797da89f57ec8c0ff+    , field'  = PrimeField "Fr" 0xd7c134aa264366862a18302575d0fb98d116bc4b6ddebca3a5a7939f+    , imports = Nothing+    }+  , parameters = Parameters+    { a = PF 0xd7c134aa264366862a18302575d1d787b09f075797da89f57ec8c0fc+    , b = PF 0x4b337d934104cd7bef271bf60ced1ed20da14c08b3bb64f18a60888d+    , h = 0x1+    , q = 0xd7c134aa264366862a18302575d1d787b09f075797da89f57ec8c0ff+    , r = 0xd7c134aa264366862a18302575d0fb98d116bc4b6ddebca3a5a7939f+    , x = PF 0x6ab1e344ce25ff3896424e7ffe14762ecb49f8928ac0c76029b4d580+    , y = PF 0x374e9f5143e568cd23f3f4d7c0d4b1e41c8cc0d1c6abd5f1a46db4c+    }+  }++brainpoolp256r1 :: Curve+brainpoolp256r1 = Curve+  { types = Types+    { curve   = "BrainpoolP256R1"+    , field   = PrimeField "Fq" 0xa9fb57dba1eea9bc3e660a909d838d726e3bf623d52620282013481d1f6e5377+    , field'  = PrimeField "Fr" 0xa9fb57dba1eea9bc3e660a909d838d718c397aa3b561a6f7901e0e82974856a7+    , imports = Nothing+    }+  , parameters = Parameters+    { a = PF 0x7d5a0975fc2c3057eef67530417affe7fb8055c126dc5c6ce94a4b44f330b5d9+    , b = PF 0x26dc5c6ce94a4b44f330b5d9bbd77cbf958416295cf7e1ce6bccdc18ff8c07b6+    , h = 0x1+    , q = 0xa9fb57dba1eea9bc3e660a909d838d726e3bf623d52620282013481d1f6e5377+    , r = 0xa9fb57dba1eea9bc3e660a909d838d718c397aa3b561a6f7901e0e82974856a7+    , x = PF 0x8bd2aeb9cb7e57cb2c4b482ffc81b7afb9de27e1e3bd23c23a4453bd9ace3262+    , y = PF 0x547ef835c3dac4fd97f8461a14611dc9c27745132ded8e545c1d54c72f046997+    }+  }++brainpoolp256t1 :: Curve+brainpoolp256t1 = Curve+  { types = Types+    { curve   = "BrainpoolP256T1"+    , field   = PrimeField "Fq" 0xa9fb57dba1eea9bc3e660a909d838d726e3bf623d52620282013481d1f6e5377+    , field'  = PrimeField "Fr" 0xa9fb57dba1eea9bc3e660a909d838d718c397aa3b561a6f7901e0e82974856a7+    , imports = Nothing+    }+  , parameters = Parameters+    { a = PF 0xa9fb57dba1eea9bc3e660a909d838d726e3bf623d52620282013481d1f6e5374+    , b = PF 0x662c61c430d84ea4fe66a7733d0b76b7bf93ebc4af2f49256ae58101fee92b04+    , h = 0x1+    , q = 0xa9fb57dba1eea9bc3e660a909d838d726e3bf623d52620282013481d1f6e5377+    , r = 0xa9fb57dba1eea9bc3e660a909d838d718c397aa3b561a6f7901e0e82974856a7+    , x = PF 0xa3e8eb3cc1cfe7b7732213b23a656149afa142c47aafbc2b79a191562e1305f4+    , y = PF 0x2d996c823439c56d7f7b22e14644417e69bcb6de39d027001dabe8f35b25c9be+    }+  }++brainpoolp320r1 :: Curve+brainpoolp320r1 = Curve+  { types = Types+    { curve   = "BrainpoolP320R1"+    , field   = PrimeField "Fq" 0xd35e472036bc4fb7e13c785ed201e065f98fcfa6f6f40def4f92b9ec7893ec28fcd412b1f1b32e27+    , field'  = PrimeField "Fr" 0xd35e472036bc4fb7e13c785ed201e065f98fcfa5b68f12a32d482ec7ee8658e98691555b44c59311+    , imports = Nothing+    }+  , parameters = Parameters+    { a = PF 0x3ee30b568fbab0f883ccebd46d3f3bb8a2a73513f5eb79da66190eb085ffa9f492f375a97d860eb4+    , b = PF 0x520883949dfdbc42d3ad198640688a6fe13f41349554b49acc31dccd884539816f5eb4ac8fb1f1a6+    , h = 0x1+    , q = 0xd35e472036bc4fb7e13c785ed201e065f98fcfa6f6f40def4f92b9ec7893ec28fcd412b1f1b32e27+    , r = 0xd35e472036bc4fb7e13c785ed201e065f98fcfa5b68f12a32d482ec7ee8658e98691555b44c59311+    , x = PF 0x43bd7e9afb53d8b85289bcc48ee5bfe6f20137d10a087eb6e7871e2a10a599c710af8d0d39e20611+    , y = PF 0x14fdd05545ec1cc8ab4093247f77275e0743ffed117182eaa9c77877aaac6ac7d35245d1692e8ee1+    }+  }++brainpoolp320t1 :: Curve+brainpoolp320t1 = Curve+  { types = Types+    { curve   = "BrainpoolP320T1"+    , field   = PrimeField "Fq" 0xd35e472036bc4fb7e13c785ed201e065f98fcfa6f6f40def4f92b9ec7893ec28fcd412b1f1b32e27+    , field'  = PrimeField "Fr" 0xd35e472036bc4fb7e13c785ed201e065f98fcfa5b68f12a32d482ec7ee8658e98691555b44c59311+    , imports = Nothing+    }+  , parameters = Parameters+    { a = PF 0xd35e472036bc4fb7e13c785ed201e065f98fcfa6f6f40def4f92b9ec7893ec28fcd412b1f1b32e24+    , b = PF 0xa7f561e038eb1ed560b3d147db782013064c19f27ed27c6780aaf77fb8a547ceb5b4fef422340353+    , h = 0x1+    , q = 0xd35e472036bc4fb7e13c785ed201e065f98fcfa6f6f40def4f92b9ec7893ec28fcd412b1f1b32e27+    , r = 0xd35e472036bc4fb7e13c785ed201e065f98fcfa5b68f12a32d482ec7ee8658e98691555b44c59311+    , x = PF 0x925be9fb01afc6fb4d3e7d4990010f813408ab106c4f09cb7ee07868cc136fff3357f624a21bed52+    , y = PF 0x63ba3a7a27483ebf6671dbef7abb30ebee084e58a0b077ad42a5a0989d1ee71b1b9bc0455fb0d2c3+    }+  }++brainpoolp384r1 :: Curve+brainpoolp384r1 = Curve+  { types = Types+    { curve   = "BrainpoolP384R1"+    , field   = PrimeField "Fq" 0x8cb91e82a3386d280f5d6f7e50e641df152f7109ed5456b412b1da197fb71123acd3a729901d1a71874700133107ec53+    , field'  = PrimeField "Fr" 0x8cb91e82a3386d280f5d6f7e50e641df152f7109ed5456b31f166e6cac0425a7cf3ab6af6b7fc3103b883202e9046565+    , imports = Nothing+    }+  , parameters = Parameters+    { a = PF 0x7bc382c63d8c150c3c72080ace05afa0c2bea28e4fb22787139165efba91f90f8aa5814a503ad4eb04a8c7dd22ce2826+    , b = PF 0x4a8c7dd22ce28268b39b55416f0447c2fb77de107dcd2a62e880ea53eeb62d57cb4390295dbc9943ab78696fa504c11+    , h = 0x1+    , q = 0x8cb91e82a3386d280f5d6f7e50e641df152f7109ed5456b412b1da197fb71123acd3a729901d1a71874700133107ec53+    , r = 0x8cb91e82a3386d280f5d6f7e50e641df152f7109ed5456b31f166e6cac0425a7cf3ab6af6b7fc3103b883202e9046565+    , x = PF 0x1d1c64f068cf45ffa2a63a81b7c13f6b8847a3e77ef14fe3db7fcafe0cbd10e8e826e03436d646aaef87b2e247d4af1e+    , y = PF 0x8abe1d7520f9c2a45cb1eb8e95cfd55262b70b29feec5864e19c054ff99129280e4646217791811142820341263c5315+    }+  }++brainpoolp384t1 :: Curve+brainpoolp384t1 = Curve+  { types = Types+    { curve   = "BrainpoolP384T1"+    , field   = PrimeField "Fq" 0x8cb91e82a3386d280f5d6f7e50e641df152f7109ed5456b412b1da197fb71123acd3a729901d1a71874700133107ec53+    , field'  = PrimeField "Fr" 0x8cb91e82a3386d280f5d6f7e50e641df152f7109ed5456b31f166e6cac0425a7cf3ab6af6b7fc3103b883202e9046565+    , imports = Nothing+    }+  , parameters = Parameters+    { a = PF 0x8cb91e82a3386d280f5d6f7e50e641df152f7109ed5456b412b1da197fb71123acd3a729901d1a71874700133107ec50+    , b = PF 0x7f519eada7bda81bd826dba647910f8c4b9346ed8ccdc64e4b1abd11756dce1d2074aa263b88805ced70355a33b471ee+    , h = 0x1+    , q = 0x8cb91e82a3386d280f5d6f7e50e641df152f7109ed5456b412b1da197fb71123acd3a729901d1a71874700133107ec53+    , r = 0x8cb91e82a3386d280f5d6f7e50e641df152f7109ed5456b31f166e6cac0425a7cf3ab6af6b7fc3103b883202e9046565+    , x = PF 0x18de98b02db9a306f2afcd7235f72a819b80ab12ebd653172476fecd462aabffc4ff191b946a5f54d8d0aa2f418808cc+    , y = PF 0x25ab056962d30651a114afd2755ad336747f93475b7a1fca3b88f2b6a208ccfe469408584dc2b2912675bf5b9e582928+    }+  }++brainpoolp512r1 :: Curve+brainpoolp512r1 = Curve+  { types = Types+    { curve   = "BrainpoolP512R1"+    , field   = PrimeField "Fq" 0xaadd9db8dbe9c48b3fd4e6ae33c9fc07cb308db3b3c9d20ed6639cca703308717d4d9b009bc66842aecda12ae6a380e62881ff2f2d82c68528aa6056583a48f3+    , field'  = PrimeField "Fr" 0xaadd9db8dbe9c48b3fd4e6ae33c9fc07cb308db3b3c9d20ed6639cca70330870553e5c414ca92619418661197fac10471db1d381085ddaddb58796829ca90069+    , imports = Nothing+    }+  , parameters = Parameters+    { a = PF 0x7830a3318b603b89e2327145ac234cc594cbdd8d3df91610a83441caea9863bc2ded5d5aa8253aa10a2ef1c98b9ac8b57f1117a72bf2c7b9e7c1ac4d77fc94ca+    , b = PF 0x3df91610a83441caea9863bc2ded5d5aa8253aa10a2ef1c98b9ac8b57f1117a72bf2c7b9e7c1ac4d77fc94cadc083e67984050b75ebae5dd2809bd638016f723+    , h = 0x1+    , q = 0xaadd9db8dbe9c48b3fd4e6ae33c9fc07cb308db3b3c9d20ed6639cca703308717d4d9b009bc66842aecda12ae6a380e62881ff2f2d82c68528aa6056583a48f3+    , r = 0xaadd9db8dbe9c48b3fd4e6ae33c9fc07cb308db3b3c9d20ed6639cca70330870553e5c414ca92619418661197fac10471db1d381085ddaddb58796829ca90069+    , x = PF 0x81aee4bdd82ed9645a21322e9c4c6a9385ed9f70b5d916c1b43b62eef4d0098eff3b1f78e2d0d48d50d1687b93b97d5f7c6d5047406a5e688b352209bcb9f822+    , y = PF 0x7dde385d566332ecc0eabfa9cf7822fdf209f70024a57b1aa000c55b881f8111b2dcde494a5f485e5bca4bd88a2763aed1ca2b2fa8f0540678cd1e0f3ad80892+    }+  }++brainpoolp512t1 :: Curve+brainpoolp512t1 = Curve+  { types = Types+    { curve   = "BrainpoolP512T1"+    , field   = PrimeField "Fq" 0xaadd9db8dbe9c48b3fd4e6ae33c9fc07cb308db3b3c9d20ed6639cca703308717d4d9b009bc66842aecda12ae6a380e62881ff2f2d82c68528aa6056583a48f3+    , field'  = PrimeField "Fr" 0xaadd9db8dbe9c48b3fd4e6ae33c9fc07cb308db3b3c9d20ed6639cca70330870553e5c414ca92619418661197fac10471db1d381085ddaddb58796829ca90069+    , imports = Nothing+    }+  , parameters = Parameters+    { a = PF 0xaadd9db8dbe9c48b3fd4e6ae33c9fc07cb308db3b3c9d20ed6639cca703308717d4d9b009bc66842aecda12ae6a380e62881ff2f2d82c68528aa6056583a48f0+    , b = PF 0x7cbbbcf9441cfab76e1890e46884eae321f70c0bcb4981527897504bec3e36a62bcdfa2304976540f6450085f2dae145c22553b465763689180ea2571867423e+    , h = 0x1+    , q = 0xaadd9db8dbe9c48b3fd4e6ae33c9fc07cb308db3b3c9d20ed6639cca703308717d4d9b009bc66842aecda12ae6a380e62881ff2f2d82c68528aa6056583a48f3+    , r = 0xaadd9db8dbe9c48b3fd4e6ae33c9fc07cb308db3b3c9d20ed6639cca70330870553e5c414ca92619418661197fac10471db1d381085ddaddb58796829ca90069+    , x = PF 0x640ece5c12788717b9c1ba06cbc2a6feba85842458c56dde9db1758d39c0313d82ba51735cdb3ea499aa77a7d6943a64f7a3f25fe26f06b51baa2696fa9035da+    , y = PF 0x5b534bd595f5af0fa2c892376c84ace1bb4e3019b71634c01131159cae03cee9d9932184beef216bd71df2dadf86a627306ecff96dbb8bace198b61e00f8b332+    }+  }++secp112r1 :: Curve+secp112r1 = Curve+  { types = Types+    { curve   = "SECP112R1"+    , field   = PrimeField "Fq" 0xdb7c2abf62e35e668076bead208b+    , field'  = PrimeField "Fr" 0xdb7c2abf62e35e7628dfac6561c5+    , imports = Nothing+    }+  , parameters = Parameters+    { a = PF 0xdb7c2abf62e35e668076bead2088+    , b = PF 0x659ef8ba043916eede8911702b22+    , h = 0x1+    , q = 0xdb7c2abf62e35e668076bead208b+    , r = 0xdb7c2abf62e35e7628dfac6561c5+    , x = PF 0x9487239995a5ee76b55f9c2f098+    , y = PF 0xa89ce5af8724c0a23e0e0ff77500+    }+  }++secp112r2 :: Curve+secp112r2 = Curve+  { types = Types+    { curve   = "SECP112R2"+    , field   = PrimeField "Fq" 0xdb7c2abf62e35e668076bead208b+    , field'  = PrimeField "Fr" 0x36df0aafd8b8d7597ca10520d04b+    , imports = Nothing+    }+  , parameters = Parameters+    { a = PF 0x6127c24c05f38a0aaaf65c0ef02c+    , b = PF 0x51def1815db5ed74fcc34c85d709+    , h = 0x4+    , q = 0xdb7c2abf62e35e668076bead208b+    , r = 0x36df0aafd8b8d7597ca10520d04b+    , x = PF 0x4ba30ab5e892b4e1649dd0928643+    , y = PF 0xadcd46f5882e3747def36e956e97+    }+  }++secp128r1 :: Curve+secp128r1 = Curve+  { types = Types+    { curve   = "SECP128R1"+    , field   = PrimeField "Fq" 0xfffffffdffffffffffffffffffffffff+    , field'  = PrimeField "Fr" 0xfffffffe0000000075a30d1b9038a115+    , imports = Nothing+    }+  , parameters = Parameters+    { a = PF 0xfffffffdfffffffffffffffffffffffc+    , b = PF 0xe87579c11079f43dd824993c2cee5ed3+    , h = 0x1+    , q = 0xfffffffdffffffffffffffffffffffff+    , r = 0xfffffffe0000000075a30d1b9038a115+    , x = PF 0x161ff7528b899b2d0c28607ca52c5b86+    , y = PF 0xcf5ac8395bafeb13c02da292dded7a83+    }+  }++secp128r2 :: Curve+secp128r2 = Curve+  { types = Types+    { curve   = "SECP128R2"+    , field   = PrimeField "Fq" 0xfffffffdffffffffffffffffffffffff+    , field'  = PrimeField "Fr" 0x3fffffff7fffffffbe0024720613b5a3+    , imports = Nothing+    }+  , parameters = Parameters+    { a = PF 0xd6031998d1b3bbfebf59cc9bbff9aee1+    , b = PF 0x5eeefca380d02919dc2c6558bb6d8a5d+    , h = 0x4+    , q = 0xfffffffdffffffffffffffffffffffff+    , r = 0x3fffffff7fffffffbe0024720613b5a3+    , x = PF 0x7b6aa5d85e572983e6fb32a7cdebc140+    , y = PF 0x27b6916a894d3aee7106fe805fc34b44+    }+  }++secp160k1 :: Curve+secp160k1 = Curve+  { types = Types+    { curve   = "SECP160K1"+    , field   = PrimeField "Fq" 0xfffffffffffffffffffffffffffffffeffffac73+    , field'  = PrimeField "Fr" 0x100000000000000000001b8fa16dfab9aca16b6b3+    , imports = Nothing+    }+  , parameters = Parameters+    { a = PF 0x0+    , b = PF 0x7+    , h = 0x1+    , q = 0xfffffffffffffffffffffffffffffffeffffac73+    , r = 0x100000000000000000001b8fa16dfab9aca16b6b3+    , x = PF 0x3b4c382ce37aa192a4019e763036f4f5dd4d7ebb+    , y = PF 0x938cf935318fdced6bc28286531733c3f03c4fee+    }+  }++secp160r1 :: Curve+secp160r1 = Curve+  { types = Types+    { curve   = "SECP160R1"+    , field   = PrimeField "Fq" 0xffffffffffffffffffffffffffffffff7fffffff+    , field'  = PrimeField "Fr" 0x100000000000000000001f4c8f927aed3ca752257+    , imports = Nothing+    }+  , parameters = Parameters+    { a = PF 0xffffffffffffffffffffffffffffffff7ffffffc+    , b = PF 0x1c97befc54bd7a8b65acf89f81d4d4adc565fa45+    , h = 0x1+    , q = 0xffffffffffffffffffffffffffffffff7fffffff+    , r = 0x100000000000000000001f4c8f927aed3ca752257+    , x = PF 0x4a96b5688ef573284664698968c38bb913cbfc82+    , y = PF 0x23a628553168947d59dcc912042351377ac5fb32+    }+  }++secp160r2 :: Curve+secp160r2 = Curve+  { types = Types+    { curve   = "SECP160R2"+    , field   = PrimeField "Fq" 0xfffffffffffffffffffffffffffffffeffffac73+    , field'  = PrimeField "Fr" 0x100000000000000000000351ee786a818f3a1a16b+    , imports = Nothing+    }+  , parameters = Parameters+    { a = PF 0xfffffffffffffffffffffffffffffffeffffac70+    , b = PF 0xb4e134d3fb59eb8bab57274904664d5af50388ba+    , h = 0x1+    , q = 0xfffffffffffffffffffffffffffffffeffffac73+    , r = 0x100000000000000000000351ee786a818f3a1a16b+    , x = PF 0x52dcb034293a117e1f4ff11b30f7199d3144ce6d+    , y = PF 0xfeaffef2e331f296e071fa0df9982cfea7d43f2e+    }+  }++secp192k1 :: Curve+secp192k1 = Curve+  { types = Types+    { curve   = "SECP192K1"+    , field   = PrimeField "Fq" 0xfffffffffffffffffffffffffffffffffffffffeffffee37+    , field'  = PrimeField "Fr" 0xfffffffffffffffffffffffe26f2fc170f69466a74defd8d+    , imports = Nothing+    }+  , parameters = Parameters+    { a = PF 0x0+    , b = PF 0x3+    , h = 0x1+    , q = 0xfffffffffffffffffffffffffffffffffffffffeffffee37+    , r = 0xfffffffffffffffffffffffe26f2fc170f69466a74defd8d+    , x = PF 0xdb4ff10ec057e9ae26b07d0280b7f4341da5d1b1eae06c7d+    , y = PF 0x9b2f2f6d9c5628a7844163d015be86344082aa88d95e2f9d+    }+  }++secp192r1 :: Curve+secp192r1 = Curve+  { types = Types+    { curve   = "SECP192R1"+    , field   = PrimeField "Fq" 0xfffffffffffffffffffffffffffffffeffffffffffffffff+    , field'  = PrimeField "Fr" 0xffffffffffffffffffffffff99def836146bc9b1b4d22831+    , imports = Nothing+    }+  , parameters = Parameters+    { a = PF 0xfffffffffffffffffffffffffffffffefffffffffffffffc+    , b = PF 0x64210519e59c80e70fa7e9ab72243049feb8deecc146b9b1+    , h = 0x1+    , q = 0xfffffffffffffffffffffffffffffffeffffffffffffffff+    , r = 0xffffffffffffffffffffffff99def836146bc9b1b4d22831+    , x = PF 0x188da80eb03090f67cbf20eb43a18800f4ff0afd82ff1012+    , y = PF 0x7192b95ffc8da78631011ed6b24cdd573f977a11e794811+    }+  }++secp224k1 :: Curve+secp224k1 = Curve+  { types = Types+    { curve   = "SECP224K1"+    , field   = PrimeField "Fq" 0xfffffffffffffffffffffffffffffffffffffffffffffffeffffe56d+    , field'  = PrimeField "Fr" 0x10000000000000000000000000001dce8d2ec6184caf0a971769fb1f7+    , imports = Nothing+    }+  , parameters = Parameters+    { a = PF 0x0+    , b = PF 0x5+    , h = 0x1+    , q = 0xfffffffffffffffffffffffffffffffffffffffffffffffeffffe56d+    , r = 0x10000000000000000000000000001dce8d2ec6184caf0a971769fb1f7+    , x = PF 0xa1455b334df099df30fc28a169a467e9e47075a90f7e650eb6b7a45c+    , y = PF 0x7e089fed7fba344282cafbd6f7e319f7c0b0bd59e2ca4bdb556d61a5+    }+  }++secp224r1 :: Curve+secp224r1 = Curve+  { types = Types+    { curve   = "SECP224R1"+    , field   = PrimeField "Fq" 0xffffffffffffffffffffffffffffffff000000000000000000000001+    , field'  = PrimeField "Fr" 0xffffffffffffffffffffffffffff16a2e0b8f03e13dd29455c5c2a3d+    , imports = Nothing+    }+  , parameters = Parameters+    { a = PF 0xfffffffffffffffffffffffffffffffefffffffffffffffffffffffe+    , b = PF 0xb4050a850c04b3abf54132565044b0b7d7bfd8ba270b39432355ffb4+    , h = 0x1+    , q = 0xffffffffffffffffffffffffffffffff000000000000000000000001+    , r = 0xffffffffffffffffffffffffffff16a2e0b8f03e13dd29455c5c2a3d+    , x = PF 0xb70e0cbd6bb4bf7f321390b94a03c1d356c21122343280d6115c1d21+    , y = PF 0xbd376388b5f723fb4c22dfe6cd4375a05a07476444d5819985007e34+    }+  }++secp256k1 :: Curve+secp256k1 = Curve+  { types = Types+    { curve   = "SECP256K1"+    , field   = PrimeField "Fq" 0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f+    , field'  = PrimeField "Fr" 0xfffffffffffffffffffffffffffffffebaaedce6af48a03bbfd25e8cd0364141+    , imports = Nothing+    }+  , parameters = Parameters+    { a = PF 0x0+    , b = PF 0x7+    , h = 0x1+    , q = 0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f+    , r = 0xfffffffffffffffffffffffffffffffebaaedce6af48a03bbfd25e8cd0364141+    , x = PF 0x79be667ef9dcbbac55a06295ce870b07029bfcdb2dce28d959f2815b16f81798+    , y = PF 0x483ada7726a3c4655da4fbfc0e1108a8fd17b448a68554199c47d08ffb10d4b8+    }+  }++secp256r1 :: Curve+secp256r1 = Curve+  { types = Types+    { curve   = "SECP256R1"+    , field   = PrimeField "Fq" 0xffffffff00000001000000000000000000000000ffffffffffffffffffffffff+    , field'  = PrimeField "Fr" 0xffffffff00000000ffffffffffffffffbce6faada7179e84f3b9cac2fc632551+    , imports = Nothing+    }+  , parameters = Parameters+    { a = PF 0xffffffff00000001000000000000000000000000fffffffffffffffffffffffc+    , b = PF 0x5ac635d8aa3a93e7b3ebbd55769886bc651d06b0cc53b0f63bce3c3e27d2604b+    , h = 0x1+    , q = 0xffffffff00000001000000000000000000000000ffffffffffffffffffffffff+    , r = 0xffffffff00000000ffffffffffffffffbce6faada7179e84f3b9cac2fc632551+    , x = PF 0x6b17d1f2e12c4247f8bce6e563a440f277037d812deb33a0f4a13945d898c296+    , y = PF 0x4fe342e2fe1a7f9b8ee7eb4a7c0f9e162bce33576b315ececbb6406837bf51f5+    }+  }++secp384r1 :: Curve+secp384r1 = Curve+  { types = Types+    { curve   = "SECP384R1"+    , field   = PrimeField "Fq" 0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffeffffffff0000000000000000ffffffff+    , field'  = PrimeField "Fr" 0xffffffffffffffffffffffffffffffffffffffffffffffffc7634d81f4372ddf581a0db248b0a77aecec196accc52973+    , imports = Nothing+    }+  , parameters = Parameters+    { a = PF 0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffeffffffff0000000000000000fffffffc+    , b = PF 0xb3312fa7e23ee7e4988e056be3f82d19181d9c6efe8141120314088f5013875ac656398d8a2ed19d2a85c8edd3ec2aef+    , h = 0x1+    , q = 0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffeffffffff0000000000000000ffffffff+    , r = 0xffffffffffffffffffffffffffffffffffffffffffffffffc7634d81f4372ddf581a0db248b0a77aecec196accc52973+    , x = PF 0xaa87ca22be8b05378eb1c71ef320ad746e1d3b628ba79b9859f741e082542a385502f25dbf55296c3a545e3872760ab7+    , y = PF 0x3617de4a96262c6f5d9e98bf9292dc29f8f41dbd289a147ce9da3113b5f0b8c00a60b1ce1d7e819d7a431d7c90ea0e5f+    }+  }++secp521r1 :: Curve+secp521r1 = Curve+  { types = Types+    { curve   = "SECP521R1"+    , field   = PrimeField "Fq" 0x1ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff+    , field'  = PrimeField "Fr" 0x1fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffa51868783bf2f966b7fcc0148f709a5d03bb5c9b8899c47aebb6fb71e91386409+    , imports = Nothing+    }+  , parameters = Parameters+    { a = PF 0x1fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffc+    , b = PF 0x51953eb9618e1c9a1f929a21a0b68540eea2da725b99b315f3b8b489918ef109e156193951ec7e937b1652c0bd3bb1bf073573df883d2c34f1ef451fd46b503f00+    , h = 0x1+    , q = 0x1ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff+    , r = 0x1fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffa51868783bf2f966b7fcc0148f709a5d03bb5c9b8899c47aebb6fb71e91386409+    , x = PF 0xc6858e06b70404e9cd9e3ecb662395b4429c648139053fb521f828af606b4d3dbaa14b5e77efe75928fe1dc127a2ffa8de3348b3c1856a429bf97e7e31c2e5bd66+    , y = PF 0x11839296a789a3bc0045c8a5fb42c7d1bd998f54449579b446817afbd17273e662c97ee72995ef42640c550b9013fad0761353c7086a272c24088be94769fd16650+    }+  }

+ generate/Generate/Weierstrass/Types.hs view

@@ -0,0 +1,27 @@+module Generate.Weierstrass.Types+  ( module Generate.Weierstrass.Types+  , module Generate.Types+  ) where++import Protolude++import Generate.Types++-------------------------------------------------------------------------------+-- Types+-------------------------------------------------------------------------------++data Curve = Curve+  { types      :: Types+  , parameters :: Parameters+  }++data Parameters = Parameters+  { a :: Element+  , b :: Element+  , h :: Integer+  , q :: Integer+  , r :: Integer+  , x :: Element+  , y :: Element+  }

+ generate/Main.hs view

@@ -0,0 +1,104 @@+module Main where++import Protolude++import Data.Text (unpack)++import qualified Generate.Binary.Curve as Binary+import qualified Generate.Binary.Generate as Binary+import qualified Generate.Binary.Parameters as Binary+import qualified Generate.Binary.Types as Binary+import qualified Generate.Edwards.Curve as Edwards+import qualified Generate.Edwards.Generate as Edwards+import qualified Generate.Edwards.Parameters as Edwards+import qualified Generate.Edwards.Types as Edwards+import qualified Generate.Montgomery.Curve as Montgomery+import qualified Generate.Montgomery.Generate as Montgomery+import qualified Generate.Montgomery.Parameters as Montgomery+import qualified Generate.Montgomery.Types as Montgomery+import qualified Generate.Weierstrass.Curve as Weierstrass+import qualified Generate.Weierstrass.Generate as Weierstrass+import qualified Generate.Weierstrass.Parameters as Weierstrass+import qualified Generate.Weierstrass.Types as Weierstrass++-------------------------------------------------------------------------------+-- Curve generator+-------------------------------------------------------------------------------++generateCurve :: IO ()+generateCurve = do+  mapM_ (uncurry writeFile) generateBinaryCurve+  mapM_ (uncurry writeFile) generateEdwardsCurve+  mapM_ (uncurry writeFile) generateMontgomeryCurve+  mapM_ (uncurry writeFile) generateWeierstrassCurve++generateBinaryCurve :: [(FilePath, Text)]+generateBinaryCurve = map generateBinaryCurve' Binary.curves+  where+    generateBinaryCurve' :: Binary.Curve -> (FilePath, Text)+    generateBinaryCurve' = generateCurve'+      "Binary" Binary.curve Binary.types Binary.prettyCurve++generateEdwardsCurve :: [(FilePath, Text)]+generateEdwardsCurve = map generateEdwardsCurve' Edwards.curves+  where+    generateEdwardsCurve' :: Edwards.Curve -> (FilePath, Text)+    generateEdwardsCurve' = generateCurve'+      "Edwards" Edwards.curve Edwards.types Edwards.prettyCurve++generateMontgomeryCurve :: [(FilePath, Text)]+generateMontgomeryCurve = map generateMontgomeryCurve' Montgomery.curves+  where+    generateMontgomeryCurve' :: Montgomery.Curve -> (FilePath, Text)+    generateMontgomeryCurve' = generateCurve'+      "Montgomery" Montgomery.curve Montgomery.types Montgomery.prettyCurve++generateWeierstrassCurve :: [(FilePath, Text)]+generateWeierstrassCurve = map generateWeierstrassCurve' Weierstrass.curves+  where+    generateWeierstrassCurve' :: Weierstrass.Curve -> (FilePath, Text)+    generateWeierstrassCurve' = generateCurve'+      "Weierstrass" Weierstrass.curve Weierstrass.types Weierstrass.prettyCurve++generateCurve' :: Show doc => Text -> (types -> Text)+  -> (curve -> types) -> (curve -> doc) -> curve -> (FilePath, Text)+generateCurve' form curve types pretty = (,)+  <$> unpack . (<> ".hs") . (<>) ("../src/Curve/" <> form <> "/") . curve . types+  <*> show . pretty++-------------------------------------------------------------------------------+-- Generate generator+-------------------------------------------------------------------------------++generateGenerate :: IO ()+generateGenerate = do+  writeFile "Generate/Binary/Parameters.hs" generateBinaryGenerate+  writeFile "Generate/Edwards/Parameters.hs" generateEdwardsGenerate+  writeFile "Generate/Montgomery/Parameters.hs" generateMontgomeryGenerate+  writeFile "Generate/Weierstrass/Parameters.hs" generateWeierstrassGenerate++generateBinaryGenerate :: Text+generateBinaryGenerate = generateGenerate'+  Binary.prettyGenerate Binary.curves++generateEdwardsGenerate :: Text+generateEdwardsGenerate = generateGenerate'+  Edwards.prettyGenerate Edwards.curves++generateMontgomeryGenerate :: Text+generateMontgomeryGenerate = generateGenerate'+  Montgomery.prettyGenerate Montgomery.curves++generateWeierstrassGenerate :: Text+generateWeierstrassGenerate = generateGenerate'+  Weierstrass.prettyGenerate Weierstrass.curves++generateGenerate' :: Show doc => (curve -> doc) -> curve -> Text+generateGenerate' = (.) show++-------------------------------------------------------------------------------+-- Main generator+-------------------------------------------------------------------------------++main :: IO ()+main = generateGenerate >> generateCurve

src/Curve.hs view

@@ -1,65 +1,103 @@ module Curve-  ( Curve(..)+  ( module Curve+  , module Group   ) where  import Protolude -import Control.Monad.Random (MonadRandom)+import Control.Monad.Random (Random(..)) import GaloisField (GaloisField)+import PrimeField (PrimeField, toInt)+import Test.Tasty.QuickCheck (Arbitrary(..), suchThatMap) +import Group (Group(..))+ ------------------------------------------------------------------------------- -- Types ------------------------------------------------------------------------------- --- | Elliptic curves over Galois fields.-class GaloisField k => Curve r c k where-  {-# MINIMAL id, inv, add, def, disc, point, rnd #-}+-- | Elliptic curves.+class (GaloisField q, GaloisField r, Group (Point f c e q r))+  => Curve (f :: Form) (c :: Coordinates) e q r where+  {-# MINIMAL char, cof, disc, fromA, point, pointX, toA, yX #-} +  -- Parameters++  -- | Curve characteristic.+  char :: Point f c e q r -> Integer++  -- | Curve cofactor.+  cof :: Point f c e q r -> Integer++  -- | Curve discriminant.+  disc :: Point f c e q r -> q++  -- Points+   -- | Curve point.-  data family Point r c k :: *+  data family Point f c e q r :: * -  -- | Point identity.-  id :: Point r c k+  -- | Curve point multiplication.+  mul :: r ~ PrimeField p => Point f c e q r -> r -> Point f c e q r+  mul = (. toInt) . mul'+  {-# INLINABLE mul #-} -  -- | Point inversion.-  inv :: Point r c k -> Point r c k+  -- | Get point from X and Y coordinates.+  point :: q -> q -> Maybe (Point f c e q r) -  -- | Point addition.-  add :: Point r c k -> Point r c k -> Point r c k+  -- | Get point from X coordinate.+  pointX :: q -> Maybe (Point f c e q r) -  -- | Point doubling.-  double :: Point r c k -> Point r c k-  double = join add-  {-# INLINE double #-}+  -- | Get Y coordinate from X coordinate.+  yX :: Point f c e q r -> q -> Maybe q -  -- | Point multiplication.-  mul :: Integral n => n -> Point r c k -> Point r c k-  mul n p-    | n < 0     = inv (mul (-n) p)-    | n == 0    = id-    | n == 1    = p-    | even n    = p'-    | otherwise = add p p'-    where-      p' = mul (div n 2) (double p)-  {-# INLINE mul #-}+  -- Coordinates -  -- | Point is well-defined.-  def :: Point r c k -> Bool+  -- | Transform from affine coordinates.+  fromA :: Point f 'Affine e q r -> Point f c e q r -  -- | Get curve discriminant.-  disc :: Point r c k -> k+  -- | Transform to affine coordinates.+  toA :: Point f c e q r -> Point f 'Affine e q r -  -- | Get point from x coordinate.-  point :: k -> Maybe (Point r c k)+-- | Curve forms.+data Form = Binary+          | Edwards+          | Montgomery+          | Weierstrass -  -- | Get random point.-  rnd :: MonadRandom m => m (Point r c k)+-- | Curve coordinates.+data Coordinates = Affine+                 | Jacobian+                 | Projective --- Elliptic curves are semigroups.-instance Curve r c k => Semigroup (Point r c k) where-  (<>) = add+-------------------------------------------------------------------------------+-- Instances+------------------------------------------------------------------------------- --- Elliptic curves are monoids.-instance Curve r c k => Monoid (Point r c k) where+-- Elliptic curve points are monoids.+instance Curve f c e q r => Monoid (Point f c e q r) where+   mempty = id+  {-# INLINABLE mempty #-}++-- Elliptic curve points are semigroups.+instance Curve f c e q r => Semigroup (Point f c e q r) where++  p <> q = if p == q then dbl p else add p q+  {-# INLINABLE (<>) #-}++-- Elliptic curve points are arbitrary.+instance Curve f c e q r => Arbitrary (Point f c e q r) where++  arbitrary = suchThatMap arbitrary pointX+  {-# INLINABLE arbitrary #-}++-- Elliptic curve points are random.+instance Curve f c e q r => Random (Point f c e q r) where++  random g = let (x, g') = random g in case pointX x of+    Just p -> (p, g')+    _      -> random g'+  {-# INLINABLE random #-}++  randomR = panic "not implemented."

src/Curve/Binary.hs view

@@ -1,112 +1,250 @@+{-# OPTIONS -fno-warn-orphans #-}+ module Curve.Binary-  ( BCurve(..)-  , BPoint-  , Point(..)+  ( module Curve+  , module Curve.Binary+  , module Group   ) where  import Protolude -import Control.Monad.Random (Random(..), getRandom) import GaloisField (GaloisField(..))-import Test.Tasty.QuickCheck (Arbitrary(..)) import Text.PrettyPrint.Leijen.Text (Pretty(..)) -import Curve (Curve(..))+import Curve (Coordinates(..), Curve(..), Form(..))+import Group (Group(..))  ---------------------------------------------------------------------------------- Types+-- Binary form ------------------------------------------------------------------------------- --- | Binary curve representation.-data B+-- | Binary points.+type BPoint = Point 'Binary --- | Binary curve points.-type BPoint = Point B+-- | Binary curves.+class (GaloisField q, GaloisField r, Curve 'Binary c e q r) => BCurve c e q r where+  {-# MINIMAL a_, b_, h_, p_, r_, x_, y_ #-}+  a_ :: BPoint c e q r -> q       -- ^ Coefficient @A@.+  b_ :: BPoint c e q r -> q       -- ^ Coefficient @B@.+  h_ :: BPoint c e q r -> Integer -- ^ Curve cofactor.+  p_ :: BPoint c e q r -> Integer -- ^ Curve polynomial.+  r_ :: BPoint c e q r -> Integer -- ^ Curve order.+  x_ :: BPoint c e q r -> q       -- ^ Coordinate @X@.+  y_ :: BPoint c e q r -> q       -- ^ Coordinate @Y@. --- | Binary curves @y^2 + xy = x^3 + Ax^2 + B@.-class Curve B c k => BCurve c k where-  a_ :: c -> k     -- ^ Coefficient @A@.-  b_ :: c -> k     -- ^ Coefficient @B@.-  g_ :: BPoint c k -- ^ Curve generator.+-------------------------------------------------------------------------------+-- Affine coordinates+------------------------------------------------------------------------------- --- Binary points are arbitrary.-instance (GaloisField k, BCurve c k) => Arbitrary (Point B c k) where-  arbitrary = return g_-  -- arbitrary = flip mul g_ <$> (arbitrary :: Gen Int)-  -- arbitrary = suchThatMap arbitrary point+-- | Binary affine points.+type BAPoint = BPoint 'Affine --- Binary points are pretty.-instance (GaloisField k, BCurve c k) => Pretty (Point B c k) where-  pretty (A x y) = pretty (x, y)-  pretty O       = "O"+-- | Binary affine curves @y^2 + xy = x^3 + Ax^2 + B@.+class BCurve 'Affine e q r => BACurve e q r where+  {-# MINIMAL gA_ #-}+  gA_ :: BAPoint e q r -- ^ Curve generator. --- Binary points are random.-instance (GaloisField k, BCurve c k) => Random (Point B c k) where-  random g = case point x of-    Just p -> (p, g')-    _      -> random g'-    where-      (x, g') = random g-  {-# INLINE random #-}-  randomR  = panic "not implemented."+-- Binary affine curves are elliptic curves.+instance BACurve e q r => Curve 'Binary 'Affine e q r where ----------------------------------------------------------------------------------- Operations--------------------------------------------------------------------------------+  data instance Point 'Binary 'Affine e q r = A q q -- ^ Affine point.+                                            | O     -- ^ Infinite point.+    deriving (Eq, Generic, NFData, Read, Show) --- Binary curves are elliptic curves.-instance (GaloisField k, BCurve c k) => Curve B c k where+  char = const 2+  {-# INLINABLE char #-} -  data instance Point B c k = A k k -- ^ Affine point.-                            | O     -- ^ Infinite point.-    deriving (Eq, Generic, NFData, Read, Show)+  cof = h_+  {-# INLINABLE cof #-} -  id = O-  {-# INLINE id #-}+  disc _ = b_ (witness :: BAPoint e q r)+  {-# INLINABLE disc #-} -  inv O       = O-  inv (A x y) = A x (x + y)-  {-# INLINE inv #-}+  fromA = identity+  {-# INLINABLE fromA #-} -  add p O          = p-  add O q          = q-  add p@(A x1 y1) (A x2 y2)-    | xx /= 0      = A x3 y3-    | yy + x2 /= 0 = double p-    | otherwise    = O+  point x y = let p = A x y in if def p then Just p else Nothing+  {-# INLINABLE point #-}++  pointX x = A x <$> yX (witness :: BAPoint e q r) x+  {-# INLINABLE pointX #-}++  toA = identity+  {-# INLINABLE toA #-}++  yX _ x = quad 1 x ((x + a) * x * x + b)     where+      a = a_ (witness :: BAPoint e q r)+      b = b_ (witness :: BAPoint e q r)+  {-# INLINABLE yX #-}++-- Binary affine points are groups.+instance BACurve e q r => Group (BAPoint e q r) where++  add p  O      = p+  add O q       = q+  add (A x1 y1) (A x2 y2)+    | xx == 0   = O+    | otherwise = A x3 y3+    where+      a  = a_ (witness :: BAPoint e q r)       xx = x1 + x2       yy = y1 + y2       l  = yy / xx-      x3 = l * (l + 1) + xx + a_ (witness :: c)+      x3 = l * (l + 1) + xx + a       y3 = l * (x1 + x3) + x3 + y1-  {-# INLINE add #-}+  {-# INLINABLE add #-} -  double O       = O-  double (A x y) = A x' y'+  dbl O         = O+  dbl (A x y)+    | x == 0    = O+    | otherwise = A x' y'     where+      a  = a_ (witness :: BAPoint e q r)       l  = x + y / x       l' = l + 1-      x' = l * l' + a_ (witness :: c)+      x' = l * l' + a       y' = x * x + l' * x'-  {-# INLINE double #-}+  {-# INLINABLE dbl #-}    def O       = True   def (A x y) = ((x + a) * x + y) * x + b + y * y == 0     where-      a = a_ (witness :: c)-      b = b_ (witness :: c)-  {-# INLINE def #-}+      a = a_ (witness :: BAPoint e q r)+      b = b_ (witness :: BAPoint e q r)+  {-# INLINABLE def #-} -  disc _ = b_ (witness :: c)-  {-# INLINE disc #-}+  gen = gA_+  {-# INLINABLE gen #-} -  point 0 = A 0 <$> sr (b_ (witness :: c))-  point x = A x <$> quad 1 x ((x + a) * x * x + b)+  id = O+  {-# INLINABLE id #-}++  inv O       = O+  inv (A x y) = A x (x + y)+  {-# INLINABLE inv #-}++  order = r_+  {-# INLINABLE order #-}++-- Binary affine points are pretty.+instance BACurve e q r => Pretty (BAPoint e q r) where++  pretty (A x y) = pretty (x, y)+  pretty O       = "O"++-------------------------------------------------------------------------------+-- Projective coordinates+-------------------------------------------------------------------------------++-- | Binary projective points.+type BPPoint = BPoint 'Projective++-- | Binary projective curves @y^2z + xyz = x^3 + Ax^2z + Bz@.+class BCurve 'Projective e q r => BPCurve e q r where+  {-# MINIMAL gP_ #-}+  gP_ :: BPPoint e q r -- ^ Curve generator.++-- Binary projective curves are elliptic curves.+instance BPCurve e q r => Curve 'Binary 'Projective e q r where++  data instance Point 'Binary 'Projective e q r = P q q q -- ^ Projective point.+    deriving (Generic, NFData, Read, Show)++  char = const 2+  {-# INLINABLE char #-}++  cof = h_+  {-# INLINABLE cof #-}++  disc _ = b_ (witness :: BPPoint e q r)+  {-# INLINABLE disc #-}++  fromA (A x y) = P x y 1+  fromA _       = P 0 1 0+  {-# INLINABLE fromA #-}++  point x y = let p = P x y 1 in if def p then Just p else Nothing+  {-# INLINABLE point #-}++  pointX x = flip (P x) 1 <$> yX (witness :: BPPoint e q r) x+  {-# INLINABLE pointX #-}++  toA (P _ _ 0) = O+  toA (P x y z) = A (x / z) (y / z)+  {-# INLINABLE toA #-}++  yX _ x = quad 1 x ((x + a) * x * x + b)     where-      a = a_ (witness :: c)-      b = b_ (witness :: c)-  {-# INLINE point #-}+      a = a_ (witness :: BPPoint e q r)+      b = b_ (witness :: BPPoint e q r)+  {-# INLINABLE yX #-} -  rnd = getRandom-  {-# INLINE rnd #-}+-- Binary projective points are groups.+instance BPCurve e q r => Group (BPPoint e q r) where++  -- Addition formula add-2008-bl+  add  p           (P  _  _  0) = p+  add (P  _  _  0)  q           = q+  add (P x1 y1 z1) (P x2 y2 z2) = P x3 y3 z3+    where+      a'   = a_ (witness :: BPPoint e q r)+      y1z2 = y1 * z2+      x1z2 = x1 * z2+      a    = y1z2 + z1 * y2+      b    = x1z2 + z1 * x2+      ab   = a + b+      c    = b * b+      d    = z1 * z2+      e    = b * c+      f    = (a * ab + a' * c) * d + e+      x3   = b * f+      y3   = c * (a * x1z2 + b * y1z2) + ab * f+      z3   = e * d+  {-# INLINABLE add #-}++  -- Doubling formula dbl-2008-bl+  dbl (P  _  _  0) = P  0  1  0+  dbl (P x1 y1 z1) = P x3 y3 z3+    where+      a' = a_ (witness :: BPPoint e q r)+      a  = x1 * x1+      b  = a + y1 * z1+      c  = x1 * z1+      bc = b + c+      d  = c * c+      e  = b * bc + a' * d+      x3 = c * e+      y3 = bc * e + a * a * c+      z3 = c * d+  {-# INLINABLE dbl #-}++  def (P x y z) = ((x + a * z) * x + yz) * x + y * yz + b * z * z * z == 0+    where+      a  = a_ (witness :: BPPoint e q r)+      b  = b_ (witness :: BPPoint e q r)+      yz = y * z+  {-# INLINABLE def #-}++  gen = gP_+  {-# INLINABLE gen #-}++  id = P 0 1 0+  {-# INLINABLE id #-}++  inv (P x y z) = P x (x + y) z+  {-# INLINABLE inv #-}++  order = r_+  {-# INLINABLE order #-}++-- Binary projective points are equatable.+instance BPCurve e q r => Eq (BPPoint e q r) where++  P x1 y1 z1 == P x2 y2 z2 = z1 == 0 && z2 == 0+    || x1 * z2 == x2 * z1 && y1 * z2 == y2 * z1++-- Binary projective points are pretty.+instance BPCurve e q r => Pretty (BPPoint e q r) where++  pretty (P x y z) = pretty (x, y, z)

src/Curve/Binary/SECT113R1.hs view

@@ -1,74 +1,106 @@ module Curve.Binary.SECT113R1-  ( F2m-  , P-  , _a-  , _b-  , _f-  , _g-  , _h-  , _n+  ( module Curve.Binary+  , module Curve.Binary.SECT113R1   ) where  import Protolude -import BinaryField (BinaryField)+import BinaryField+import PrimeField -import Curve.Binary (BCurve(..), BPoint, Point(..))+import Curve.Binary  ------------------------------------------------------------------------------- -- Types ------------------------------------------------------------------------------- --- | SECT113R1 curve+-- | SECT113R1 curve. data SECT113R1 --- | Field of SECT113R1 curve+-- | Field of points of SECT113R1 curve. type F2m = BinaryField 0x20000000000000000000000000201 --- | SECT113R1 curve is a binary curve-instance BCurve SECT113R1 F2m where+-- | Field of coefficients of SECT113R1 curve.+type Fr = PrimeField 0x100000000000000d9ccec8a39e56f++-- | SECT113R1 curve is a binary curve.+instance Curve 'Binary c SECT113R1 F2m Fr => BCurve c SECT113R1 F2m Fr where   a_ = const _a-  {-# INLINE a_ #-}+  {-# INLINABLE a_ #-}   b_ = const _b-  {-# INLINE b_ #-}-  g_ = _g-  {-# INLINE g_ #-}+  {-# INLINABLE b_ #-}+  h_ = const _h+  {-# INLINABLE h_ #-}+  p_ = const _p+  {-# INLINABLE p_ #-}+  r_ = const _r+  {-# INLINABLE r_ #-}+  x_ = const _x+  {-# INLINABLE x_ #-}+  y_ = const _y+  {-# INLINABLE y_ #-} --- | Point of SECT113R1 curve-type P = BPoint SECT113R1 F2m+-- | Affine SECT113R1 curve point.+type PA = BAPoint SECT113R1 F2m Fr +-- | Affine SECT113R1 curve is a binary affine curve.+instance BACurve SECT113R1 F2m Fr where+  gA_ = gA+  {-# INLINABLE gA_ #-}++-- | Projective SECT113R1 point.+type PP = BPPoint SECT113R1 F2m Fr++-- | Projective SECT113R1 curve is a binary projective curve.+instance BPCurve SECT113R1 F2m Fr where+  gP_ = gP+  {-# INLINABLE gP_ #-}+ ------------------------------------------------------------------------------- -- Parameters ------------------------------------------------------------------------------- --- | Coefficient @A@ of SECT113R1 curve+-- | Coefficient @A@ of SECT113R1 curve. _a :: F2m _a = 0x3088250ca6e7c7fe649ce85820f7-{-# INLINE _a #-}+{-# INLINABLE _a #-} --- | Coefficient @B@ of SECT113R1 curve+-- | Coefficient @B@ of SECT113R1 curve. _b :: F2m _b = 0xe8bee4d3e2260744188be0e9c723-{-# INLINE _b #-}+{-# INLINABLE _b #-} --- | Polynomial of SECT113R1 curve-_f :: Integer-_f = 0x20000000000000000000000000201-{-# INLINE _f #-}+-- | Cofactor of SECT113R1 curve.+_h :: Integer+_h = 0x2+{-# INLINABLE _h #-} --- | Generator of SECT113R1 curve-_g :: P-_g = A-     0x9d73616f35f4ab1407d73562c10f-     0xa52830277958ee84d1315ed31886-{-# INLINE _g #-}+-- | Polynomial of SECT113R1 curve.+_p :: Integer+_p = 0x20000000000000000000000000201+{-# INLINABLE _p #-} --- | Cofactor of SECT113R1 curve-_h :: Integer-_h = 2-{-# INLINE _h #-}+-- | Order of SECT113R1 curve.+_r :: Integer+_r = 0x100000000000000d9ccec8a39e56f+{-# INLINABLE _r #-} --- | Order of SECT113R1 curve-_n :: Integer-_n = 0x100000000000000d9ccec8a39e56f-{-# INLINE _n #-}+-- | Coordinate @X@ of SECT113R1 curve.+_x :: F2m+_x = 0x9d73616f35f4ab1407d73562c10f+{-# INLINABLE _x #-}++-- | Coordinate @Y@ of SECT113R1 curve.+_y :: F2m+_y = 0xa52830277958ee84d1315ed31886+{-# INLINABLE _y #-}++-- | Generator of affine SECT113R1 curve.+gA :: PA+gA = A _x _y+{-# INLINABLE gA #-}++-- | Generator of projective SECT113R1 curve.+gP :: PP+gP = P _x _y 1+{-# INLINABLE gP #-}

src/Curve/Binary/SECT113R2.hs view

@@ -1,74 +1,106 @@ module Curve.Binary.SECT113R2-  ( F2m-  , P-  , _a-  , _b-  , _f-  , _g-  , _h-  , _n+  ( module Curve.Binary+  , module Curve.Binary.SECT113R2   ) where  import Protolude -import BinaryField (BinaryField)+import BinaryField+import PrimeField -import Curve.Binary (BCurve(..), BPoint, Point(..))+import Curve.Binary  ------------------------------------------------------------------------------- -- Types ------------------------------------------------------------------------------- --- | SECT113R2 curve+-- | SECT113R2 curve. data SECT113R2 --- | Field of SECT113R2 curve+-- | Field of points of SECT113R2 curve. type F2m = BinaryField 0x20000000000000000000000000201 --- | SECT113R2 curve is a binary curve-instance BCurve SECT113R2 F2m where+-- | Field of coefficients of SECT113R2 curve.+type Fr = PrimeField 0x10000000000000108789b2496af93++-- | SECT113R2 curve is a binary curve.+instance Curve 'Binary c SECT113R2 F2m Fr => BCurve c SECT113R2 F2m Fr where   a_ = const _a-  {-# INLINE a_ #-}+  {-# INLINABLE a_ #-}   b_ = const _b-  {-# INLINE b_ #-}-  g_ = _g-  {-# INLINE g_ #-}+  {-# INLINABLE b_ #-}+  h_ = const _h+  {-# INLINABLE h_ #-}+  p_ = const _p+  {-# INLINABLE p_ #-}+  r_ = const _r+  {-# INLINABLE r_ #-}+  x_ = const _x+  {-# INLINABLE x_ #-}+  y_ = const _y+  {-# INLINABLE y_ #-} --- | Point of SECT113R2 curve-type P = BPoint SECT113R2 F2m+-- | Affine SECT113R2 curve point.+type PA = BAPoint SECT113R2 F2m Fr +-- | Affine SECT113R2 curve is a binary affine curve.+instance BACurve SECT113R2 F2m Fr where+  gA_ = gA+  {-# INLINABLE gA_ #-}++-- | Projective SECT113R2 point.+type PP = BPPoint SECT113R2 F2m Fr++-- | Projective SECT113R2 curve is a binary projective curve.+instance BPCurve SECT113R2 F2m Fr where+  gP_ = gP+  {-# INLINABLE gP_ #-}+ ------------------------------------------------------------------------------- -- Parameters ------------------------------------------------------------------------------- --- | Coefficient @A@ of SECT113R2 curve+-- | Coefficient @A@ of SECT113R2 curve. _a :: F2m _a = 0x689918dbec7e5a0dd6dfc0aa55c7-{-# INLINE _a #-}+{-# INLINABLE _a #-} --- | Coefficient @B@ of SECT113R2 curve+-- | Coefficient @B@ of SECT113R2 curve. _b :: F2m _b = 0x95e9a9ec9b297bd4bf36e059184f-{-# INLINE _b #-}+{-# INLINABLE _b #-} --- | Polynomial of SECT113R2 curve-_f :: Integer-_f = 0x20000000000000000000000000201-{-# INLINE _f #-}+-- | Cofactor of SECT113R2 curve.+_h :: Integer+_h = 0x2+{-# INLINABLE _h #-} --- | Generator of SECT113R2 curve-_g :: P-_g = A-     0x1a57a6a7b26ca5ef52fcdb8164797-     0xb3adc94ed1fe674c06e695baba1d-{-# INLINE _g #-}+-- | Polynomial of SECT113R2 curve.+_p :: Integer+_p = 0x20000000000000000000000000201+{-# INLINABLE _p #-} --- | Cofactor of SECT113R2 curve-_h :: Integer-_h = 2-{-# INLINE _h #-}+-- | Order of SECT113R2 curve.+_r :: Integer+_r = 0x10000000000000108789b2496af93+{-# INLINABLE _r #-} --- | Order of SECT113R2 curve-_n :: Integer-_n = 0x10000000000000108789b2496af93-{-# INLINE _n #-}+-- | Coordinate @X@ of SECT113R2 curve.+_x :: F2m+_x = 0x1a57a6a7b26ca5ef52fcdb8164797+{-# INLINABLE _x #-}++-- | Coordinate @Y@ of SECT113R2 curve.+_y :: F2m+_y = 0xb3adc94ed1fe674c06e695baba1d+{-# INLINABLE _y #-}++-- | Generator of affine SECT113R2 curve.+gA :: PA+gA = A _x _y+{-# INLINABLE gA #-}++-- | Generator of projective SECT113R2 curve.+gP :: PP+gP = P _x _y 1+{-# INLINABLE gP #-}

src/Curve/Binary/SECT131R1.hs view

@@ -1,74 +1,106 @@ module Curve.Binary.SECT131R1-  ( F2m-  , P-  , _a-  , _b-  , _f-  , _g-  , _h-  , _n+  ( module Curve.Binary+  , module Curve.Binary.SECT131R1   ) where  import Protolude -import BinaryField (BinaryField)+import BinaryField+import PrimeField -import Curve.Binary (BCurve(..), BPoint, Point(..))+import Curve.Binary  ------------------------------------------------------------------------------- -- Types ------------------------------------------------------------------------------- --- | SECT131R1 curve+-- | SECT131R1 curve. data SECT131R1 --- | Field of SECT131R1 curve+-- | Field of points of SECT131R1 curve. type F2m = BinaryField 0x80000000000000000000000000000010d --- | SECT131R1 curve is a binary curve-instance BCurve SECT131R1 F2m where+-- | Field of coefficients of SECT131R1 curve.+type Fr = PrimeField 0x400000000000000023123953a9464b54d++-- | SECT131R1 curve is a binary curve.+instance Curve 'Binary c SECT131R1 F2m Fr => BCurve c SECT131R1 F2m Fr where   a_ = const _a-  {-# INLINE a_ #-}+  {-# INLINABLE a_ #-}   b_ = const _b-  {-# INLINE b_ #-}-  g_ = _g-  {-# INLINE g_ #-}+  {-# INLINABLE b_ #-}+  h_ = const _h+  {-# INLINABLE h_ #-}+  p_ = const _p+  {-# INLINABLE p_ #-}+  r_ = const _r+  {-# INLINABLE r_ #-}+  x_ = const _x+  {-# INLINABLE x_ #-}+  y_ = const _y+  {-# INLINABLE y_ #-} --- | Point of SECT131R1 curve-type P = BPoint SECT131R1 F2m+-- | Affine SECT131R1 curve point.+type PA = BAPoint SECT131R1 F2m Fr +-- | Affine SECT131R1 curve is a binary affine curve.+instance BACurve SECT131R1 F2m Fr where+  gA_ = gA+  {-# INLINABLE gA_ #-}++-- | Projective SECT131R1 point.+type PP = BPPoint SECT131R1 F2m Fr++-- | Projective SECT131R1 curve is a binary projective curve.+instance BPCurve SECT131R1 F2m Fr where+  gP_ = gP+  {-# INLINABLE gP_ #-}+ ------------------------------------------------------------------------------- -- Parameters ------------------------------------------------------------------------------- --- | Coefficient @A@ of SECT131R1 curve+-- | Coefficient @A@ of SECT131R1 curve. _a :: F2m _a = 0x7a11b09a76b562144418ff3ff8c2570b8-{-# INLINE _a #-}+{-# INLINABLE _a #-} --- | Coefficient @B@ of SECT131R1 curve+-- | Coefficient @B@ of SECT131R1 curve. _b :: F2m _b = 0x217c05610884b63b9c6c7291678f9d341-{-# INLINE _b #-}+{-# INLINABLE _b #-} --- | Polynomial of SECT131R1 curve-_f :: Integer-_f = 0x80000000000000000000000000000010d-{-# INLINE _f #-}+-- | Cofactor of SECT131R1 curve.+_h :: Integer+_h = 0x2+{-# INLINABLE _h #-} --- | Generator of SECT131R1 curve-_g :: P-_g = A-     0x81baf91fdf9833c40f9c181343638399-     0x78c6e7ea38c001f73c8134b1b4ef9e150-{-# INLINE _g #-}+-- | Polynomial of SECT131R1 curve.+_p :: Integer+_p = 0x80000000000000000000000000000010d+{-# INLINABLE _p #-} --- | Cofactor of SECT131R1 curve-_h :: Integer-_h = 2-{-# INLINE _h #-}+-- | Order of SECT131R1 curve.+_r :: Integer+_r = 0x400000000000000023123953a9464b54d+{-# INLINABLE _r #-} --- | Order of SECT131R1 curve-_n :: Integer-_n = 0x400000000000000023123953a9464b54d-{-# INLINE _n #-}+-- | Coordinate @X@ of SECT131R1 curve.+_x :: F2m+_x = 0x81baf91fdf9833c40f9c181343638399+{-# INLINABLE _x #-}++-- | Coordinate @Y@ of SECT131R1 curve.+_y :: F2m+_y = 0x78c6e7ea38c001f73c8134b1b4ef9e150+{-# INLINABLE _y #-}++-- | Generator of affine SECT131R1 curve.+gA :: PA+gA = A _x _y+{-# INLINABLE gA #-}++-- | Generator of projective SECT131R1 curve.+gP :: PP+gP = P _x _y 1+{-# INLINABLE gP #-}

src/Curve/Binary/SECT131R2.hs view

@@ -1,74 +1,106 @@ module Curve.Binary.SECT131R2-  ( F2m-  , P-  , _a-  , _b-  , _f-  , _g-  , _h-  , _n+  ( module Curve.Binary+  , module Curve.Binary.SECT131R2   ) where  import Protolude -import BinaryField (BinaryField)+import BinaryField+import PrimeField -import Curve.Binary (BCurve(..), BPoint, Point(..))+import Curve.Binary  ------------------------------------------------------------------------------- -- Types ------------------------------------------------------------------------------- --- | SECT131R2 curve+-- | SECT131R2 curve. data SECT131R2 --- | Field of SECT131R2 curve+-- | Field of points of SECT131R2 curve. type F2m = BinaryField 0x80000000000000000000000000000010d --- | SECT131R2 curve is a binary curve-instance BCurve SECT131R2 F2m where+-- | Field of coefficients of SECT131R2 curve.+type Fr = PrimeField 0x400000000000000016954a233049ba98f++-- | SECT131R2 curve is a binary curve.+instance Curve 'Binary c SECT131R2 F2m Fr => BCurve c SECT131R2 F2m Fr where   a_ = const _a-  {-# INLINE a_ #-}+  {-# INLINABLE a_ #-}   b_ = const _b-  {-# INLINE b_ #-}-  g_ = _g-  {-# INLINE g_ #-}+  {-# INLINABLE b_ #-}+  h_ = const _h+  {-# INLINABLE h_ #-}+  p_ = const _p+  {-# INLINABLE p_ #-}+  r_ = const _r+  {-# INLINABLE r_ #-}+  x_ = const _x+  {-# INLINABLE x_ #-}+  y_ = const _y+  {-# INLINABLE y_ #-} --- | Point of SECT131R2 curve-type P = BPoint SECT131R2 F2m+-- | Affine SECT131R2 curve point.+type PA = BAPoint SECT131R2 F2m Fr +-- | Affine SECT131R2 curve is a binary affine curve.+instance BACurve SECT131R2 F2m Fr where+  gA_ = gA+  {-# INLINABLE gA_ #-}++-- | Projective SECT131R2 point.+type PP = BPPoint SECT131R2 F2m Fr++-- | Projective SECT131R2 curve is a binary projective curve.+instance BPCurve SECT131R2 F2m Fr where+  gP_ = gP+  {-# INLINABLE gP_ #-}+ ------------------------------------------------------------------------------- -- Parameters ------------------------------------------------------------------------------- --- | Coefficient @A@ of SECT131R2 curve+-- | Coefficient @A@ of SECT131R2 curve. _a :: F2m _a = 0x3e5a88919d7cafcbf415f07c2176573b2-{-# INLINE _a #-}+{-# INLINABLE _a #-} --- | Coefficient @B@ of SECT131R2 curve+-- | Coefficient @B@ of SECT131R2 curve. _b :: F2m _b = 0x4b8266a46c55657ac734ce38f018f2192-{-# INLINE _b #-}+{-# INLINABLE _b #-} --- | Polynomial of SECT131R2 curve-_f :: Integer-_f = 0x80000000000000000000000000000010d-{-# INLINE _f #-}+-- | Cofactor of SECT131R2 curve.+_h :: Integer+_h = 0x2+{-# INLINABLE _h #-} --- | Generator of SECT131R2 curve-_g :: P-_g = A-     0x356dcd8f2f95031ad652d23951bb366a8-     0x648f06d867940a5366d9e265de9eb240f-{-# INLINE _g #-}+-- | Polynomial of SECT131R2 curve.+_p :: Integer+_p = 0x80000000000000000000000000000010d+{-# INLINABLE _p #-} --- | Cofactor of SECT131R2 curve-_h :: Integer-_h = 2-{-# INLINE _h #-}+-- | Order of SECT131R2 curve.+_r :: Integer+_r = 0x400000000000000016954a233049ba98f+{-# INLINABLE _r #-} --- | Order of SECT131R2 curve-_n :: Integer-_n = 0x400000000000000016954a233049ba98f-{-# INLINE _n #-}+-- | Coordinate @X@ of SECT131R2 curve.+_x :: F2m+_x = 0x356dcd8f2f95031ad652d23951bb366a8+{-# INLINABLE _x #-}++-- | Coordinate @Y@ of SECT131R2 curve.+_y :: F2m+_y = 0x648f06d867940a5366d9e265de9eb240f+{-# INLINABLE _y #-}++-- | Generator of affine SECT131R2 curve.+gA :: PA+gA = A _x _y+{-# INLINABLE gA #-}++-- | Generator of projective SECT131R2 curve.+gP :: PP+gP = P _x _y 1+{-# INLINABLE gP #-}

src/Curve/Binary/SECT163K1.hs view

@@ -1,74 +1,106 @@ module Curve.Binary.SECT163K1-  ( F2m-  , P-  , _a-  , _b-  , _f-  , _g-  , _h-  , _n+  ( module Curve.Binary+  , module Curve.Binary.SECT163K1   ) where  import Protolude -import BinaryField (BinaryField)+import BinaryField+import PrimeField -import Curve.Binary (BCurve(..), BPoint, Point(..))+import Curve.Binary  ------------------------------------------------------------------------------- -- Types ------------------------------------------------------------------------------- --- | SECT163K1 curve+-- | SECT163K1 curve. data SECT163K1 --- | Field of SECT163K1 curve+-- | Field of points of SECT163K1 curve. type F2m = BinaryField 0x800000000000000000000000000000000000000c9 --- | SECT163K1 curve is a binary curve-instance BCurve SECT163K1 F2m where+-- | Field of coefficients of SECT163K1 curve.+type Fr = PrimeField 0x4000000000000000000020108a2e0cc0d99f8a5ef++-- | SECT163K1 curve is a binary curve.+instance Curve 'Binary c SECT163K1 F2m Fr => BCurve c SECT163K1 F2m Fr where   a_ = const _a-  {-# INLINE a_ #-}+  {-# INLINABLE a_ #-}   b_ = const _b-  {-# INLINE b_ #-}-  g_ = _g-  {-# INLINE g_ #-}+  {-# INLINABLE b_ #-}+  h_ = const _h+  {-# INLINABLE h_ #-}+  p_ = const _p+  {-# INLINABLE p_ #-}+  r_ = const _r+  {-# INLINABLE r_ #-}+  x_ = const _x+  {-# INLINABLE x_ #-}+  y_ = const _y+  {-# INLINABLE y_ #-} --- | Point of SECT163K1 curve-type P = BPoint SECT163K1 F2m+-- | Affine SECT163K1 curve point.+type PA = BAPoint SECT163K1 F2m Fr +-- | Affine SECT163K1 curve is a binary affine curve.+instance BACurve SECT163K1 F2m Fr where+  gA_ = gA+  {-# INLINABLE gA_ #-}++-- | Projective SECT163K1 point.+type PP = BPPoint SECT163K1 F2m Fr++-- | Projective SECT163K1 curve is a binary projective curve.+instance BPCurve SECT163K1 F2m Fr where+  gP_ = gP+  {-# INLINABLE gP_ #-}+ ------------------------------------------------------------------------------- -- Parameters ------------------------------------------------------------------------------- --- | Coefficient @A@ of SECT163K1 curve+-- | Coefficient @A@ of SECT163K1 curve. _a :: F2m-_a = 1-{-# INLINE _a #-}+_a = 0x1+{-# INLINABLE _a #-} --- | Coefficient @B@ of SECT163K1 curve+-- | Coefficient @B@ of SECT163K1 curve. _b :: F2m-_b = 1-{-# INLINE _b #-}+_b = 0x1+{-# INLINABLE _b #-} --- | Polynomial of SECT163K1 curve-_f :: Integer-_f = 0x800000000000000000000000000000000000000c9-{-# INLINE _f #-}+-- | Cofactor of SECT163K1 curve.+_h :: Integer+_h = 0x2+{-# INLINABLE _h #-} --- | Generator of SECT163K1 curve-_g :: P-_g = A-     0x2fe13c0537bbc11acaa07d793de4e6d5e5c94eee8-     0x289070fb05d38ff58321f2e800536d538ccdaa3d9-{-# INLINE _g #-}+-- | Polynomial of SECT163K1 curve.+_p :: Integer+_p = 0x800000000000000000000000000000000000000c9+{-# INLINABLE _p #-} --- | Cofactor of SECT163K1 curve-_h :: Integer-_h = 2-{-# INLINE _h #-}+-- | Order of SECT163K1 curve.+_r :: Integer+_r = 0x4000000000000000000020108a2e0cc0d99f8a5ef+{-# INLINABLE _r #-} --- | Order of SECT163K1 curve-_n :: Integer-_n = 0x4000000000000000000020108a2e0cc0d99f8a5ef-{-# INLINE _n #-}+-- | Coordinate @X@ of SECT163K1 curve.+_x :: F2m+_x = 0x2fe13c0537bbc11acaa07d793de4e6d5e5c94eee8+{-# INLINABLE _x #-}++-- | Coordinate @Y@ of SECT163K1 curve.+_y :: F2m+_y = 0x289070fb05d38ff58321f2e800536d538ccdaa3d9+{-# INLINABLE _y #-}++-- | Generator of affine SECT163K1 curve.+gA :: PA+gA = A _x _y+{-# INLINABLE gA #-}++-- | Generator of projective SECT163K1 curve.+gP :: PP+gP = P _x _y 1+{-# INLINABLE gP #-}

src/Curve/Binary/SECT163R1.hs view

@@ -1,74 +1,106 @@ module Curve.Binary.SECT163R1-  ( F2m-  , P-  , _a-  , _b-  , _f-  , _g-  , _h-  , _n+  ( module Curve.Binary+  , module Curve.Binary.SECT163R1   ) where  import Protolude -import BinaryField (BinaryField)+import BinaryField+import PrimeField -import Curve.Binary (BCurve(..), BPoint, Point(..))+import Curve.Binary  ------------------------------------------------------------------------------- -- Types ------------------------------------------------------------------------------- --- | SECT163R1 curve+-- | SECT163R1 curve. data SECT163R1 --- | Field of SECT163R1 curve+-- | Field of points of SECT163R1 curve. type F2m = BinaryField 0x800000000000000000000000000000000000000c9 --- | SECT163R1 curve is a binary curve-instance BCurve SECT163R1 F2m where+-- | Field of coefficients of SECT163R1 curve.+type Fr = PrimeField 0x3ffffffffffffffffffff48aab689c29ca710279b++-- | SECT163R1 curve is a binary curve.+instance Curve 'Binary c SECT163R1 F2m Fr => BCurve c SECT163R1 F2m Fr where   a_ = const _a-  {-# INLINE a_ #-}+  {-# INLINABLE a_ #-}   b_ = const _b-  {-# INLINE b_ #-}-  g_ = _g-  {-# INLINE g_ #-}+  {-# INLINABLE b_ #-}+  h_ = const _h+  {-# INLINABLE h_ #-}+  p_ = const _p+  {-# INLINABLE p_ #-}+  r_ = const _r+  {-# INLINABLE r_ #-}+  x_ = const _x+  {-# INLINABLE x_ #-}+  y_ = const _y+  {-# INLINABLE y_ #-} --- | Point of SECT163R1 curve-type P = BPoint SECT163R1 F2m+-- | Affine SECT163R1 curve point.+type PA = BAPoint SECT163R1 F2m Fr +-- | Affine SECT163R1 curve is a binary affine curve.+instance BACurve SECT163R1 F2m Fr where+  gA_ = gA+  {-# INLINABLE gA_ #-}++-- | Projective SECT163R1 point.+type PP = BPPoint SECT163R1 F2m Fr++-- | Projective SECT163R1 curve is a binary projective curve.+instance BPCurve SECT163R1 F2m Fr where+  gP_ = gP+  {-# INLINABLE gP_ #-}+ ------------------------------------------------------------------------------- -- Parameters ------------------------------------------------------------------------------- --- | Coefficient @A@ of SECT163R1 curve+-- | Coefficient @A@ of SECT163R1 curve. _a :: F2m _a = 0x7b6882caaefa84f9554ff8428bd88e246d2782ae2-{-# INLINE _a #-}+{-# INLINABLE _a #-} --- | Coefficient @B@ of SECT163R1 curve+-- | Coefficient @B@ of SECT163R1 curve. _b :: F2m _b = 0x713612dcddcb40aab946bda29ca91f73af958afd9-{-# INLINE _b #-}+{-# INLINABLE _b #-} --- | Polynomial of SECT163R1 curve-_f :: Integer-_f = 0x800000000000000000000000000000000000000c9-{-# INLINE _f #-}+-- | Cofactor of SECT163R1 curve.+_h :: Integer+_h = 0x2+{-# INLINABLE _h #-} --- | Generator of SECT163R1 curve-_g :: P-_g = A-     0x369979697ab43897789566789567f787a7876a654-     0x435edb42efafb2989d51fefce3c80988f41ff883-{-# INLINE _g #-}+-- | Polynomial of SECT163R1 curve.+_p :: Integer+_p = 0x800000000000000000000000000000000000000c9+{-# INLINABLE _p #-} --- | Cofactor of SECT163R1 curve-_h :: Integer-_h = 2-{-# INLINE _h #-}+-- | Order of SECT163R1 curve.+_r :: Integer+_r = 0x3ffffffffffffffffffff48aab689c29ca710279b+{-# INLINABLE _r #-} --- | Order of SECT163R1 curve-_n :: Integer-_n = 0x3ffffffffffffffffffff48aab689c29ca710279b-{-# INLINE _n #-}+-- | Coordinate @X@ of SECT163R1 curve.+_x :: F2m+_x = 0x369979697ab43897789566789567f787a7876a654+{-# INLINABLE _x #-}++-- | Coordinate @Y@ of SECT163R1 curve.+_y :: F2m+_y = 0x435edb42efafb2989d51fefce3c80988f41ff883+{-# INLINABLE _y #-}++-- | Generator of affine SECT163R1 curve.+gA :: PA+gA = A _x _y+{-# INLINABLE gA #-}++-- | Generator of projective SECT163R1 curve.+gP :: PP+gP = P _x _y 1+{-# INLINABLE gP #-}

src/Curve/Binary/SECT163R2.hs view

@@ -1,74 +1,106 @@ module Curve.Binary.SECT163R2-  ( F2m-  , P-  , _a-  , _b-  , _f-  , _g-  , _h-  , _n+  ( module Curve.Binary+  , module Curve.Binary.SECT163R2   ) where  import Protolude -import BinaryField (BinaryField)+import BinaryField+import PrimeField -import Curve.Binary (BCurve(..), BPoint, Point(..))+import Curve.Binary  ------------------------------------------------------------------------------- -- Types ------------------------------------------------------------------------------- --- | SECT163R2 curve+-- | SECT163R2 curve. data SECT163R2 --- | Field of SECT163R2 curve+-- | Field of points of SECT163R2 curve. type F2m = BinaryField 0x800000000000000000000000000000000000000c9 --- | SECT163R2 curve is a binary curve-instance BCurve SECT163R2 F2m where+-- | Field of coefficients of SECT163R2 curve.+type Fr = PrimeField 0x40000000000000000000292fe77e70c12a4234c33++-- | SECT163R2 curve is a binary curve.+instance Curve 'Binary c SECT163R2 F2m Fr => BCurve c SECT163R2 F2m Fr where   a_ = const _a-  {-# INLINE a_ #-}+  {-# INLINABLE a_ #-}   b_ = const _b-  {-# INLINE b_ #-}-  g_ = _g-  {-# INLINE g_ #-}+  {-# INLINABLE b_ #-}+  h_ = const _h+  {-# INLINABLE h_ #-}+  p_ = const _p+  {-# INLINABLE p_ #-}+  r_ = const _r+  {-# INLINABLE r_ #-}+  x_ = const _x+  {-# INLINABLE x_ #-}+  y_ = const _y+  {-# INLINABLE y_ #-} --- | Point of SECT163R2 curve-type P = BPoint SECT163R2 F2m+-- | Affine SECT163R2 curve point.+type PA = BAPoint SECT163R2 F2m Fr +-- | Affine SECT163R2 curve is a binary affine curve.+instance BACurve SECT163R2 F2m Fr where+  gA_ = gA+  {-# INLINABLE gA_ #-}++-- | Projective SECT163R2 point.+type PP = BPPoint SECT163R2 F2m Fr++-- | Projective SECT163R2 curve is a binary projective curve.+instance BPCurve SECT163R2 F2m Fr where+  gP_ = gP+  {-# INLINABLE gP_ #-}+ ------------------------------------------------------------------------------- -- Parameters ------------------------------------------------------------------------------- --- | Coefficient @A@ of SECT163R2 curve+-- | Coefficient @A@ of SECT163R2 curve. _a :: F2m-_a = 1-{-# INLINE _a #-}+_a = 0x1+{-# INLINABLE _a #-} --- | Coefficient @B@ of SECT163R2 curve+-- | Coefficient @B@ of SECT163R2 curve. _b :: F2m _b = 0x20a601907b8c953ca1481eb10512f78744a3205fd-{-# INLINE _b #-}+{-# INLINABLE _b #-} --- | Polynomial of SECT163R2 curve-_f :: Integer-_f = 0x800000000000000000000000000000000000000c9-{-# INLINE _f #-}+-- | Cofactor of SECT163R2 curve.+_h :: Integer+_h = 0x2+{-# INLINABLE _h #-} --- | Generator of SECT163R2 curve-_g :: P-_g = A-     0x3f0eba16286a2d57ea0991168d4994637e8343e36-     0xd51fbc6c71a0094fa2cdd545b11c5c0c797324f1-{-# INLINE _g #-}+-- | Polynomial of SECT163R2 curve.+_p :: Integer+_p = 0x800000000000000000000000000000000000000c9+{-# INLINABLE _p #-} --- | Cofactor of SECT163R2 curve-_h :: Integer-_h = 2-{-# INLINE _h #-}+-- | Order of SECT163R2 curve.+_r :: Integer+_r = 0x40000000000000000000292fe77e70c12a4234c33+{-# INLINABLE _r #-} --- | Order of SECT163R2 curve-_n :: Integer-_n = 0x40000000000000000000292fe77e70c12a4234c33-{-# INLINE _n #-}+-- | Coordinate @X@ of SECT163R2 curve.+_x :: F2m+_x = 0x3f0eba16286a2d57ea0991168d4994637e8343e36+{-# INLINABLE _x #-}++-- | Coordinate @Y@ of SECT163R2 curve.+_y :: F2m+_y = 0xd51fbc6c71a0094fa2cdd545b11c5c0c797324f1+{-# INLINABLE _y #-}++-- | Generator of affine SECT163R2 curve.+gA :: PA+gA = A _x _y+{-# INLINABLE gA #-}++-- | Generator of projective SECT163R2 curve.+gP :: PP+gP = P _x _y 1+{-# INLINABLE gP #-}

src/Curve/Binary/SECT193R1.hs view

@@ -1,74 +1,106 @@ module Curve.Binary.SECT193R1-  ( F2m-  , P-  , _a-  , _b-  , _f-  , _g-  , _h-  , _n+  ( module Curve.Binary+  , module Curve.Binary.SECT193R1   ) where  import Protolude -import BinaryField (BinaryField)+import BinaryField+import PrimeField -import Curve.Binary (BCurve(..), BPoint, Point(..))+import Curve.Binary  ------------------------------------------------------------------------------- -- Types ------------------------------------------------------------------------------- --- | SECT193R1 curve+-- | SECT193R1 curve. data SECT193R1 --- | Field of SECT193R1 curve+-- | Field of points of SECT193R1 curve. type F2m = BinaryField 0x2000000000000000000000000000000000000000000008001 --- | SECT193R1 curve is a binary curve-instance BCurve SECT193R1 F2m where+-- | Field of coefficients of SECT193R1 curve.+type Fr = PrimeField 0x1000000000000000000000000c7f34a778f443acc920eba49++-- | SECT193R1 curve is a binary curve.+instance Curve 'Binary c SECT193R1 F2m Fr => BCurve c SECT193R1 F2m Fr where   a_ = const _a-  {-# INLINE a_ #-}+  {-# INLINABLE a_ #-}   b_ = const _b-  {-# INLINE b_ #-}-  g_ = _g-  {-# INLINE g_ #-}+  {-# INLINABLE b_ #-}+  h_ = const _h+  {-# INLINABLE h_ #-}+  p_ = const _p+  {-# INLINABLE p_ #-}+  r_ = const _r+  {-# INLINABLE r_ #-}+  x_ = const _x+  {-# INLINABLE x_ #-}+  y_ = const _y+  {-# INLINABLE y_ #-} --- | Point of SECT193R1 curve-type P = BPoint SECT193R1 F2m+-- | Affine SECT193R1 curve point.+type PA = BAPoint SECT193R1 F2m Fr +-- | Affine SECT193R1 curve is a binary affine curve.+instance BACurve SECT193R1 F2m Fr where+  gA_ = gA+  {-# INLINABLE gA_ #-}++-- | Projective SECT193R1 point.+type PP = BPPoint SECT193R1 F2m Fr++-- | Projective SECT193R1 curve is a binary projective curve.+instance BPCurve SECT193R1 F2m Fr where+  gP_ = gP+  {-# INLINABLE gP_ #-}+ ------------------------------------------------------------------------------- -- Parameters ------------------------------------------------------------------------------- --- | Coefficient @A@ of SECT193R1 curve+-- | Coefficient @A@ of SECT193R1 curve. _a :: F2m _a = 0x17858feb7a98975169e171f77b4087de098ac8a911df7b01-{-# INLINE _a #-}+{-# INLINABLE _a #-} --- | Coefficient @B@ of SECT193R1 curve+-- | Coefficient @B@ of SECT193R1 curve. _b :: F2m _b = 0xfdfb49bfe6c3a89facadaa7a1e5bbc7cc1c2e5d831478814-{-# INLINE _b #-}+{-# INLINABLE _b #-} --- | Polynomial of SECT193R1 curve-_f :: Integer-_f = 0x2000000000000000000000000000000000000000000008001-{-# INLINE _f #-}+-- | Cofactor of SECT193R1 curve.+_h :: Integer+_h = 0x2+{-# INLINABLE _h #-} --- | Generator of SECT193R1 curve-_g :: P-_g = A-     0x1f481bc5f0ff84a74ad6cdf6fdef4bf6179625372d8c0c5e1-     0x25e399f2903712ccf3ea9e3a1ad17fb0b3201b6af7ce1b05-{-# INLINE _g #-}+-- | Polynomial of SECT193R1 curve.+_p :: Integer+_p = 0x2000000000000000000000000000000000000000000008001+{-# INLINABLE _p #-} --- | Cofactor of SECT193R1 curve-_h :: Integer-_h = 2-{-# INLINE _h #-}+-- | Order of SECT193R1 curve.+_r :: Integer+_r = 0x1000000000000000000000000c7f34a778f443acc920eba49+{-# INLINABLE _r #-} --- | Order of SECT193R1 curve-_n :: Integer-_n = 0x1000000000000000000000000c7f34a778f443acc920eba49-{-# INLINE _n #-}+-- | Coordinate @X@ of SECT193R1 curve.+_x :: F2m+_x = 0x1f481bc5f0ff84a74ad6cdf6fdef4bf6179625372d8c0c5e1+{-# INLINABLE _x #-}++-- | Coordinate @Y@ of SECT193R1 curve.+_y :: F2m+_y = 0x25e399f2903712ccf3ea9e3a1ad17fb0b3201b6af7ce1b05+{-# INLINABLE _y #-}++-- | Generator of affine SECT193R1 curve.+gA :: PA+gA = A _x _y+{-# INLINABLE gA #-}++-- | Generator of projective SECT193R1 curve.+gP :: PP+gP = P _x _y 1+{-# INLINABLE gP #-}

src/Curve/Binary/SECT193R2.hs view

@@ -1,74 +1,106 @@ module Curve.Binary.SECT193R2-  ( F2m-  , P-  , _a-  , _b-  , _f-  , _g-  , _h-  , _n+  ( module Curve.Binary+  , module Curve.Binary.SECT193R2   ) where  import Protolude -import BinaryField (BinaryField)+import BinaryField+import PrimeField -import Curve.Binary (BCurve(..), BPoint, Point(..))+import Curve.Binary  ------------------------------------------------------------------------------- -- Types ------------------------------------------------------------------------------- --- | SECT193R2 curve+-- | SECT193R2 curve. data SECT193R2 --- | Field of SECT193R2 curve+-- | Field of points of SECT193R2 curve. type F2m = BinaryField 0x2000000000000000000000000000000000000000000008001 --- | SECT193R2 curve is a binary curve-instance BCurve SECT193R2 F2m where+-- | Field of coefficients of SECT193R2 curve.+type Fr = PrimeField 0x10000000000000000000000015aab561b005413ccd4ee99d5++-- | SECT193R2 curve is a binary curve.+instance Curve 'Binary c SECT193R2 F2m Fr => BCurve c SECT193R2 F2m Fr where   a_ = const _a-  {-# INLINE a_ #-}+  {-# INLINABLE a_ #-}   b_ = const _b-  {-# INLINE b_ #-}-  g_ = _g-  {-# INLINE g_ #-}+  {-# INLINABLE b_ #-}+  h_ = const _h+  {-# INLINABLE h_ #-}+  p_ = const _p+  {-# INLINABLE p_ #-}+  r_ = const _r+  {-# INLINABLE r_ #-}+  x_ = const _x+  {-# INLINABLE x_ #-}+  y_ = const _y+  {-# INLINABLE y_ #-} --- | Point of SECT193R2 curve-type P = BPoint SECT193R2 F2m+-- | Affine SECT193R2 curve point.+type PA = BAPoint SECT193R2 F2m Fr +-- | Affine SECT193R2 curve is a binary affine curve.+instance BACurve SECT193R2 F2m Fr where+  gA_ = gA+  {-# INLINABLE gA_ #-}++-- | Projective SECT193R2 point.+type PP = BPPoint SECT193R2 F2m Fr++-- | Projective SECT193R2 curve is a binary projective curve.+instance BPCurve SECT193R2 F2m Fr where+  gP_ = gP+  {-# INLINABLE gP_ #-}+ ------------------------------------------------------------------------------- -- Parameters ------------------------------------------------------------------------------- --- | Coefficient @A@ of SECT193R2 curve+-- | Coefficient @A@ of SECT193R2 curve. _a :: F2m _a = 0x163f35a5137c2ce3ea6ed8667190b0bc43ecd69977702709b-{-# INLINE _a #-}+{-# INLINABLE _a #-} --- | Coefficient @B@ of SECT193R2 curve+-- | Coefficient @B@ of SECT193R2 curve. _b :: F2m _b = 0xc9bb9e8927d4d64c377e2ab2856a5b16e3efb7f61d4316ae-{-# INLINE _b #-}+{-# INLINABLE _b #-} --- | Polynomial of SECT193R2 curve-_f :: Integer-_f = 0x2000000000000000000000000000000000000000000008001-{-# INLINE _f #-}+-- | Cofactor of SECT193R2 curve.+_h :: Integer+_h = 0x2+{-# INLINABLE _h #-} --- | Generator of SECT193R2 curve-_g :: P-_g = A-     0xd9b67d192e0367c803f39e1a7e82ca14a651350aae617e8f-     0x1ce94335607c304ac29e7defbd9ca01f596f927224cdecf6c-{-# INLINE _g #-}+-- | Polynomial of SECT193R2 curve.+_p :: Integer+_p = 0x2000000000000000000000000000000000000000000008001+{-# INLINABLE _p #-} --- | Cofactor of SECT193R2 curve-_h :: Integer-_h = 2-{-# INLINE _h #-}+-- | Order of SECT193R2 curve.+_r :: Integer+_r = 0x10000000000000000000000015aab561b005413ccd4ee99d5+{-# INLINABLE _r #-} --- | Order of SECT193R2 curve-_n :: Integer-_n = 0x10000000000000000000000015aab561b005413ccd4ee99d5-{-# INLINE _n #-}+-- | Coordinate @X@ of SECT193R2 curve.+_x :: F2m+_x = 0xd9b67d192e0367c803f39e1a7e82ca14a651350aae617e8f+{-# INLINABLE _x #-}++-- | Coordinate @Y@ of SECT193R2 curve.+_y :: F2m+_y = 0x1ce94335607c304ac29e7defbd9ca01f596f927224cdecf6c+{-# INLINABLE _y #-}++-- | Generator of affine SECT193R2 curve.+gA :: PA+gA = A _x _y+{-# INLINABLE gA #-}++-- | Generator of projective SECT193R2 curve.+gP :: PP+gP = P _x _y 1+{-# INLINABLE gP #-}

src/Curve/Binary/SECT233K1.hs view

@@ -1,74 +1,106 @@ module Curve.Binary.SECT233K1-  ( F2m-  , P-  , _a-  , _b-  , _f-  , _g-  , _h-  , _n+  ( module Curve.Binary+  , module Curve.Binary.SECT233K1   ) where  import Protolude -import BinaryField (BinaryField)+import BinaryField+import PrimeField -import Curve.Binary (BCurve(..), BPoint, Point(..))+import Curve.Binary  ------------------------------------------------------------------------------- -- Types ------------------------------------------------------------------------------- --- | SECT233K1 curve+-- | SECT233K1 curve. data SECT233K1 --- | Field of SECT233K1 curve+-- | Field of points of SECT233K1 curve. type F2m = BinaryField 0x20000000000000000000000000000000000000004000000000000000001 --- | SECT233K1 curve is a binary curve-instance BCurve SECT233K1 F2m where+-- | Field of coefficients of SECT233K1 curve.+type Fr = PrimeField 0x8000000000000000000000000000069d5bb915bcd46efb1ad5f173abdf++-- | SECT233K1 curve is a binary curve.+instance Curve 'Binary c SECT233K1 F2m Fr => BCurve c SECT233K1 F2m Fr where   a_ = const _a-  {-# INLINE a_ #-}+  {-# INLINABLE a_ #-}   b_ = const _b-  {-# INLINE b_ #-}-  g_ = _g-  {-# INLINE g_ #-}+  {-# INLINABLE b_ #-}+  h_ = const _h+  {-# INLINABLE h_ #-}+  p_ = const _p+  {-# INLINABLE p_ #-}+  r_ = const _r+  {-# INLINABLE r_ #-}+  x_ = const _x+  {-# INLINABLE x_ #-}+  y_ = const _y+  {-# INLINABLE y_ #-} --- | Point of SECT233K1 curve-type P = BPoint SECT233K1 F2m+-- | Affine SECT233K1 curve point.+type PA = BAPoint SECT233K1 F2m Fr +-- | Affine SECT233K1 curve is a binary affine curve.+instance BACurve SECT233K1 F2m Fr where+  gA_ = gA+  {-# INLINABLE gA_ #-}++-- | Projective SECT233K1 point.+type PP = BPPoint SECT233K1 F2m Fr++-- | Projective SECT233K1 curve is a binary projective curve.+instance BPCurve SECT233K1 F2m Fr where+  gP_ = gP+  {-# INLINABLE gP_ #-}+ ------------------------------------------------------------------------------- -- Parameters ------------------------------------------------------------------------------- --- | Coefficient @A@ of SECT233K1 curve+-- | Coefficient @A@ of SECT233K1 curve. _a :: F2m-_a = 0-{-# INLINE _a #-}+_a = 0x0+{-# INLINABLE _a #-} --- | Coefficient @B@ of SECT233K1 curve+-- | Coefficient @B@ of SECT233K1 curve. _b :: F2m-_b = 1-{-# INLINE _b #-}+_b = 0x1+{-# INLINABLE _b #-} --- | Polynomial of SECT233K1 curve-_f :: Integer-_f = 0x20000000000000000000000000000000000000004000000000000000001-{-# INLINE _f #-}+-- | Cofactor of SECT233K1 curve.+_h :: Integer+_h = 0x4+{-# INLINABLE _h #-} --- | Generator of SECT233K1 curve-_g :: P-_g = A-     0x17232ba853a7e731af129f22ff4149563a419c26bf50a4c9d6eefad6126-     0x1db537dece819b7f70f555a67c427a8cd9bf18aeb9b56e0c11056fae6a3-{-# INLINE _g #-}+-- | Polynomial of SECT233K1 curve.+_p :: Integer+_p = 0x20000000000000000000000000000000000000004000000000000000001+{-# INLINABLE _p #-} --- | Cofactor of SECT233K1 curve-_h :: Integer-_h = 4-{-# INLINE _h #-}+-- | Order of SECT233K1 curve.+_r :: Integer+_r = 0x8000000000000000000000000000069d5bb915bcd46efb1ad5f173abdf+{-# INLINABLE _r #-} --- | Order of SECT233K1 curve-_n :: Integer-_n = 0x8000000000000000000000000000069d5bb915bcd46efb1ad5f173abdf-{-# INLINE _n #-}+-- | Coordinate @X@ of SECT233K1 curve.+_x :: F2m+_x = 0x17232ba853a7e731af129f22ff4149563a419c26bf50a4c9d6eefad6126+{-# INLINABLE _x #-}++-- | Coordinate @Y@ of SECT233K1 curve.+_y :: F2m+_y = 0x1db537dece819b7f70f555a67c427a8cd9bf18aeb9b56e0c11056fae6a3+{-# INLINABLE _y #-}++-- | Generator of affine SECT233K1 curve.+gA :: PA+gA = A _x _y+{-# INLINABLE gA #-}++-- | Generator of projective SECT233K1 curve.+gP :: PP+gP = P _x _y 1+{-# INLINABLE gP #-}

src/Curve/Binary/SECT233R1.hs view

@@ -1,74 +1,106 @@ module Curve.Binary.SECT233R1-  ( F2m-  , P-  , _a-  , _b-  , _f-  , _g-  , _h-  , _n+  ( module Curve.Binary+  , module Curve.Binary.SECT233R1   ) where  import Protolude -import BinaryField (BinaryField)+import BinaryField+import PrimeField -import Curve.Binary (BCurve(..), BPoint, Point(..))+import Curve.Binary  ------------------------------------------------------------------------------- -- Types ------------------------------------------------------------------------------- --- | SECT233R1 curve+-- | SECT233R1 curve. data SECT233R1 --- | Field of SECT233R1 curve+-- | Field of points of SECT233R1 curve. type F2m = BinaryField 0x20000000000000000000000000000000000000004000000000000000001 --- | SECT233R1 curve is a binary curve-instance BCurve SECT233R1 F2m where+-- | Field of coefficients of SECT233R1 curve.+type Fr = PrimeField 0x1000000000000000000000000000013e974e72f8a6922031d2603cfe0d7++-- | SECT233R1 curve is a binary curve.+instance Curve 'Binary c SECT233R1 F2m Fr => BCurve c SECT233R1 F2m Fr where   a_ = const _a-  {-# INLINE a_ #-}+  {-# INLINABLE a_ #-}   b_ = const _b-  {-# INLINE b_ #-}-  g_ = _g-  {-# INLINE g_ #-}+  {-# INLINABLE b_ #-}+  h_ = const _h+  {-# INLINABLE h_ #-}+  p_ = const _p+  {-# INLINABLE p_ #-}+  r_ = const _r+  {-# INLINABLE r_ #-}+  x_ = const _x+  {-# INLINABLE x_ #-}+  y_ = const _y+  {-# INLINABLE y_ #-} --- | Point of SECT233R1 curve-type P = BPoint SECT233R1 F2m+-- | Affine SECT233R1 curve point.+type PA = BAPoint SECT233R1 F2m Fr +-- | Affine SECT233R1 curve is a binary affine curve.+instance BACurve SECT233R1 F2m Fr where+  gA_ = gA+  {-# INLINABLE gA_ #-}++-- | Projective SECT233R1 point.+type PP = BPPoint SECT233R1 F2m Fr++-- | Projective SECT233R1 curve is a binary projective curve.+instance BPCurve SECT233R1 F2m Fr where+  gP_ = gP+  {-# INLINABLE gP_ #-}+ ------------------------------------------------------------------------------- -- Parameters ------------------------------------------------------------------------------- --- | Coefficient @A@ of SECT233R1 curve+-- | Coefficient @A@ of SECT233R1 curve. _a :: F2m-_a = 1-{-# INLINE _a #-}+_a = 0x1+{-# INLINABLE _a #-} --- | Coefficient @B@ of SECT233R1 curve+-- | Coefficient @B@ of SECT233R1 curve. _b :: F2m _b = 0x66647ede6c332c7f8c0923bb58213b333b20e9ce4281fe115f7d8f90ad-{-# INLINE _b #-}+{-# INLINABLE _b #-} --- | Polynomial of SECT233R1 curve-_f :: Integer-_f = 0x20000000000000000000000000000000000000004000000000000000001-{-# INLINE _f #-}+-- | Cofactor of SECT233R1 curve.+_h :: Integer+_h = 0x2+{-# INLINABLE _h #-} --- | Generator of SECT233R1 curve-_g :: P-_g = A-     0xfac9dfcbac8313bb2139f1bb755fef65bc391f8b36f8f8eb7371fd558b-     0x1006a08a41903350678e58528bebf8a0beff867a7ca36716f7e01f81052-{-# INLINE _g #-}+-- | Polynomial of SECT233R1 curve.+_p :: Integer+_p = 0x20000000000000000000000000000000000000004000000000000000001+{-# INLINABLE _p #-} --- | Cofactor of SECT233R1 curve-_h :: Integer-_h = 2-{-# INLINE _h #-}+-- | Order of SECT233R1 curve.+_r :: Integer+_r = 0x1000000000000000000000000000013e974e72f8a6922031d2603cfe0d7+{-# INLINABLE _r #-} --- | Order of SECT233R1 curve-_n :: Integer-_n = 0x1000000000000000000000000000013e974e72f8a6922031d2603cfe0d7-{-# INLINE _n #-}+-- | Coordinate @X@ of SECT233R1 curve.+_x :: F2m+_x = 0xfac9dfcbac8313bb2139f1bb755fef65bc391f8b36f8f8eb7371fd558b+{-# INLINABLE _x #-}++-- | Coordinate @Y@ of SECT233R1 curve.+_y :: F2m+_y = 0x1006a08a41903350678e58528bebf8a0beff867a7ca36716f7e01f81052+{-# INLINABLE _y #-}++-- | Generator of affine SECT233R1 curve.+gA :: PA+gA = A _x _y+{-# INLINABLE gA #-}++-- | Generator of projective SECT233R1 curve.+gP :: PP+gP = P _x _y 1+{-# INLINABLE gP #-}

src/Curve/Binary/SECT239K1.hs view

@@ -1,74 +1,106 @@ module Curve.Binary.SECT239K1-  ( F2m-  , P-  , _a-  , _b-  , _f-  , _g-  , _h-  , _n+  ( module Curve.Binary+  , module Curve.Binary.SECT239K1   ) where  import Protolude -import BinaryField (BinaryField)+import BinaryField+import PrimeField -import Curve.Binary (BCurve(..), BPoint, Point(..))+import Curve.Binary  ------------------------------------------------------------------------------- -- Types ------------------------------------------------------------------------------- --- | SECT239K1 curve+-- | SECT239K1 curve. data SECT239K1 --- | Field of SECT239K1 curve+-- | Field of points of SECT239K1 curve. type F2m = BinaryField 0x800000000000000000004000000000000000000000000000000000000001 --- | SECT239K1 curve is a binary curve-instance BCurve SECT239K1 F2m where+-- | Field of coefficients of SECT239K1 curve.+type Fr = PrimeField 0x2000000000000000000000000000005a79fec67cb6e91f1c1da800e478a5++-- | SECT239K1 curve is a binary curve.+instance Curve 'Binary c SECT239K1 F2m Fr => BCurve c SECT239K1 F2m Fr where   a_ = const _a-  {-# INLINE a_ #-}+  {-# INLINABLE a_ #-}   b_ = const _b-  {-# INLINE b_ #-}-  g_ = _g-  {-# INLINE g_ #-}+  {-# INLINABLE b_ #-}+  h_ = const _h+  {-# INLINABLE h_ #-}+  p_ = const _p+  {-# INLINABLE p_ #-}+  r_ = const _r+  {-# INLINABLE r_ #-}+  x_ = const _x+  {-# INLINABLE x_ #-}+  y_ = const _y+  {-# INLINABLE y_ #-} --- | Point of SECT239K1 curve-type P = BPoint SECT239K1 F2m+-- | Affine SECT239K1 curve point.+type PA = BAPoint SECT239K1 F2m Fr +-- | Affine SECT239K1 curve is a binary affine curve.+instance BACurve SECT239K1 F2m Fr where+  gA_ = gA+  {-# INLINABLE gA_ #-}++-- | Projective SECT239K1 point.+type PP = BPPoint SECT239K1 F2m Fr++-- | Projective SECT239K1 curve is a binary projective curve.+instance BPCurve SECT239K1 F2m Fr where+  gP_ = gP+  {-# INLINABLE gP_ #-}+ ------------------------------------------------------------------------------- -- Parameters ------------------------------------------------------------------------------- --- | Coefficient @A@ of SECT239K1 curve+-- | Coefficient @A@ of SECT239K1 curve. _a :: F2m-_a = 0-{-# INLINE _a #-}+_a = 0x0+{-# INLINABLE _a #-} --- | Coefficient @B@ of SECT239K1 curve+-- | Coefficient @B@ of SECT239K1 curve. _b :: F2m-_b = 1-{-# INLINE _b #-}+_b = 0x1+{-# INLINABLE _b #-} --- | Polynomial of SECT239K1 curve-_f :: Integer-_f = 0x800000000000000000004000000000000000000000000000000000000001-{-# INLINE _f #-}+-- | Cofactor of SECT239K1 curve.+_h :: Integer+_h = 0x4+{-# INLINABLE _h #-} --- | Generator of SECT239K1 curve-_g :: P-_g = A-     0x29a0b6a887a983e9730988a68727a8b2d126c44cc2cc7b2a6555193035dc-     0x76310804f12e549bdb011c103089e73510acb275fc312a5dc6b76553f0ca-{-# INLINE _g #-}+-- | Polynomial of SECT239K1 curve.+_p :: Integer+_p = 0x800000000000000000004000000000000000000000000000000000000001+{-# INLINABLE _p #-} --- | Cofactor of SECT239K1 curve-_h :: Integer-_h = 4-{-# INLINE _h #-}+-- | Order of SECT239K1 curve.+_r :: Integer+_r = 0x2000000000000000000000000000005a79fec67cb6e91f1c1da800e478a5+{-# INLINABLE _r #-} --- | Order of SECT239K1 curve-_n :: Integer-_n = 0x2000000000000000000000000000005a79fec67cb6e91f1c1da800e478a5-{-# INLINE _n #-}+-- | Coordinate @X@ of SECT239K1 curve.+_x :: F2m+_x = 0x29a0b6a887a983e9730988a68727a8b2d126c44cc2cc7b2a6555193035dc+{-# INLINABLE _x #-}++-- | Coordinate @Y@ of SECT239K1 curve.+_y :: F2m+_y = 0x76310804f12e549bdb011c103089e73510acb275fc312a5dc6b76553f0ca+{-# INLINABLE _y #-}++-- | Generator of affine SECT239K1 curve.+gA :: PA+gA = A _x _y+{-# INLINABLE gA #-}++-- | Generator of projective SECT239K1 curve.+gP :: PP+gP = P _x _y 1+{-# INLINABLE gP #-}

src/Curve/Binary/SECT283K1.hs view

@@ -1,74 +1,106 @@ module Curve.Binary.SECT283K1-  ( F2m-  , P-  , _a-  , _b-  , _f-  , _g-  , _h-  , _n+  ( module Curve.Binary+  , module Curve.Binary.SECT283K1   ) where  import Protolude -import BinaryField (BinaryField)+import BinaryField+import PrimeField -import Curve.Binary (BCurve(..), BPoint, Point(..))+import Curve.Binary  ------------------------------------------------------------------------------- -- Types ------------------------------------------------------------------------------- --- | SECT283K1 curve+-- | SECT283K1 curve. data SECT283K1 --- | Field of SECT283K1 curve+-- | Field of points of SECT283K1 curve. type F2m = BinaryField 0x800000000000000000000000000000000000000000000000000000000000000000010a1 --- | SECT283K1 curve is a binary curve-instance BCurve SECT283K1 F2m where+-- | Field of coefficients of SECT283K1 curve.+type Fr = PrimeField 0x1ffffffffffffffffffffffffffffffffffe9ae2ed07577265dff7f94451e061e163c61++-- | SECT283K1 curve is a binary curve.+instance Curve 'Binary c SECT283K1 F2m Fr => BCurve c SECT283K1 F2m Fr where   a_ = const _a-  {-# INLINE a_ #-}+  {-# INLINABLE a_ #-}   b_ = const _b-  {-# INLINE b_ #-}-  g_ = _g-  {-# INLINE g_ #-}+  {-# INLINABLE b_ #-}+  h_ = const _h+  {-# INLINABLE h_ #-}+  p_ = const _p+  {-# INLINABLE p_ #-}+  r_ = const _r+  {-# INLINABLE r_ #-}+  x_ = const _x+  {-# INLINABLE x_ #-}+  y_ = const _y+  {-# INLINABLE y_ #-} --- | Point of SECT283K1 curve-type P = BPoint SECT283K1 F2m+-- | Affine SECT283K1 curve point.+type PA = BAPoint SECT283K1 F2m Fr +-- | Affine SECT283K1 curve is a binary affine curve.+instance BACurve SECT283K1 F2m Fr where+  gA_ = gA+  {-# INLINABLE gA_ #-}++-- | Projective SECT283K1 point.+type PP = BPPoint SECT283K1 F2m Fr++-- | Projective SECT283K1 curve is a binary projective curve.+instance BPCurve SECT283K1 F2m Fr where+  gP_ = gP+  {-# INLINABLE gP_ #-}+ ------------------------------------------------------------------------------- -- Parameters ------------------------------------------------------------------------------- --- | Coefficient @A@ of SECT283K1 curve+-- | Coefficient @A@ of SECT283K1 curve. _a :: F2m-_a = 0-{-# INLINE _a #-}+_a = 0x0+{-# INLINABLE _a #-} --- | Coefficient @B@ of SECT283K1 curve+-- | Coefficient @B@ of SECT283K1 curve. _b :: F2m-_b = 1-{-# INLINE _b #-}+_b = 0x1+{-# INLINABLE _b #-} --- | Polynomial of SECT283K1 curve-_f :: Integer-_f = 0x800000000000000000000000000000000000000000000000000000000000000000010a1-{-# INLINE _f #-}+-- | Cofactor of SECT283K1 curve.+_h :: Integer+_h = 0x4+{-# INLINABLE _h #-} --- | Generator of SECT283K1 curve-_g :: P-_g = A-     0x503213f78ca44883f1a3b8162f188e553cd265f23c1567a16876913b0c2ac2458492836-     0x1ccda380f1c9e318d90f95d07e5426fe87e45c0e8184698e45962364e34116177dd2259-{-# INLINE _g #-}+-- | Polynomial of SECT283K1 curve.+_p :: Integer+_p = 0x800000000000000000000000000000000000000000000000000000000000000000010a1+{-# INLINABLE _p #-} --- | Cofactor of SECT283K1 curve-_h :: Integer-_h = 4-{-# INLINE _h #-}+-- | Order of SECT283K1 curve.+_r :: Integer+_r = 0x1ffffffffffffffffffffffffffffffffffe9ae2ed07577265dff7f94451e061e163c61+{-# INLINABLE _r #-} --- | Order of SECT283K1 curve-_n :: Integer-_n = 0x1ffffffffffffffffffffffffffffffffffe9ae2ed07577265dff7f94451e061e163c61-{-# INLINE _n #-}+-- | Coordinate @X@ of SECT283K1 curve.+_x :: F2m+_x = 0x503213f78ca44883f1a3b8162f188e553cd265f23c1567a16876913b0c2ac2458492836+{-# INLINABLE _x #-}++-- | Coordinate @Y@ of SECT283K1 curve.+_y :: F2m+_y = 0x1ccda380f1c9e318d90f95d07e5426fe87e45c0e8184698e45962364e34116177dd2259+{-# INLINABLE _y #-}++-- | Generator of affine SECT283K1 curve.+gA :: PA+gA = A _x _y+{-# INLINABLE gA #-}++-- | Generator of projective SECT283K1 curve.+gP :: PP+gP = P _x _y 1+{-# INLINABLE gP #-}

src/Curve/Binary/SECT283R1.hs view

@@ -1,74 +1,106 @@ module Curve.Binary.SECT283R1-  ( F2m-  , P-  , _a-  , _b-  , _f-  , _g-  , _h-  , _n+  ( module Curve.Binary+  , module Curve.Binary.SECT283R1   ) where  import Protolude -import BinaryField (BinaryField)+import BinaryField+import PrimeField -import Curve.Binary (BCurve(..), BPoint, Point(..))+import Curve.Binary  ------------------------------------------------------------------------------- -- Types ------------------------------------------------------------------------------- --- | SECT283R1 curve+-- | SECT283R1 curve. data SECT283R1 --- | Field of SECT283R1 curve+-- | Field of points of SECT283R1 curve. type F2m = BinaryField 0x800000000000000000000000000000000000000000000000000000000000000000010a1 --- | SECT283R1 curve is a binary curve-instance BCurve SECT283R1 F2m where+-- | Field of coefficients of SECT283R1 curve.+type Fr = PrimeField 0x3ffffffffffffffffffffffffffffffffffef90399660fc938a90165b042a7cefadb307++-- | SECT283R1 curve is a binary curve.+instance Curve 'Binary c SECT283R1 F2m Fr => BCurve c SECT283R1 F2m Fr where   a_ = const _a-  {-# INLINE a_ #-}+  {-# INLINABLE a_ #-}   b_ = const _b-  {-# INLINE b_ #-}-  g_ = _g-  {-# INLINE g_ #-}+  {-# INLINABLE b_ #-}+  h_ = const _h+  {-# INLINABLE h_ #-}+  p_ = const _p+  {-# INLINABLE p_ #-}+  r_ = const _r+  {-# INLINABLE r_ #-}+  x_ = const _x+  {-# INLINABLE x_ #-}+  y_ = const _y+  {-# INLINABLE y_ #-} --- | Point of SECT283R1 curve-type P = BPoint SECT283R1 F2m+-- | Affine SECT283R1 curve point.+type PA = BAPoint SECT283R1 F2m Fr +-- | Affine SECT283R1 curve is a binary affine curve.+instance BACurve SECT283R1 F2m Fr where+  gA_ = gA+  {-# INLINABLE gA_ #-}++-- | Projective SECT283R1 point.+type PP = BPPoint SECT283R1 F2m Fr++-- | Projective SECT283R1 curve is a binary projective curve.+instance BPCurve SECT283R1 F2m Fr where+  gP_ = gP+  {-# INLINABLE gP_ #-}+ ------------------------------------------------------------------------------- -- Parameters ------------------------------------------------------------------------------- --- | Coefficient @A@ of SECT283R1 curve+-- | Coefficient @A@ of SECT283R1 curve. _a :: F2m-_a = 1-{-# INLINE _a #-}+_a = 0x1+{-# INLINABLE _a #-} --- | Coefficient @B@ of SECT283R1 curve+-- | Coefficient @B@ of SECT283R1 curve. _b :: F2m _b = 0x27b680ac8b8596da5a4af8a19a0303fca97fd7645309fa2a581485af6263e313b79a2f5-{-# INLINE _b #-}+{-# INLINABLE _b #-} --- | Polynomial of SECT283R1 curve-_f :: Integer-_f = 0x800000000000000000000000000000000000000000000000000000000000000000010a1-{-# INLINE _f #-}+-- | Cofactor of SECT283R1 curve.+_h :: Integer+_h = 0x2+{-# INLINABLE _h #-} --- | Generator of SECT283R1 curve-_g :: P-_g = A-     0x5f939258db7dd90e1934f8c70b0dfec2eed25b8557eac9c80e2e198f8cdbecd86b12053-     0x3676854fe24141cb98fe6d4b20d02b4516ff702350eddb0826779c813f0df45be8112f4-{-# INLINE _g #-}+-- | Polynomial of SECT283R1 curve.+_p :: Integer+_p = 0x800000000000000000000000000000000000000000000000000000000000000000010a1+{-# INLINABLE _p #-} --- | Cofactor of SECT283R1 curve-_h :: Integer-_h = 2-{-# INLINE _h #-}+-- | Order of SECT283R1 curve.+_r :: Integer+_r = 0x3ffffffffffffffffffffffffffffffffffef90399660fc938a90165b042a7cefadb307+{-# INLINABLE _r #-} --- | Order of SECT283R1 curve-_n :: Integer-_n = 0x3ffffffffffffffffffffffffffffffffffef90399660fc938a90165b042a7cefadb307-{-# INLINE _n #-}+-- | Coordinate @X@ of SECT283R1 curve.+_x :: F2m+_x = 0x5f939258db7dd90e1934f8c70b0dfec2eed25b8557eac9c80e2e198f8cdbecd86b12053+{-# INLINABLE _x #-}++-- | Coordinate @Y@ of SECT283R1 curve.+_y :: F2m+_y = 0x3676854fe24141cb98fe6d4b20d02b4516ff702350eddb0826779c813f0df45be8112f4+{-# INLINABLE _y #-}++-- | Generator of affine SECT283R1 curve.+gA :: PA+gA = A _x _y+{-# INLINABLE gA #-}++-- | Generator of projective SECT283R1 curve.+gP :: PP+gP = P _x _y 1+{-# INLINABLE gP #-}

src/Curve/Binary/SECT409K1.hs view

@@ -1,74 +1,106 @@ module Curve.Binary.SECT409K1-  ( F2m-  , P-  , _a-  , _b-  , _f-  , _g-  , _h-  , _n+  ( module Curve.Binary+  , module Curve.Binary.SECT409K1   ) where  import Protolude -import BinaryField (BinaryField)+import BinaryField+import PrimeField -import Curve.Binary (BCurve(..), BPoint, Point(..))+import Curve.Binary  ------------------------------------------------------------------------------- -- Types ------------------------------------------------------------------------------- --- | SECT409K1 curve+-- | SECT409K1 curve. data SECT409K1 --- | Field of SECT409K1 curve+-- | Field of points of SECT409K1 curve. type F2m = BinaryField 0x2000000000000000000000000000000000000000000000000000000000000000000000000000000008000000000000000000001 --- | SECT409K1 curve is a binary curve-instance BCurve SECT409K1 F2m where+-- | Field of coefficients of SECT409K1 curve.+type Fr = PrimeField 0x7ffffffffffffffffffffffffffffffffffffffffffffffffffe5f83b2d4ea20400ec4557d5ed3e3e7ca5b4b5c83b8e01e5fcf++-- | SECT409K1 curve is a binary curve.+instance Curve 'Binary c SECT409K1 F2m Fr => BCurve c SECT409K1 F2m Fr where   a_ = const _a-  {-# INLINE a_ #-}+  {-# INLINABLE a_ #-}   b_ = const _b-  {-# INLINE b_ #-}-  g_ = _g-  {-# INLINE g_ #-}+  {-# INLINABLE b_ #-}+  h_ = const _h+  {-# INLINABLE h_ #-}+  p_ = const _p+  {-# INLINABLE p_ #-}+  r_ = const _r+  {-# INLINABLE r_ #-}+  x_ = const _x+  {-# INLINABLE x_ #-}+  y_ = const _y+  {-# INLINABLE y_ #-} --- | Point of SECT409K1 curve-type P = BPoint SECT409K1 F2m+-- | Affine SECT409K1 curve point.+type PA = BAPoint SECT409K1 F2m Fr +-- | Affine SECT409K1 curve is a binary affine curve.+instance BACurve SECT409K1 F2m Fr where+  gA_ = gA+  {-# INLINABLE gA_ #-}++-- | Projective SECT409K1 point.+type PP = BPPoint SECT409K1 F2m Fr++-- | Projective SECT409K1 curve is a binary projective curve.+instance BPCurve SECT409K1 F2m Fr where+  gP_ = gP+  {-# INLINABLE gP_ #-}+ ------------------------------------------------------------------------------- -- Parameters ------------------------------------------------------------------------------- --- | Coefficient @A@ of SECT409K1 curve+-- | Coefficient @A@ of SECT409K1 curve. _a :: F2m-_a = 0-{-# INLINE _a #-}+_a = 0x0+{-# INLINABLE _a #-} --- | Coefficient @B@ of SECT409K1 curve+-- | Coefficient @B@ of SECT409K1 curve. _b :: F2m-_b = 1-{-# INLINE _b #-}+_b = 0x1+{-# INLINABLE _b #-} --- | Polynomial of SECT409K1 curve-_f :: Integer-_f = 0x2000000000000000000000000000000000000000000000000000000000000000000000000000000008000000000000000000001-{-# INLINE _f #-}+-- | Cofactor of SECT409K1 curve.+_h :: Integer+_h = 0x4+{-# INLINABLE _h #-} --- | Generator of SECT409K1 curve-_g :: P-_g = A-     0x60f05f658f49c1ad3ab1890f7184210efd0987e307c84c27accfb8f9f67cc2c460189eb5aaaa62ee222eb1b35540cfe9023746-     0x1e369050b7c4e42acba1dacbf04299c3460782f918ea427e6325165e9ea10e3da5f6c42e9c55215aa9ca27a5863ec48d8e0286b-{-# INLINE _g #-}+-- | Polynomial of SECT409K1 curve.+_p :: Integer+_p = 0x2000000000000000000000000000000000000000000000000000000000000000000000000000000008000000000000000000001+{-# INLINABLE _p #-} --- | Cofactor of SECT409K1 curve-_h :: Integer-_h = 4-{-# INLINE _h #-}+-- | Order of SECT409K1 curve.+_r :: Integer+_r = 0x7ffffffffffffffffffffffffffffffffffffffffffffffffffe5f83b2d4ea20400ec4557d5ed3e3e7ca5b4b5c83b8e01e5fcf+{-# INLINABLE _r #-} --- | Order of SECT409K1 curve-_n :: Integer-_n = 0x7ffffffffffffffffffffffffffffffffffffffffffffffffffe5f83b2d4ea20400ec4557d5ed3e3e7ca5b4b5c83b8e01e5fcf-{-# INLINE _n #-}+-- | Coordinate @X@ of SECT409K1 curve.+_x :: F2m+_x = 0x60f05f658f49c1ad3ab1890f7184210efd0987e307c84c27accfb8f9f67cc2c460189eb5aaaa62ee222eb1b35540cfe9023746+{-# INLINABLE _x #-}++-- | Coordinate @Y@ of SECT409K1 curve.+_y :: F2m+_y = 0x1e369050b7c4e42acba1dacbf04299c3460782f918ea427e6325165e9ea10e3da5f6c42e9c55215aa9ca27a5863ec48d8e0286b+{-# INLINABLE _y #-}++-- | Generator of affine SECT409K1 curve.+gA :: PA+gA = A _x _y+{-# INLINABLE gA #-}++-- | Generator of projective SECT409K1 curve.+gP :: PP+gP = P _x _y 1+{-# INLINABLE gP #-}

src/Curve/Binary/SECT409R1.hs view

@@ -1,74 +1,106 @@ module Curve.Binary.SECT409R1-  ( F2m-  , P-  , _a-  , _b-  , _f-  , _g-  , _h-  , _n+  ( module Curve.Binary+  , module Curve.Binary.SECT409R1   ) where  import Protolude -import BinaryField (BinaryField)+import BinaryField+import PrimeField -import Curve.Binary (BCurve(..), BPoint, Point(..))+import Curve.Binary  ------------------------------------------------------------------------------- -- Types ------------------------------------------------------------------------------- --- | SECT409R1 curve+-- | SECT409R1 curve. data SECT409R1 --- | Field of SECT409R1 curve+-- | Field of points of SECT409R1 curve. type F2m = BinaryField 0x2000000000000000000000000000000000000000000000000000000000000000000000000000000008000000000000000000001 --- | SECT409R1 curve is a binary curve-instance BCurve SECT409R1 F2m where+-- | Field of coefficients of SECT409R1 curve.+type Fr = PrimeField 0x10000000000000000000000000000000000000000000000000001e2aad6a612f33307be5fa47c3c9e052f838164cd37d9a21173++-- | SECT409R1 curve is a binary curve.+instance Curve 'Binary c SECT409R1 F2m Fr => BCurve c SECT409R1 F2m Fr where   a_ = const _a-  {-# INLINE a_ #-}+  {-# INLINABLE a_ #-}   b_ = const _b-  {-# INLINE b_ #-}-  g_ = _g-  {-# INLINE g_ #-}+  {-# INLINABLE b_ #-}+  h_ = const _h+  {-# INLINABLE h_ #-}+  p_ = const _p+  {-# INLINABLE p_ #-}+  r_ = const _r+  {-# INLINABLE r_ #-}+  x_ = const _x+  {-# INLINABLE x_ #-}+  y_ = const _y+  {-# INLINABLE y_ #-} --- | Point of SECT409R1 curve-type P = BPoint SECT409R1 F2m+-- | Affine SECT409R1 curve point.+type PA = BAPoint SECT409R1 F2m Fr +-- | Affine SECT409R1 curve is a binary affine curve.+instance BACurve SECT409R1 F2m Fr where+  gA_ = gA+  {-# INLINABLE gA_ #-}++-- | Projective SECT409R1 point.+type PP = BPPoint SECT409R1 F2m Fr++-- | Projective SECT409R1 curve is a binary projective curve.+instance BPCurve SECT409R1 F2m Fr where+  gP_ = gP+  {-# INLINABLE gP_ #-}+ ------------------------------------------------------------------------------- -- Parameters ------------------------------------------------------------------------------- --- | Coefficient @A@ of SECT409R1 curve+-- | Coefficient @A@ of SECT409R1 curve. _a :: F2m-_a = 1-{-# INLINE _a #-}+_a = 0x1+{-# INLINABLE _a #-} --- | Coefficient @B@ of SECT409R1 curve+-- | Coefficient @B@ of SECT409R1 curve. _b :: F2m _b = 0x21a5c2c8ee9feb5c4b9a753b7b476b7fd6422ef1f3dd674761fa99d6ac27c8a9a197b272822f6cd57a55aa4f50ae317b13545f-{-# INLINE _b #-}+{-# INLINABLE _b #-} --- | Polynomial of SECT409R1 curve-_f :: Integer-_f = 0x2000000000000000000000000000000000000000000000000000000000000000000000000000000008000000000000000000001-{-# INLINE _f #-}+-- | Cofactor of SECT409R1 curve.+_h :: Integer+_h = 0x2+{-# INLINABLE _h #-} --- | Generator of SECT409R1 curve-_g :: P-_g = A-     0x15d4860d088ddb3496b0c6064756260441cde4af1771d4db01ffe5b34e59703dc255a868a1180515603aeab60794e54bb7996a7-     0x61b1cfab6be5f32bbfa78324ed106a7636b9c5a7bd198d0158aa4f5488d08f38514f1fdf4b4f40d2181b3681c364ba0273c706-{-# INLINE _g #-}+-- | Polynomial of SECT409R1 curve.+_p :: Integer+_p = 0x2000000000000000000000000000000000000000000000000000000000000000000000000000000008000000000000000000001+{-# INLINABLE _p #-} --- | Cofactor of SECT409R1 curve-_h :: Integer-_h = 2-{-# INLINE _h #-}+-- | Order of SECT409R1 curve.+_r :: Integer+_r = 0x10000000000000000000000000000000000000000000000000001e2aad6a612f33307be5fa47c3c9e052f838164cd37d9a21173+{-# INLINABLE _r #-} --- | Order of SECT409R1 curve-_n :: Integer-_n = 0x10000000000000000000000000000000000000000000000000001e2aad6a612f33307be5fa47c3c9e052f838164cd37d9a21173-{-# INLINE _n #-}+-- | Coordinate @X@ of SECT409R1 curve.+_x :: F2m+_x = 0x15d4860d088ddb3496b0c6064756260441cde4af1771d4db01ffe5b34e59703dc255a868a1180515603aeab60794e54bb7996a7+{-# INLINABLE _x #-}++-- | Coordinate @Y@ of SECT409R1 curve.+_y :: F2m+_y = 0x61b1cfab6be5f32bbfa78324ed106a7636b9c5a7bd198d0158aa4f5488d08f38514f1fdf4b4f40d2181b3681c364ba0273c706+{-# INLINABLE _y #-}++-- | Generator of affine SECT409R1 curve.+gA :: PA+gA = A _x _y+{-# INLINABLE gA #-}++-- | Generator of projective SECT409R1 curve.+gP :: PP+gP = P _x _y 1+{-# INLINABLE gP #-}

src/Curve/Binary/SECT571K1.hs view

@@ -1,74 +1,106 @@ module Curve.Binary.SECT571K1-  ( F2m-  , P-  , _a-  , _b-  , _f-  , _g-  , _h-  , _n+  ( module Curve.Binary+  , module Curve.Binary.SECT571K1   ) where  import Protolude -import BinaryField (BinaryField)+import BinaryField+import PrimeField -import Curve.Binary (BCurve(..), BPoint, Point(..))+import Curve.Binary  ------------------------------------------------------------------------------- -- Types ------------------------------------------------------------------------------- --- | SECT571K1 curve+-- | SECT571K1 curve. data SECT571K1 --- | Field of SECT571K1 curve+-- | Field of points of SECT571K1 curve. type F2m = BinaryField 0x80000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000425 --- | SECT571K1 curve is a binary curve-instance BCurve SECT571K1 F2m where+-- | Field of coefficients of SECT571K1 curve.+type Fr = PrimeField 0x20000000000000000000000000000000000000000000000000000000000000000000000131850e1f19a63e4b391a8db917f4138b630d84be5d639381e91deb45cfe778f637c1001++-- | SECT571K1 curve is a binary curve.+instance Curve 'Binary c SECT571K1 F2m Fr => BCurve c SECT571K1 F2m Fr where   a_ = const _a-  {-# INLINE a_ #-}+  {-# INLINABLE a_ #-}   b_ = const _b-  {-# INLINE b_ #-}-  g_ = _g-  {-# INLINE g_ #-}+  {-# INLINABLE b_ #-}+  h_ = const _h+  {-# INLINABLE h_ #-}+  p_ = const _p+  {-# INLINABLE p_ #-}+  r_ = const _r+  {-# INLINABLE r_ #-}+  x_ = const _x+  {-# INLINABLE x_ #-}+  y_ = const _y+  {-# INLINABLE y_ #-} --- | Point of SECT571K1 curve-type P = BPoint SECT571K1 F2m+-- | Affine SECT571K1 curve point.+type PA = BAPoint SECT571K1 F2m Fr +-- | Affine SECT571K1 curve is a binary affine curve.+instance BACurve SECT571K1 F2m Fr where+  gA_ = gA+  {-# INLINABLE gA_ #-}++-- | Projective SECT571K1 point.+type PP = BPPoint SECT571K1 F2m Fr++-- | Projective SECT571K1 curve is a binary projective curve.+instance BPCurve SECT571K1 F2m Fr where+  gP_ = gP+  {-# INLINABLE gP_ #-}+ ------------------------------------------------------------------------------- -- Parameters ------------------------------------------------------------------------------- --- | Coefficient @A@ of SECT571K1 curve+-- | Coefficient @A@ of SECT571K1 curve. _a :: F2m-_a = 0-{-# INLINE _a #-}+_a = 0x0+{-# INLINABLE _a #-} --- | Coefficient @B@ of SECT571K1 curve+-- | Coefficient @B@ of SECT571K1 curve. _b :: F2m-_b = 1-{-# INLINE _b #-}+_b = 0x1+{-# INLINABLE _b #-} --- | Polynomial of SECT571K1 curve-_f :: Integer-_f = 0x80000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000425-{-# INLINE _f #-}+-- | Cofactor of SECT571K1 curve.+_h :: Integer+_h = 0x4+{-# INLINABLE _h #-} --- | Generator of SECT571K1 curve-_g :: P-_g = A-     0x26eb7a859923fbc82189631f8103fe4ac9ca2970012d5d46024804801841ca44370958493b205e647da304db4ceb08cbbd1ba39494776fb988b47174dca88c7e2945283a01c8972-     0x349dc807f4fbf374f4aeade3bca95314dd58cec9f307a54ffc61efc006d8a2c9d4979c0ac44aea74fbebbb9f772aedcb620b01a7ba7af1b320430c8591984f601cd4c143ef1c7a3-{-# INLINE _g #-}+-- | Polynomial of SECT571K1 curve.+_p :: Integer+_p = 0x80000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000425+{-# INLINABLE _p #-} --- | Cofactor of SECT571K1 curve-_h :: Integer-_h = 4-{-# INLINE _h #-}+-- | Order of SECT571K1 curve.+_r :: Integer+_r = 0x20000000000000000000000000000000000000000000000000000000000000000000000131850e1f19a63e4b391a8db917f4138b630d84be5d639381e91deb45cfe778f637c1001+{-# INLINABLE _r #-} --- | Order of SECT571K1 curve-_n :: Integer-_n = 0x20000000000000000000000000000000000000000000000000000000000000000000000131850e1f19a63e4b391a8db917f4138b630d84be5d639381e91deb45cfe778f637c1001-{-# INLINE _n #-}+-- | Coordinate @X@ of SECT571K1 curve.+_x :: F2m+_x = 0x26eb7a859923fbc82189631f8103fe4ac9ca2970012d5d46024804801841ca44370958493b205e647da304db4ceb08cbbd1ba39494776fb988b47174dca88c7e2945283a01c8972+{-# INLINABLE _x #-}++-- | Coordinate @Y@ of SECT571K1 curve.+_y :: F2m+_y = 0x349dc807f4fbf374f4aeade3bca95314dd58cec9f307a54ffc61efc006d8a2c9d4979c0ac44aea74fbebbb9f772aedcb620b01a7ba7af1b320430c8591984f601cd4c143ef1c7a3+{-# INLINABLE _y #-}++-- | Generator of affine SECT571K1 curve.+gA :: PA+gA = A _x _y+{-# INLINABLE gA #-}++-- | Generator of projective SECT571K1 curve.+gP :: PP+gP = P _x _y 1+{-# INLINABLE gP #-}

src/Curve/Binary/SECT571R1.hs view

@@ -1,74 +1,106 @@ module Curve.Binary.SECT571R1-  ( F2m-  , P-  , _a-  , _b-  , _f-  , _g-  , _h-  , _n+  ( module Curve.Binary+  , module Curve.Binary.SECT571R1   ) where  import Protolude -import BinaryField (BinaryField)+import BinaryField+import PrimeField -import Curve.Binary (BCurve(..), BPoint, Point(..))+import Curve.Binary  ------------------------------------------------------------------------------- -- Types ------------------------------------------------------------------------------- --- | SECT571R1 curve+-- | SECT571R1 curve. data SECT571R1 --- | Field of SECT571R1 curve+-- | Field of points of SECT571R1 curve. type F2m = BinaryField 0x80000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000425 --- | SECT571R1 curve is a binary curve-instance BCurve SECT571R1 F2m where+-- | Field of coefficients of SECT571R1 curve.+type Fr = PrimeField 0x3ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffe661ce18ff55987308059b186823851ec7dd9ca1161de93d5174d66e8382e9bb2fe84e47++-- | SECT571R1 curve is a binary curve.+instance Curve 'Binary c SECT571R1 F2m Fr => BCurve c SECT571R1 F2m Fr where   a_ = const _a-  {-# INLINE a_ #-}+  {-# INLINABLE a_ #-}   b_ = const _b-  {-# INLINE b_ #-}-  g_ = _g-  {-# INLINE g_ #-}+  {-# INLINABLE b_ #-}+  h_ = const _h+  {-# INLINABLE h_ #-}+  p_ = const _p+  {-# INLINABLE p_ #-}+  r_ = const _r+  {-# INLINABLE r_ #-}+  x_ = const _x+  {-# INLINABLE x_ #-}+  y_ = const _y+  {-# INLINABLE y_ #-} --- | Point of SECT571R1 curve-type P = BPoint SECT571R1 F2m+-- | Affine SECT571R1 curve point.+type PA = BAPoint SECT571R1 F2m Fr +-- | Affine SECT571R1 curve is a binary affine curve.+instance BACurve SECT571R1 F2m Fr where+  gA_ = gA+  {-# INLINABLE gA_ #-}++-- | Projective SECT571R1 point.+type PP = BPPoint SECT571R1 F2m Fr++-- | Projective SECT571R1 curve is a binary projective curve.+instance BPCurve SECT571R1 F2m Fr where+  gP_ = gP+  {-# INLINABLE gP_ #-}+ ------------------------------------------------------------------------------- -- Parameters ------------------------------------------------------------------------------- --- | Coefficient @A@ of SECT571R1 curve+-- | Coefficient @A@ of SECT571R1 curve. _a :: F2m-_a = 1-{-# INLINE _a #-}+_a = 0x1+{-# INLINABLE _a #-} --- | Coefficient @B@ of SECT571R1 curve+-- | Coefficient @B@ of SECT571R1 curve. _b :: F2m _b = 0x2f40e7e2221f295de297117b7f3d62f5c6a97ffcb8ceff1cd6ba8ce4a9a18ad84ffabbd8efa59332be7ad6756a66e294afd185a78ff12aa520e4de739baca0c7ffeff7f2955727a-{-# INLINE _b #-}+{-# INLINABLE _b #-} --- | Polynomial of SECT571R1 curve-_f :: Integer-_f = 0x80000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000425-{-# INLINE _f #-}+-- | Cofactor of SECT571R1 curve.+_h :: Integer+_h = 0x2+{-# INLINABLE _h #-} --- | Generator of SECT571R1 curve-_g :: P-_g = A-     0x303001d34b856296c16c0d40d3cd7750a93d1d2955fa80aa5f40fc8db7b2abdbde53950f4c0d293cdd711a35b67fb1499ae60038614f1394abfa3b4c850d927e1e7769c8eec2d19-     0x37bf27342da639b6dccfffeb73d69d78c6c27a6009cbbca1980f8533921e8a684423e43bab08a576291af8f461bb2a8b3531d2f0485c19b16e2f1516e23dd3c1a4827af1b8ac15b-{-# INLINE _g #-}+-- | Polynomial of SECT571R1 curve.+_p :: Integer+_p = 0x80000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000425+{-# INLINABLE _p #-} --- | Cofactor of SECT571R1 curve-_h :: Integer-_h = 2-{-# INLINE _h #-}+-- | Order of SECT571R1 curve.+_r :: Integer+_r = 0x3ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffe661ce18ff55987308059b186823851ec7dd9ca1161de93d5174d66e8382e9bb2fe84e47+{-# INLINABLE _r #-} --- | Order of SECT571R1 curve-_n :: Integer-_n = 0x3ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffe661ce18ff55987308059b186823851ec7dd9ca1161de93d5174d66e8382e9bb2fe84e47-{-# INLINE _n #-}+-- | Coordinate @X@ of SECT571R1 curve.+_x :: F2m+_x = 0x303001d34b856296c16c0d40d3cd7750a93d1d2955fa80aa5f40fc8db7b2abdbde53950f4c0d293cdd711a35b67fb1499ae60038614f1394abfa3b4c850d927e1e7769c8eec2d19+{-# INLINABLE _x #-}++-- | Coordinate @Y@ of SECT571R1 curve.+_y :: F2m+_y = 0x37bf27342da639b6dccfffeb73d69d78c6c27a6009cbbca1980f8533921e8a684423e43bab08a576291af8f461bb2a8b3531d2f0485c19b16e2f1516e23dd3c1a4827af1b8ac15b+{-# INLINABLE _y #-}++-- | Generator of affine SECT571R1 curve.+gA :: PA+gA = A _x _y+{-# INLINABLE gA #-}++-- | Generator of projective SECT571R1 curve.+gP :: PP+gP = P _x _y 1+{-# INLINABLE gP #-}

src/Curve/Edwards.hs view

@@ -1,72 +1,92 @@+{-# OPTIONS -fno-warn-orphans #-}+ module Curve.Edwards-  ( ECurve(..)-  , EPoint-  , Point(..)+  ( module Curve+  , module Curve.Edwards+  , module Group   ) where  import Protolude -import Control.Monad.Random (Random(..), getRandom) import GaloisField (GaloisField(..))-import Test.Tasty.QuickCheck (Arbitrary(..), suchThatMap) import Text.PrettyPrint.Leijen.Text (Pretty(..)) -import Curve (Curve(..))+import Curve (Coordinates(..), Curve(..), Form(..))+import Group (Group(..))  ---------------------------------------------------------------------------------- Types+-- Edwards form ------------------------------------------------------------------------------- --- | Edwards curve representation.-data E+-- | Edwards points.+type EPoint = Point 'Edwards --- | Edwards curve points.-type EPoint = Point E+-- | Edwards curves.+class (GaloisField q, GaloisField r, Curve 'Edwards c e q r) => ECurve c e q r where+  {-# MINIMAL a_, d_, h_, q_, r_, x_, y_ #-}+  a_ :: EPoint c e q r -> q       -- ^ Coefficient @A@.+  d_ :: EPoint c e q r -> q       -- ^ Coefficient @D@.+  h_ :: EPoint c e q r -> Integer -- ^ Curve cofactor.+  q_ :: EPoint c e q r -> Integer -- ^ Curve characteristic.+  r_ :: EPoint c e q r -> Integer -- ^ Curve order.+  x_ :: EPoint c e q r -> q       -- ^ Coordinate @X@.+  y_ :: EPoint c e q r -> q       -- ^ Coordinate @Y@. --- | Edwards curves @Ax^2 + y^2 = 1 + Dx^2y^2@.-class Curve E c k => ECurve c k where-  a_ :: c -> k     -- ^ Coefficient @A@.-  d_ :: c -> k     -- ^ Coefficient @D@.-  g_ :: EPoint c k -- ^ Curve generator.+-------------------------------------------------------------------------------+-- Affine coordinates+------------------------------------------------------------------------------- --- Edwards points are arbitrary.-instance (GaloisField k, ECurve c k) => Arbitrary (Point E c k) where-  arbitrary = suchThatMap arbitrary point+-- | Edwards affine curves.+type EAPoint = EPoint 'Affine --- Edwards points are pretty.-instance (GaloisField k, ECurve c k) => Pretty (Point E c k) where-  pretty (A x y) = pretty (x, y)+-- | Edwards affine curves @Ax^2 + y^2 = 1 + Dx^2y^2@.+class ECurve 'Affine e q r => EACurve e q r where+  {-# MINIMAL gA_ #-}+  gA_ :: EAPoint e q r -- ^ Curve generator. --- Edwards points are random.-instance (GaloisField k, ECurve c k) => Random (Point E c k) where-  random g = case point x of-    Just p -> (p, g')-    _      -> random g'+-- Edwards affine curves are elliptic curves.+instance EACurve e q r => Curve 'Edwards 'Affine e q r where++  data instance Point 'Edwards 'Affine e q r = A q q -- ^ Affine point.+    deriving (Eq, Generic, NFData, Read, Show)++  char = q_+  {-# INLINABLE char #-}++  cof = h_+  {-# INLINABLE cof #-}++  disc _ = d * (1 - d)     where-      (x, g') = random g-  {-# INLINE random #-}-  randomR  = panic "not implemented."+      d = d_ (witness :: EAPoint e q r)+  {-# INLINABLE disc #-} ----------------------------------------------------------------------------------- Operations--------------------------------------------------------------------------------+  fromA = identity+  {-# INLINABLE fromA #-} --- Edwards curves are elliptic curves.-instance (GaloisField k, ECurve c k) => Curve E c k where+  point x y = let p = A x y in if def p then Just p else Nothing+  {-# INLINABLE point #-} -  data instance Point E c k = A k k -- ^ Affine point.-    deriving (Eq, Generic, NFData, Read, Show)+  pointX x = A x <$> yX (witness :: EAPoint e q r) x+  {-# INLINABLE pointX #-} -  id = A 0 1-  {-# INLINE id #-}+  toA = identity+  {-# INLINABLE toA #-} -  inv (A x y) = A (-x) y-  {-# INLINE inv #-}+  yX _ x = sr ((1 - a * xx) / (1 - d * xx))+    where+      a  = a_ (witness :: EAPoint e q r)+      d  = d_ (witness :: EAPoint e q r)+      xx = x * x+  {-# INLINABLE yX #-} +-- Edwards affine points are groups.+instance EACurve e q r => Group (EAPoint e q r) where+   add (A x1 y1) (A x2 y2) = A x3 y3     where-      a    = a_ (witness :: c)-      d    = d_ (witness :: c)+      a    = a_ (witness :: EAPoint e q r)+      d    = d_ (witness :: EAPoint e q r)       x1x2 = x1 * x2       y1y2 = y1 * y2       x1y2 = x1 * y2@@ -74,27 +94,149 @@       dxy  = d * x1x2 * y1y2       x3   = (x1y2 + x2y1) / (1 + dxy)       y3   = (y1y2 - a * x1x2) / (1 - dxy)-  {-# INLINE add #-}+  {-# INLINABLE add #-} +  dbl = join add+  {-# INLINABLE dbl #-}+   def (A x y) = a * xx + yy == 1 + d * xx * yy     where-      a  = a_ (witness :: c)-      d  = d_ (witness :: c)+      a  = a_ (witness :: EAPoint e q r)+      d  = d_ (witness :: EAPoint e q r)       xx = x * x       yy = y * y-  {-# INLINE def #-}+  {-# INLINABLE def #-} +  gen = gA_+  {-# INLINABLE gen #-}++  id = A 0 1+  {-# INLINABLE id #-}++  inv (A x y) = A (-x) y+  {-# INLINABLE inv #-}++  order = r_+  {-# INLINABLE order #-}++-- Edwards affine points are pretty.+instance EACurve e q r => Pretty (EAPoint e q r) where++  pretty (A x y) = pretty (x, y)++-------------------------------------------------------------------------------+-- Projective coordinates+-------------------------------------------------------------------------------++-- | Edwards projective curves.+type EPPoint = EPoint 'Projective++-- | Edwards projective curves @Ax^2z^2 + y^2z^2 = z^4 + Dx^2y^2@.+class ECurve 'Projective e q r => EPCurve e q r where+  {-# MINIMAL gP_ #-}+  gP_ :: EPPoint e q r -- ^ Curve generator.++-- Edwards projective curves are elliptic curves.+instance EPCurve e q r => Curve 'Edwards 'Projective e q r where++  data instance Point 'Edwards 'Projective e q r = P q q q -- ^ Projective point.+    deriving (Generic, NFData, Read, Show)++  char = q_+  {-# INLINABLE char #-}++  cof = h_+  {-# INLINABLE cof #-}+   disc _ = d * (1 - d)     where-      d = d_ (witness :: c)-  {-# INLINE disc #-}+      d = d_ (witness :: EPPoint e q r)+  {-# INLINABLE disc #-} -  point x = A x <$> sr ((1 - a * xx) / (1 - d * xx))+  fromA (A x y) = P x y 1+  {-# INLINABLE fromA #-}++  point x y = let p = P x y 1 in if def p then Just p else Nothing+  {-# INLINABLE point #-}++  pointX x = flip (P x) 1 <$> yX (witness :: EPPoint e q r) x+  {-# INLINABLE pointX #-}++  toA (P x y z) = A (x / z) (y / z)+  {-# INLINABLE toA #-}++  yX _ x = sr ((1 - a * xx) / (1 - d * xx))     where-      a  = a_ (witness :: c)-      d  = d_ (witness :: c)+      a  = a_ (witness :: EPPoint e q r)+      d  = d_ (witness :: EPPoint e q r)       xx = x * x-  {-# INLINE point #-}+  {-# INLINABLE yX #-} -  rnd = getRandom-  {-# INLINE rnd #-}+-- Edwards projective points are groups.+instance EPCurve e q r => Group (EPPoint e q r) where++  -- Addition formula add-2008-bbjlp+  add (P x1 y1 z1) (P x2 y2 z2) = P x3 y3 z3+    where+      a' = a_ (witness :: EPPoint e q r)+      d' = d_ (witness :: EPPoint e q r)+      a  = z1 * z2+      b  = a * a+      c  = x1 * x2+      d  = y1 * y2+      e  = d' * c * d+      f  = b - e+      g  = b + e+      x3 = a * f * ((x1 + y1) * (x2 + y2) - c - d)+      y3 = a * g * (d - a' * c)+      z3 = f * g+  {-# INLINABLE add #-}++  -- Doubling formula dbl-2008-bbjlp+  dbl (P x1 y1 z1) = P x3 y3 z3+    where+      a  = a_ (witness :: EPPoint e q r)+      xy = x1 + y1+      b  = xy * xy+      c  = x1 * x1+      d  = y1 * y1+      e  = a * c+      f  = e + d+      h  = z1 * z1+      j  = f - 2 * h+      x3 = (b - c - d) * j+      y3 = f * (e - d)+      z3 = f * j+  {-# INLINABLE dbl #-}++  def (P x y z) = (a * xx + yy - zz) * zz == d * xx * yy+    where+      a  = a_ (witness :: EPPoint e q r)+      d  = d_ (witness :: EPPoint e q r)+      xx = x * x+      yy = y * y+      zz = z * z+  {-# INLINABLE def #-}++  gen = gP_+  {-# INLINABLE gen #-}++  id = P 0 1 1+  {-# INLINABLE id #-}++  inv (P x y z) = P (-x) y z+  {-# INLINABLE inv #-}++  order = r_+  {-# INLINABLE order #-}++-- Edwards projective points are equatable.+instance EPCurve e q r => Eq (EPPoint e q r) where++  P x1 y1 z1 == P x2 y2 z2 = z1 == 0 && z2 == 0+    || x1 * z2 == x2 * z1 && y1 * z2 == y2 * z1++-- Edwards projective points are pretty.+instance EPCurve e q r => Pretty (EPPoint e q r) where++  pretty (P x y z) = pretty (x, y, z)

src/Curve/Edwards/Curve1174.hs view

@@ -1,74 +1,105 @@ module Curve.Edwards.Curve1174-  ( Fp-  , P-  , _a-  , _d-  , _g-  , _h-  , _n-  , _p+  ( module Curve.Edwards+  , module Curve.Edwards.Curve1174   ) where  import Protolude -import PrimeField (PrimeField)+import PrimeField -import Curve.Edwards (ECurve(..), EPoint, Point(..))+import Curve.Edwards  ------------------------------------------------------------------------------- -- Types ------------------------------------------------------------------------------- --- | Curve1174 curve+-- | Curve1174 curve. data Curve1174 --- | Field of Curve1174 curve-type Fp = PrimeField 0x7fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff7+-- | Field of points of Curve1174 curve.+type Fq = PrimeField 0x7fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff7 --- | Curve1174 curve is an Edwards curve-instance ECurve Curve1174 Fp where+-- | Field of coefficients of Curve1174 curve.+type Fr = PrimeField 0x1fffffffffffffffffffffffffffffff77965c4dfd307348944d45fd166c971++-- | Curve1174 curve is an Edwards curve.+instance Curve 'Edwards c Curve1174 Fq Fr => ECurve c Curve1174 Fq Fr where   a_ = const _a-  {-# INLINE a_ #-}+  {-# INLINABLE a_ #-}   d_ = const _d-  {-# INLINE d_ #-}-  g_ = _g-  {-# INLINE g_ #-}+  {-# INLINABLE d_ #-}+  h_ = const _h+  {-# INLINABLE h_ #-}+  q_ = const _q+  {-# INLINABLE q_ #-}+  r_ = const _r+  {-# INLINABLE r_ #-}+  x_ = const _x+  {-# INLINABLE x_ #-}+  y_ = const _y+  {-# INLINABLE y_ #-} --- | Point of Curve1174 curve-type P = EPoint Curve1174 Fp+-- | Affine Curve1174 curve point.+type PA = EAPoint Curve1174 Fq Fr +-- | Affine Curve1174 curve is an Edwards affine curve.+instance EACurve Curve1174 Fq Fr where+  gA_ = gA+  {-# INLINABLE gA_ #-}++-- | Projective Curve1174 point.+type PP = EPPoint Curve1174 Fq Fr++-- | Projective Curve1174 curve is an Edwards projective curve.+instance EPCurve Curve1174 Fq Fr where+  gP_ = gP+  {-# INLINABLE gP_ #-}+ ------------------------------------------------------------------------------- -- Parameters ------------------------------------------------------------------------------- --- | Coefficient @A@ of Curve1174 curve-_a :: Fp-_a = 1-{-# INLINE _a #-}+-- | Coefficient @A@ of Curve1174 curve.+_a :: Fq+_a = 0x1+{-# INLINABLE _a #-} --- | Coefficient @D@ of Curve1174 curve-_d :: Fp+-- | Coefficient @D@ of Curve1174 curve.+_d :: Fq _d = 0x7fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffb61-{-# INLINE _d #-}---- | Generator of Curve1174 curve-_g :: P-_g = A-     0x37fbb0cea308c479343aee7c029a190c021d96a492ecd6516123f27bce29eda-     0x6b72f82d47fb7cc6656841169840e0c4fe2dee2af3f976ba4ccb1bf9b46360e-{-# INLINE _g #-}+{-# INLINABLE _d #-} --- | Cofactor of Curve1174 curve+-- | Cofactor of Curve1174 curve. _h :: Integer-_h = 4-{-# INLINE _h #-}+_h = 0x4+{-# INLINABLE _h #-} --- | Order of Curve1174 curve-_n :: Integer-_n = 0x1fffffffffffffffffffffffffffffff77965c4dfd307348944d45fd166c971-{-# INLINE _n #-}+-- | Characteristic of Curve1174 curve.+_q :: Integer+_q = 0x7fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff7+{-# INLINABLE _q #-} --- | Characteristic of Curve1174 curve-_p :: Integer-_p = 0x7fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff7-{-# INLINE _p #-}+-- | Order of Curve1174 curve.+_r :: Integer+_r = 0x1fffffffffffffffffffffffffffffff77965c4dfd307348944d45fd166c971+{-# INLINABLE _r #-}++-- | Coordinate @X@ of Curve1174 curve.+_x :: Fq+_x = 0x37fbb0cea308c479343aee7c029a190c021d96a492ecd6516123f27bce29eda+{-# INLINABLE _x #-}++-- | Coordinate @Y@ of Curve1174 curve.+_y :: Fq+_y = 0x6b72f82d47fb7cc6656841169840e0c4fe2dee2af3f976ba4ccb1bf9b46360e+{-# INLINABLE _y #-}++-- | Generator of affine Curve1174 curve.+gA :: PA+gA = A _x _y+{-# INLINABLE gA #-}++-- | Generator of projective Curve1174 curve.+gP :: PP+gP = P _x _y 1+{-# INLINABLE gP #-}

src/Curve/Edwards/Curve41417.hs view

@@ -1,74 +1,105 @@ module Curve.Edwards.Curve41417-  ( Fp-  , P-  , _a-  , _d-  , _g-  , _h-  , _n-  , _p+  ( module Curve.Edwards+  , module Curve.Edwards.Curve41417   ) where  import Protolude -import PrimeField (PrimeField)+import PrimeField -import Curve.Edwards (ECurve(..), EPoint, Point(..))+import Curve.Edwards  ------------------------------------------------------------------------------- -- Types ------------------------------------------------------------------------------- --- | Curve41417 curve+-- | Curve41417 curve. data Curve41417 --- | Field of Curve41417 curve-type Fp = PrimeField 0x3fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffef+-- | Field of points of Curve41417 curve.+type Fq = PrimeField 0x3fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffef --- | Curve41417 curve is an Edwards curve-instance ECurve Curve41417 Fp where+-- | Field of coefficients of Curve41417 curve.+type Fr = PrimeField 0x7ffffffffffffffffffffffffffffffffffffffffffffffffffeb3cc92414cf706022b36f1c0338ad63cf181b0e71a5e106af79++-- | Curve41417 curve is an Edwards curve.+instance Curve 'Edwards c Curve41417 Fq Fr => ECurve c Curve41417 Fq Fr where   a_ = const _a-  {-# INLINE a_ #-}+  {-# INLINABLE a_ #-}   d_ = const _d-  {-# INLINE d_ #-}-  g_ = _g-  {-# INLINE g_ #-}+  {-# INLINABLE d_ #-}+  h_ = const _h+  {-# INLINABLE h_ #-}+  q_ = const _q+  {-# INLINABLE q_ #-}+  r_ = const _r+  {-# INLINABLE r_ #-}+  x_ = const _x+  {-# INLINABLE x_ #-}+  y_ = const _y+  {-# INLINABLE y_ #-} --- | Point of Curve41417 curve-type P = EPoint Curve41417 Fp+-- | Affine Curve41417 curve point.+type PA = EAPoint Curve41417 Fq Fr +-- | Affine Curve41417 curve is an Edwards affine curve.+instance EACurve Curve41417 Fq Fr where+  gA_ = gA+  {-# INLINABLE gA_ #-}++-- | Projective Curve41417 point.+type PP = EPPoint Curve41417 Fq Fr++-- | Projective Curve41417 curve is an Edwards projective curve.+instance EPCurve Curve41417 Fq Fr where+  gP_ = gP+  {-# INLINABLE gP_ #-}+ ------------------------------------------------------------------------------- -- Parameters ------------------------------------------------------------------------------- --- | Coefficient @A@ of Curve41417 curve-_a :: Fp-_a = 1-{-# INLINE _a #-}+-- | Coefficient @A@ of Curve41417 curve.+_a :: Fq+_a = 0x1+{-# INLINABLE _a #-} --- | Coefficient @D@ of Curve41417 curve-_d :: Fp+-- | Coefficient @D@ of Curve41417 curve.+_d :: Fq _d = 0xe21-{-# INLINE _d #-}---- | Generator of Curve41417 curve-_g :: P-_g = A-     0x1a334905141443300218c0631c326e5fcd46369f44c03ec7f57ff35498a4ab4d6d6ba111301a73faa8537c64c4fd3812f3cbc595-     0x22-{-# INLINE _g #-}+{-# INLINABLE _d #-} --- | Cofactor of Curve41417 curve+-- | Cofactor of Curve41417 curve. _h :: Integer-_h = 8-{-# INLINE _h #-}+_h = 0x8+{-# INLINABLE _h #-} --- | Order of Curve41417 curve-_n :: Integer-_n = 0x7ffffffffffffffffffffffffffffffffffffffffffffffffffeb3cc92414cf706022b36f1c0338ad63cf181b0e71a5e106af79-{-# INLINE _n #-}+-- | Characteristic of Curve41417 curve.+_q :: Integer+_q = 0x3fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffef+{-# INLINABLE _q #-} --- | Characteristic of Curve41417 curve-_p :: Integer-_p = 0x3fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffef-{-# INLINE _p #-}+-- | Order of Curve41417 curve.+_r :: Integer+_r = 0x7ffffffffffffffffffffffffffffffffffffffffffffffffffeb3cc92414cf706022b36f1c0338ad63cf181b0e71a5e106af79+{-# INLINABLE _r #-}++-- | Coordinate @X@ of Curve41417 curve.+_x :: Fq+_x = 0x1a334905141443300218c0631c326e5fcd46369f44c03ec7f57ff35498a4ab4d6d6ba111301a73faa8537c64c4fd3812f3cbc595+{-# INLINABLE _x #-}++-- | Coordinate @Y@ of Curve41417 curve.+_y :: Fq+_y = 0x22+{-# INLINABLE _y #-}++-- | Generator of affine Curve41417 curve.+gA :: PA+gA = A _x _y+{-# INLINABLE gA #-}++-- | Generator of projective Curve41417 curve.+gP :: PP+gP = P _x _y 1+{-# INLINABLE gP #-}

src/Curve/Edwards/E222.hs view

@@ -1,74 +1,105 @@ module Curve.Edwards.E222-  ( Fp-  , P-  , _a-  , _d-  , _g-  , _h-  , _n-  , _p+  ( module Curve.Edwards+  , module Curve.Edwards.E222   ) where  import Protolude -import PrimeField (PrimeField)+import PrimeField -import Curve.Edwards (ECurve(..), EPoint, Point(..))+import Curve.Edwards  ------------------------------------------------------------------------------- -- Types ------------------------------------------------------------------------------- --- | E-222 curve+-- | E222 curve. data E222 --- | Field of E-222 curve-type Fp = PrimeField 0x3fffffffffffffffffffffffffffffffffffffffffffffffffffff8b+-- | Field of points of E222 curve.+type Fq = PrimeField 0x3fffffffffffffffffffffffffffffffffffffffffffffffffffff8b --- | E-222 curve is an Edwards curve-instance ECurve E222 Fp where+-- | Field of coefficients of E222 curve.+type Fr = PrimeField 0xffffffffffffffffffffffffffff70cbc95e932f802f31423598cbf++-- | E222 curve is an Edwards curve.+instance Curve 'Edwards c E222 Fq Fr => ECurve c E222 Fq Fr where   a_ = const _a-  {-# INLINE a_ #-}+  {-# INLINABLE a_ #-}   d_ = const _d-  {-# INLINE d_ #-}-  g_ = _g-  {-# INLINE g_ #-}+  {-# INLINABLE d_ #-}+  h_ = const _h+  {-# INLINABLE h_ #-}+  q_ = const _q+  {-# INLINABLE q_ #-}+  r_ = const _r+  {-# INLINABLE r_ #-}+  x_ = const _x+  {-# INLINABLE x_ #-}+  y_ = const _y+  {-# INLINABLE y_ #-} --- | Point of E-222 curve-type P = EPoint E222 Fp+-- | Affine E222 curve point.+type PA = EAPoint E222 Fq Fr +-- | Affine E222 curve is an Edwards affine curve.+instance EACurve E222 Fq Fr where+  gA_ = gA+  {-# INLINABLE gA_ #-}++-- | Projective E222 point.+type PP = EPPoint E222 Fq Fr++-- | Projective E222 curve is an Edwards projective curve.+instance EPCurve E222 Fq Fr where+  gP_ = gP+  {-# INLINABLE gP_ #-}+ ------------------------------------------------------------------------------- -- Parameters ------------------------------------------------------------------------------- --- | Coefficient @A@ of E-222 curve-_a :: Fp-_a = 1-{-# INLINE _a #-}+-- | Coefficient @A@ of E222 curve.+_a :: Fq+_a = 0x1+{-# INLINABLE _a #-} --- | Coefficient @D@ of E-222 curve-_d :: Fp+-- | Coefficient @D@ of E222 curve.+_d :: Fq _d = 0x27166-{-# INLINE _d #-}---- | Generator of E-222 curve-_g :: P-_g = A-     0x19b12bb156a389e55c9768c303316d07c23adab3736eb2bc3eb54e51-     0x1c-{-# INLINE _g #-}+{-# INLINABLE _d #-} --- | Cofactor of E-222 curve+-- | Cofactor of E222 curve. _h :: Integer-_h = 4-{-# INLINE _h #-}+_h = 0x4+{-# INLINABLE _h #-} --- | Order of E-222 curve-_n :: Integer-_n = 0xffffffffffffffffffffffffffff70cbc95e932f802f31423598cbf-{-# INLINE _n #-}+-- | Characteristic of E222 curve.+_q :: Integer+_q = 0x3fffffffffffffffffffffffffffffffffffffffffffffffffffff8b+{-# INLINABLE _q #-} --- | Characteristic of E-222 curve-_p :: Integer-_p = 0x3fffffffffffffffffffffffffffffffffffffffffffffffffffff8b-{-# INLINE _p #-}+-- | Order of E222 curve.+_r :: Integer+_r = 0xffffffffffffffffffffffffffff70cbc95e932f802f31423598cbf+{-# INLINABLE _r #-}++-- | Coordinate @X@ of E222 curve.+_x :: Fq+_x = 0x19b12bb156a389e55c9768c303316d07c23adab3736eb2bc3eb54e51+{-# INLINABLE _x #-}++-- | Coordinate @Y@ of E222 curve.+_y :: Fq+_y = 0x1c+{-# INLINABLE _y #-}++-- | Generator of affine E222 curve.+gA :: PA+gA = A _x _y+{-# INLINABLE gA #-}++-- | Generator of projective E222 curve.+gP :: PP+gP = P _x _y 1+{-# INLINABLE gP #-}

src/Curve/Edwards/E382.hs view

@@ -1,74 +1,105 @@ module Curve.Edwards.E382-  ( Fp-  , P-  , _a-  , _d-  , _g-  , _h-  , _n-  , _p+  ( module Curve.Edwards+  , module Curve.Edwards.E382   ) where  import Protolude -import PrimeField (PrimeField)+import PrimeField -import Curve.Edwards (ECurve(..), EPoint, Point(..))+import Curve.Edwards  ------------------------------------------------------------------------------- -- Types ------------------------------------------------------------------------------- --- | E-382 curve+-- | E382 curve. data E382 --- | Field of E-382 curve-type Fp = PrimeField 0x3fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff97+-- | Field of points of E382 curve.+type Fq = PrimeField 0x3fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff97 --- | E-382 curve is an Edwards curve-instance ECurve E382 Fp where+-- | Field of coefficients of E382 curve.+type Fr = PrimeField 0xfffffffffffffffffffffffffffffffffffffffffffffffd5fb21f21e95eee17c5e69281b102d2773e27e13fd3c9719++-- | E382 curve is an Edwards curve.+instance Curve 'Edwards c E382 Fq Fr => ECurve c E382 Fq Fr where   a_ = const _a-  {-# INLINE a_ #-}+  {-# INLINABLE a_ #-}   d_ = const _d-  {-# INLINE d_ #-}-  g_ = _g-  {-# INLINE g_ #-}+  {-# INLINABLE d_ #-}+  h_ = const _h+  {-# INLINABLE h_ #-}+  q_ = const _q+  {-# INLINABLE q_ #-}+  r_ = const _r+  {-# INLINABLE r_ #-}+  x_ = const _x+  {-# INLINABLE x_ #-}+  y_ = const _y+  {-# INLINABLE y_ #-} --- | Point of E-382 curve-type P = EPoint E382 Fp+-- | Affine E382 curve point.+type PA = EAPoint E382 Fq Fr +-- | Affine E382 curve is an Edwards affine curve.+instance EACurve E382 Fq Fr where+  gA_ = gA+  {-# INLINABLE gA_ #-}++-- | Projective E382 point.+type PP = EPPoint E382 Fq Fr++-- | Projective E382 curve is an Edwards projective curve.+instance EPCurve E382 Fq Fr where+  gP_ = gP+  {-# INLINABLE gP_ #-}+ ------------------------------------------------------------------------------- -- Parameters ------------------------------------------------------------------------------- --- | Coefficient @A@ of E-382 curve-_a :: Fp-_a = 1-{-# INLINE _a #-}+-- | Coefficient @A@ of E382 curve.+_a :: Fq+_a = 0x1+{-# INLINABLE _a #-} --- | Coefficient @D@ of E-382 curve-_d :: Fp+-- | Coefficient @D@ of E382 curve.+_d :: Fq _d = 0x3ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffef8e1-{-# INLINE _d #-}---- | Generator of E-382 curve-_g :: P-_g = A-     0x196f8dd0eab20391e5f05be96e8d20ae68f840032b0b64352923bab85364841193517dbce8105398ebc0cc9470f79603-     0x11-{-# INLINE _g #-}+{-# INLINABLE _d #-} --- | Cofactor of E-382 curve+-- | Cofactor of E382 curve. _h :: Integer-_h = 4-{-# INLINE _h #-}+_h = 0x4+{-# INLINABLE _h #-} --- | Order of E-382 curve-_n :: Integer-_n = 0xfffffffffffffffffffffffffffffffffffffffffffffffd5fb21f21e95eee17c5e69281b102d2773e27e13fd3c9719-{-# INLINE _n #-}+-- | Characteristic of E382 curve.+_q :: Integer+_q = 0x3fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff97+{-# INLINABLE _q #-} --- | Characteristic of E-382 curve-_p :: Integer-_p = 0x3fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff97-{-# INLINE _p #-}+-- | Order of E382 curve.+_r :: Integer+_r = 0xfffffffffffffffffffffffffffffffffffffffffffffffd5fb21f21e95eee17c5e69281b102d2773e27e13fd3c9719+{-# INLINABLE _r #-}++-- | Coordinate @X@ of E382 curve.+_x :: Fq+_x = 0x196f8dd0eab20391e5f05be96e8d20ae68f840032b0b64352923bab85364841193517dbce8105398ebc0cc9470f79603+{-# INLINABLE _x #-}++-- | Coordinate @Y@ of E382 curve.+_y :: Fq+_y = 0x11+{-# INLINABLE _y #-}++-- | Generator of affine E382 curve.+gA :: PA+gA = A _x _y+{-# INLINABLE gA #-}++-- | Generator of projective E382 curve.+gP :: PP+gP = P _x _y 1+{-# INLINABLE gP #-}

src/Curve/Edwards/E521.hs view

@@ -1,74 +1,105 @@ module Curve.Edwards.E521-  ( Fp-  , P-  , _a-  , _d-  , _g-  , _h-  , _n-  , _p+  ( module Curve.Edwards+  , module Curve.Edwards.E521   ) where  import Protolude -import PrimeField (PrimeField)+import PrimeField -import Curve.Edwards (ECurve(..), EPoint, Point(..))+import Curve.Edwards  ------------------------------------------------------------------------------- -- Types ------------------------------------------------------------------------------- --- | E-521 curve+-- | E521 curve. data E521 --- | Field of E-521 curve-type Fp = PrimeField 0x1ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff+-- | Field of points of E521 curve.+type Fq = PrimeField 0x1ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff --- | E-521 curve is an Edwards curve-instance ECurve E521 Fp where+-- | Field of coefficients of E521 curve.+type Fr = PrimeField 0x7ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffd15b6c64746fc85f736b8af5e7ec53f04fbd8c4569a8f1f4540ea2435f5180d6b++-- | E521 curve is an Edwards curve.+instance Curve 'Edwards c E521 Fq Fr => ECurve c E521 Fq Fr where   a_ = const _a-  {-# INLINE a_ #-}+  {-# INLINABLE a_ #-}   d_ = const _d-  {-# INLINE d_ #-}-  g_ = _g-  {-# INLINE g_ #-}+  {-# INLINABLE d_ #-}+  h_ = const _h+  {-# INLINABLE h_ #-}+  q_ = const _q+  {-# INLINABLE q_ #-}+  r_ = const _r+  {-# INLINABLE r_ #-}+  x_ = const _x+  {-# INLINABLE x_ #-}+  y_ = const _y+  {-# INLINABLE y_ #-} --- | Point of E-521 curve-type P = EPoint E521 Fp+-- | Affine E521 curve point.+type PA = EAPoint E521 Fq Fr +-- | Affine E521 curve is an Edwards affine curve.+instance EACurve E521 Fq Fr where+  gA_ = gA+  {-# INLINABLE gA_ #-}++-- | Projective E521 point.+type PP = EPPoint E521 Fq Fr++-- | Projective E521 curve is an Edwards projective curve.+instance EPCurve E521 Fq Fr where+  gP_ = gP+  {-# INLINABLE gP_ #-}+ ------------------------------------------------------------------------------- -- Parameters ------------------------------------------------------------------------------- --- | Coefficient @A@ of E-521 curve-_a :: Fp-_a = 1-{-# INLINE _a #-}+-- | Coefficient @A@ of E521 curve.+_a :: Fq+_a = 0x1+{-# INLINABLE _a #-} --- | Coefficient @D@ of E-521 curve-_d :: Fp+-- | Coefficient @D@ of E521 curve.+_d :: Fq _d = 0x1fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffa4331-{-# INLINE _d #-}---- | Generator of E-521 curve-_g :: P-_g = A-     0x752cb45c48648b189df90cb2296b2878a3bfd9f42fc6c818ec8bf3c9c0c6203913f6ecc5ccc72434b1ae949d568fc99c6059d0fb13364838aa302a940a2f19ba6c-     0xc-{-# INLINE _g #-}+{-# INLINABLE _d #-} --- | Cofactor of E-521 curve+-- | Cofactor of E521 curve. _h :: Integer-_h = 4-{-# INLINE _h #-}+_h = 0x4+{-# INLINABLE _h #-} --- | Order of E-521 curve-_n :: Integer-_n = 0x7ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffd15b6c64746fc85f736b8af5e7ec53f04fbd8c4569a8f1f4540ea2435f5180d6b-{-# INLINE _n #-}+-- | Characteristic of E521 curve.+_q :: Integer+_q = 0x1ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff+{-# INLINABLE _q #-} --- | Characteristic of E-521 curve-_p :: Integer-_p = 0x1ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff-{-# INLINE _p #-}+-- | Order of E521 curve.+_r :: Integer+_r = 0x7ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffd15b6c64746fc85f736b8af5e7ec53f04fbd8c4569a8f1f4540ea2435f5180d6b+{-# INLINABLE _r #-}++-- | Coordinate @X@ of E521 curve.+_x :: Fq+_x = 0x752cb45c48648b189df90cb2296b2878a3bfd9f42fc6c818ec8bf3c9c0c6203913f6ecc5ccc72434b1ae949d568fc99c6059d0fb13364838aa302a940a2f19ba6c+{-# INLINABLE _x #-}++-- | Coordinate @Y@ of E521 curve.+_y :: Fq+_y = 0xc+{-# INLINABLE _y #-}++-- | Generator of affine E521 curve.+gA :: PA+gA = A _x _y+{-# INLINABLE gA #-}++-- | Generator of projective E521 curve.+gP :: PP+gP = P _x _y 1+{-# INLINABLE gP #-}

src/Curve/Edwards/Ed25519.hs view

@@ -1,74 +1,105 @@ module Curve.Edwards.Ed25519-  ( Fp-  , P-  , _a-  , _d-  , _g-  , _h-  , _n-  , _p+  ( module Curve.Edwards+  , module Curve.Edwards.Ed25519   ) where  import Protolude -import PrimeField (PrimeField)+import PrimeField -import Curve.Edwards (ECurve(..), EPoint, Point(..))+import Curve.Edwards  ------------------------------------------------------------------------------- -- Types ------------------------------------------------------------------------------- --- | Ed25519 curve+-- | Ed25519 curve. data Ed25519 --- | Field of Ed25519 curve-type Fp = PrimeField 0x7fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffed+-- | Field of points of Ed25519 curve.+type Fq = PrimeField 0x7fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffed --- | Ed25519 curve is an Edwards curve-instance ECurve Ed25519 Fp where+-- | Field of coefficients of Ed25519 curve.+type Fr = PrimeField 0x1000000000000000000000000000000014def9dea2f79cd65812631a5cf5d3ed++-- | Ed25519 curve is an Edwards curve.+instance Curve 'Edwards c Ed25519 Fq Fr => ECurve c Ed25519 Fq Fr where   a_ = const _a-  {-# INLINE a_ #-}+  {-# INLINABLE a_ #-}   d_ = const _d-  {-# INLINE d_ #-}-  g_ = _g-  {-# INLINE g_ #-}+  {-# INLINABLE d_ #-}+  h_ = const _h+  {-# INLINABLE h_ #-}+  q_ = const _q+  {-# INLINABLE q_ #-}+  r_ = const _r+  {-# INLINABLE r_ #-}+  x_ = const _x+  {-# INLINABLE x_ #-}+  y_ = const _y+  {-# INLINABLE y_ #-} --- | Point of Ed25519 curve-type P = EPoint Ed25519 Fp+-- | Affine Ed25519 curve point.+type PA = EAPoint Ed25519 Fq Fr +-- | Affine Ed25519 curve is an Edwards affine curve.+instance EACurve Ed25519 Fq Fr where+  gA_ = gA+  {-# INLINABLE gA_ #-}++-- | Projective Ed25519 point.+type PP = EPPoint Ed25519 Fq Fr++-- | Projective Ed25519 curve is an Edwards projective curve.+instance EPCurve Ed25519 Fq Fr where+  gP_ = gP+  {-# INLINABLE gP_ #-}+ ------------------------------------------------------------------------------- -- Parameters ------------------------------------------------------------------------------- --- | Coefficient @A@ of Ed25519 curve-_a :: Fp-_a = -1-{-# INLINE _a #-}+-- | Coefficient @A@ of Ed25519 curve.+_a :: Fq+_a = 0x7fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffec+{-# INLINABLE _a #-} --- | Coefficient @D@ of Ed25519 curve-_d :: Fp+-- | Coefficient @D@ of Ed25519 curve.+_d :: Fq _d = 0x52036cee2b6ffe738cc740797779e89800700a4d4141d8ab75eb4dca135978a3-{-# INLINE _d #-}---- | Generator of Ed25519 curve-_g :: P-_g = A-     0x216936d3cd6e53fec0a4e231fdd6dc5c692cc7609525a7b2c9562d608f25d51a-     0x6666666666666666666666666666666666666666666666666666666666666658-{-# INLINE _g #-}+{-# INLINABLE _d #-} --- | Cofactor of Ed25519 curve+-- | Cofactor of Ed25519 curve. _h :: Integer-_h = 8-{-# INLINE _h #-}+_h = 0x8+{-# INLINABLE _h #-} --- | Order of Ed25519 curve-_n :: Integer-_n = 0x1000000000000000000000000000000014def9dea2f79cd65812631a5cf5d3ed-{-# INLINE _n #-}+-- | Characteristic of Ed25519 curve.+_q :: Integer+_q = 0x7fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffed+{-# INLINABLE _q #-} --- | Characteristic of Ed25519 curve-_p :: Integer-_p = 0x7fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffed-{-# INLINE _p #-}+-- | Order of Ed25519 curve.+_r :: Integer+_r = 0x1000000000000000000000000000000014def9dea2f79cd65812631a5cf5d3ed+{-# INLINABLE _r #-}++-- | Coordinate @X@ of Ed25519 curve.+_x :: Fq+_x = 0x216936d3cd6e53fec0a4e231fdd6dc5c692cc7609525a7b2c9562d608f25d51a+{-# INLINABLE _x #-}++-- | Coordinate @Y@ of Ed25519 curve.+_y :: Fq+_y = 0x6666666666666666666666666666666666666666666666666666666666666658+{-# INLINABLE _y #-}++-- | Generator of affine Ed25519 curve.+gA :: PA+gA = A _x _y+{-# INLINABLE gA #-}++-- | Generator of projective Ed25519 curve.+gP :: PP+gP = P _x _y 1+{-# INLINABLE gP #-}

src/Curve/Edwards/Ed3363.hs view

@@ -1,74 +1,105 @@ module Curve.Edwards.Ed3363-  ( Fp-  , P-  , _a-  , _d-  , _g-  , _h-  , _n-  , _p+  ( module Curve.Edwards+  , module Curve.Edwards.Ed3363   ) where  import Protolude -import PrimeField (PrimeField)+import PrimeField -import Curve.Edwards (ECurve(..), EPoint, Point(..))+import Curve.Edwards  ------------------------------------------------------------------------------- -- Types ------------------------------------------------------------------------------- --- | Ed3363 curve+-- | Ed3363 curve. data Ed3363 --- | Field of Ed3363 curve-type Fp = PrimeField 0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffd+-- | Field of points of Ed3363 curve.+type Fq = PrimeField 0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffd --- | Ed3363 curve is an Edwards curve-instance ECurve Ed3363 Fp where+-- | Field of coefficients of Ed3363 curve.+type Fr = PrimeField 0x200000000000000000000000000000000000000000071415fa9850c0bd6b87f93baa7b2f95973e9fa805++-- | Ed3363 curve is an Edwards curve.+instance Curve 'Edwards c Ed3363 Fq Fr => ECurve c Ed3363 Fq Fr where   a_ = const _a-  {-# INLINE a_ #-}+  {-# INLINABLE a_ #-}   d_ = const _d-  {-# INLINE d_ #-}-  g_ = _g-  {-# INLINE g_ #-}+  {-# INLINABLE d_ #-}+  h_ = const _h+  {-# INLINABLE h_ #-}+  q_ = const _q+  {-# INLINABLE q_ #-}+  r_ = const _r+  {-# INLINABLE r_ #-}+  x_ = const _x+  {-# INLINABLE x_ #-}+  y_ = const _y+  {-# INLINABLE y_ #-} --- | Point of Ed3363 curve-type P = EPoint Ed3363 Fp+-- | Affine Ed3363 curve point.+type PA = EAPoint Ed3363 Fq Fr +-- | Affine Ed3363 curve is an Edwards affine curve.+instance EACurve Ed3363 Fq Fr where+  gA_ = gA+  {-# INLINABLE gA_ #-}++-- | Projective Ed3363 point.+type PP = EPPoint Ed3363 Fq Fr++-- | Projective Ed3363 curve is an Edwards projective curve.+instance EPCurve Ed3363 Fq Fr where+  gP_ = gP+  {-# INLINABLE gP_ #-}+ ------------------------------------------------------------------------------- -- Parameters ------------------------------------------------------------------------------- --- | Coefficient @A@ of Ed3363 curve-_a :: Fp-_a = 1-{-# INLINE _a #-}+-- | Coefficient @A@ of Ed3363 curve.+_a :: Fq+_a = 0x1+{-# INLINABLE _a #-} --- | Coefficient @D@ of Ed3363 curve-_d :: Fp+-- | Coefficient @D@ of Ed3363 curve.+_d :: Fq _d = 0x2b67-{-# INLINE _d #-}---- | Generator of Ed3363 curve-_g :: P-_g = A-     0xc-     0xc0dc616b56502e18e1c161d007853d1b14b46c3811c7ef435b6db5d5650ca0365db12bec68505fe8632-{-# INLINE _g #-}+{-# INLINABLE _d #-} --- | Cofactor of Ed3363 curve+-- | Cofactor of Ed3363 curve. _h :: Integer-_h = 8-{-# INLINE _h #-}+_h = 0x8+{-# INLINABLE _h #-} --- | Order of Ed3363 curve-_n :: Integer-_n = 0x200000000000000000000000000000000000000000071415fa9850c0bd6b87f93baa7b2f95973e9fa805-{-# INLINE _n #-}+-- | Characteristic of Ed3363 curve.+_q :: Integer+_q = 0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffd+{-# INLINABLE _q #-} --- | Characteristic of Ed3363 curve-_p :: Integer-_p = 0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffd-{-# INLINE _p #-}+-- | Order of Ed3363 curve.+_r :: Integer+_r = 0x200000000000000000000000000000000000000000071415fa9850c0bd6b87f93baa7b2f95973e9fa805+{-# INLINABLE _r #-}++-- | Coordinate @X@ of Ed3363 curve.+_x :: Fq+_x = 0xc+{-# INLINABLE _x #-}++-- | Coordinate @Y@ of Ed3363 curve.+_y :: Fq+_y = 0xc0dc616b56502e18e1c161d007853d1b14b46c3811c7ef435b6db5d5650ca0365db12bec68505fe8632+{-# INLINABLE _y #-}++-- | Generator of affine Ed3363 curve.+gA :: PA+gA = A _x _y+{-# INLINABLE gA #-}++-- | Generator of projective Ed3363 curve.+gP :: PP+gP = P _x _y 1+{-# INLINABLE gP #-}

src/Curve/Edwards/Ed448.hs view

@@ -1,74 +1,105 @@ module Curve.Edwards.Ed448-  ( Fp-  , P-  , _a-  , _d-  , _g-  , _h-  , _n-  , _p+  ( module Curve.Edwards+  , module Curve.Edwards.Ed448   ) where  import Protolude -import PrimeField (PrimeField)+import PrimeField -import Curve.Edwards (ECurve(..), EPoint, Point(..))+import Curve.Edwards  ------------------------------------------------------------------------------- -- Types ------------------------------------------------------------------------------- --- | Ed448 curve+-- | Ed448 curve. data Ed448 --- | Field of Ed448 curve-type Fp = PrimeField 0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffeffffffffffffffffffffffffffffffffffffffffffffffffffffffff+-- | Field of points of Ed448 curve.+type Fq = PrimeField 0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffeffffffffffffffffffffffffffffffffffffffffffffffffffffffff --- | Ed448 curve is an Edwards curve-instance ECurve Ed448 Fp where+-- | Field of coefficients of Ed448 curve.+type Fr = PrimeField 0x3fffffffffffffffffffffffffffffffffffffffffffffffffffffff7cca23e9c44edb49aed63690216cc2728dc58f552378c292ab5844f3++-- | Ed448 curve is an Edwards curve.+instance Curve 'Edwards c Ed448 Fq Fr => ECurve c Ed448 Fq Fr where   a_ = const _a-  {-# INLINE a_ #-}+  {-# INLINABLE a_ #-}   d_ = const _d-  {-# INLINE d_ #-}-  g_ = _g-  {-# INLINE g_ #-}+  {-# INLINABLE d_ #-}+  h_ = const _h+  {-# INLINABLE h_ #-}+  q_ = const _q+  {-# INLINABLE q_ #-}+  r_ = const _r+  {-# INLINABLE r_ #-}+  x_ = const _x+  {-# INLINABLE x_ #-}+  y_ = const _y+  {-# INLINABLE y_ #-} --- | Point of Ed448 curve-type P = EPoint Ed448 Fp+-- | Affine Ed448 curve point.+type PA = EAPoint Ed448 Fq Fr +-- | Affine Ed448 curve is an Edwards affine curve.+instance EACurve Ed448 Fq Fr where+  gA_ = gA+  {-# INLINABLE gA_ #-}++-- | Projective Ed448 point.+type PP = EPPoint Ed448 Fq Fr++-- | Projective Ed448 curve is an Edwards projective curve.+instance EPCurve Ed448 Fq Fr where+  gP_ = gP+  {-# INLINABLE gP_ #-}+ ------------------------------------------------------------------------------- -- Parameters ------------------------------------------------------------------------------- --- | Coefficient @A@ of Ed448 curve-_a :: Fp-_a = 1-{-# INLINE _a #-}+-- | Coefficient @A@ of Ed448 curve.+_a :: Fq+_a = 0x1+{-# INLINABLE _a #-} --- | Coefficient @D@ of Ed448 curve-_d :: Fp+-- | Coefficient @D@ of Ed448 curve.+_d :: Fq _d = 0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffeffffffffffffffffffffffffffffffffffffffffffffffffffff6756-{-# INLINE _d #-}---- | Generator of Ed448 curve-_g :: P-_g = A-     0x297ea0ea2692ff1b4faff46098453a6a26adf733245f065c3c59d0709cecfa96147eaaf3932d94c63d96c170033f4ba0c7f0de840aed939f-     0x13-{-# INLINE _g #-}+{-# INLINABLE _d #-} --- | Cofactor of Ed448 curve+-- | Cofactor of Ed448 curve. _h :: Integer-_h = 4-{-# INLINE _h #-}+_h = 0x4+{-# INLINABLE _h #-} --- | Order of Ed448 curve-_n :: Integer-_n = 0x3fffffffffffffffffffffffffffffffffffffffffffffffffffffff7cca23e9c44edb49aed63690216cc2728dc58f552378c292ab5844f3-{-# INLINE _n #-}+-- | Characteristic of Ed448 curve.+_q :: Integer+_q = 0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffeffffffffffffffffffffffffffffffffffffffffffffffffffffffff+{-# INLINABLE _q #-} --- | Characteristic of Ed448 curve-_p :: Integer-_p = 0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffeffffffffffffffffffffffffffffffffffffffffffffffffffffffff-{-# INLINE _p #-}+-- | Order of Ed448 curve.+_r :: Integer+_r = 0x3fffffffffffffffffffffffffffffffffffffffffffffffffffffff7cca23e9c44edb49aed63690216cc2728dc58f552378c292ab5844f3+{-# INLINABLE _r #-}++-- | Coordinate @X@ of Ed448 curve.+_x :: Fq+_x = 0x297ea0ea2692ff1b4faff46098453a6a26adf733245f065c3c59d0709cecfa96147eaaf3932d94c63d96c170033f4ba0c7f0de840aed939f+{-# INLINABLE _x #-}++-- | Coordinate @Y@ of Ed448 curve.+_y :: Fq+_y = 0x13+{-# INLINABLE _y #-}++-- | Generator of affine Ed448 curve.+gA :: PA+gA = A _x _y+{-# INLINABLE gA #-}++-- | Generator of projective Ed448 curve.+gP :: PP+gP = P _x _y 1+{-# INLINABLE gP #-}

src/Curve/Edwards/JubJub.hs view

@@ -1,74 +1,105 @@ module Curve.Edwards.JubJub-  ( Fp-  , P-  , _a-  , _d-  , _g-  , _h-  , _n-  , _p+  ( module Curve.Edwards+  , module Curve.Edwards.JubJub   ) where  import Protolude -import PrimeField (PrimeField)+import PrimeField -import Curve.Edwards (ECurve(..), EPoint, Point(..))+import Curve.Edwards  ------------------------------------------------------------------------------- -- Types ------------------------------------------------------------------------------- --- | JubJub curve+-- | JubJub curve. data JubJub --- | Field of JubJub curve-type Fp = PrimeField 0x73eda753299d7d483339d80809a1d80553bda402fffe5bfeffffffff00000001+-- | Field of points of JubJub curve.+type Fq = PrimeField 0x73eda753299d7d483339d80809a1d80553bda402fffe5bfeffffffff00000001 --- | JubJub curve is an Edwards curve-instance ECurve JubJub Fp where+-- | Field of coefficients of JubJub curve.+type Fr = PrimeField 0xe7db4ea6533afa906673b0101343b00a6682093ccc81082d0970e5ed6f72cb7++-- | JubJub curve is an Edwards curve.+instance Curve 'Edwards c JubJub Fq Fr => ECurve c JubJub Fq Fr where   a_ = const _a-  {-# INLINE a_ #-}+  {-# INLINABLE a_ #-}   d_ = const _d-  {-# INLINE d_ #-}-  g_ = _g-  {-# INLINE g_ #-}+  {-# INLINABLE d_ #-}+  h_ = const _h+  {-# INLINABLE h_ #-}+  q_ = const _q+  {-# INLINABLE q_ #-}+  r_ = const _r+  {-# INLINABLE r_ #-}+  x_ = const _x+  {-# INLINABLE x_ #-}+  y_ = const _y+  {-# INLINABLE y_ #-} --- | Point of JubJub curve-type P = EPoint JubJub Fp+-- | Affine JubJub curve point.+type PA = EAPoint JubJub Fq Fr +-- | Affine JubJub curve is an Edwards affine curve.+instance EACurve JubJub Fq Fr where+  gA_ = gA+  {-# INLINABLE gA_ #-}++-- | Projective JubJub point.+type PP = EPPoint JubJub Fq Fr++-- | Projective JubJub curve is an Edwards projective curve.+instance EPCurve JubJub Fq Fr where+  gP_ = gP+  {-# INLINABLE gP_ #-}+ ------------------------------------------------------------------------------- -- Parameters ------------------------------------------------------------------------------- --- | Coefficient @A@ of JubJub curve-_a :: Fp-_a = -1-{-# INLINE _a #-}+-- | Coefficient @A@ of JubJub curve.+_a :: Fq+_a = 0x73eda753299d7d483339d80809a1d80553bda402fffe5bfeffffffff00000000+{-# INLINABLE _a #-} --- | Coefficient @D@ of JubJub curve-_d :: Fp+-- | Coefficient @D@ of JubJub curve.+_d :: Fq _d = 0x2a9318e74bfa2b48f5fd9207e6bd7fd4292d7f6d37579d2601065fd6d6343eb1-{-# INLINE _d #-}---- | Generator of JubJub curve-_g :: P-_g = A-     0x5183972af8eff38ca624b4df00384882000c546bf2f39ede7f4ecf1a74f976c4-     0x3b43f8472ca2fc2c9e8fcc5abd9dc308096c8707ffa6833b146bad709349702e-{-# INLINE _g #-}+{-# INLINABLE _d #-} --- | Cofactor of JubJub curve+-- | Cofactor of JubJub curve. _h :: Integer-_h = 8-{-# INLINE _h #-}+_h = 0x8+{-# INLINABLE _h #-} --- | Order of JubJub curve-_n :: Integer-_n = 0xe7db4ea6533afa906673b0101343b00a6682093ccc81082d0970e5ed6f72cb7-{-# INLINE _n #-}+-- | Characteristic of JubJub curve.+_q :: Integer+_q = 0x73eda753299d7d483339d80809a1d80553bda402fffe5bfeffffffff00000001+{-# INLINABLE _q #-} --- | Characteristic of JubJub curve-_p :: Integer-_p = 0x73eda753299d7d483339d80809a1d80553bda402fffe5bfeffffffff00000001-{-# INLINE _p #-}+-- | Order of JubJub curve.+_r :: Integer+_r = 0xe7db4ea6533afa906673b0101343b00a6682093ccc81082d0970e5ed6f72cb7+{-# INLINABLE _r #-}++-- | Coordinate @X@ of JubJub curve.+_x :: Fq+_x = 0x5183972af8eff38ca624b4df00384882000c546bf2f39ede7f4ecf1a74f976c4+{-# INLINABLE _x #-}++-- | Coordinate @Y@ of JubJub curve.+_y :: Fq+_y = 0x3b43f8472ca2fc2c9e8fcc5abd9dc308096c8707ffa6833b146bad709349702e+{-# INLINABLE _y #-}++-- | Generator of affine JubJub curve.+gA :: PA+gA = A _x _y+{-# INLINABLE gA #-}++-- | Generator of projective JubJub curve.+gP :: PP+gP = P _x _y 1+{-# INLINABLE gP #-}

src/Curve/Montgomery.hs view

@@ -1,114 +1,136 @@+{-# OPTIONS -fno-warn-orphans #-}+ module Curve.Montgomery-  ( Point(..)-  , MCurve(..)-  , MPoint+  ( module Curve+  , module Curve.Montgomery+  , module Group   ) where  import Protolude -import Control.Monad.Random (Random(..), getRandom) import GaloisField (GaloisField(..))-import Test.Tasty.QuickCheck (Arbitrary(..), suchThatMap) import Text.PrettyPrint.Leijen.Text (Pretty(..)) -import Curve (Curve(..))+import Curve (Coordinates(..), Curve(..), Form(..))+import Group (Group(..))  ---------------------------------------------------------------------------------- Types+-- Montgomery form ------------------------------------------------------------------------------- --- | Montgomery curve representation.-data M+-- | Montgomery points.+type MPoint = Point 'Montgomery --- | Montgomery curve points.-type MPoint = Point M+-- | Montgomery curves.+class (GaloisField q, GaloisField r, Curve 'Montgomery c e q r) => MCurve c e q r where+  {-# MINIMAL a_, b_, h_, q_, r_, x_, y_ #-}+  a_ :: MPoint c e q r -> q       -- ^ Coefficient @A@.+  b_ :: MPoint c e q r -> q       -- ^ Coefficient @B@.+  h_ :: MPoint c e q r -> Integer -- ^ Curve cofactor.+  q_ :: MPoint c e q r -> Integer -- ^ Curve characteristic.+  r_ :: MPoint c e q r -> Integer -- ^ Curve order.+  x_ :: MPoint c e q r -> q       -- ^ Coordinate @X@.+  y_ :: MPoint c e q r -> q       -- ^ Coordinate @Y@. --- | Montgomery curves @By^2 = x^3 + Ax^2 + x@.-class Curve M c k => MCurve c k where-  a_ :: c -> k     -- ^ Coefficient @A@.-  b_ :: c -> k     -- ^ Coefficient @B@.-  g_ :: MPoint c k -- ^ Curve generator.+-------------------------------------------------------------------------------+-- Affine coordinates+------------------------------------------------------------------------------- --- Montgomery points are arbitrary.-instance (GaloisField k, MCurve c k) => Arbitrary (Point M c k) where-  arbitrary = suchThatMap arbitrary point+-- | Montgomery affine points.+type MAPoint = MPoint 'Affine --- Montgomery points are pretty.-instance (GaloisField k, MCurve c k) => Pretty (Point M c k) where-  pretty (A x y) = pretty (x, y)-  pretty O       = "O"+-- | Montgomery affine curves @By^2 = x^3 + Ax^2 + x@.+class MCurve 'Affine e q r => MACurve e q r where+  {-# MINIMAL gA_ #-}+  gA_ :: MAPoint e q r -- ^ Curve generator. --- Montgomery points are random.-instance (GaloisField k, MCurve c k) => Random (Point M c k) where-  random g = case point x of-    Just p -> (p, g')-    _      -> random g'+-- Montgomery affine curves are elliptic curves.+instance MACurve e q r => Curve 'Montgomery 'Affine e q r where++  data instance Point 'Montgomery 'Affine e q r = A q q -- ^ Affine point.+                                                | O     -- ^ Infinite point.+    deriving (Eq, Generic, NFData, Read, Show)++  char = q_+  {-# INLINABLE char #-}++  cof = h_+  {-# INLINABLE cof #-}++  disc _ = b * (a * a - 4)     where-      (x, g') = random g-  {-# INLINE random #-}-  randomR  = panic "not implemented."+      a = a_ (witness :: MAPoint e q r)+      b = b_ (witness :: MAPoint e q r)+  {-# INLINABLE disc #-} ----------------------------------------------------------------------------------- Operations--------------------------------------------------------------------------------+  fromA = identity+  {-# INLINABLE fromA #-} --- Montgomery curves are elliptic curves.-instance (GaloisField k, MCurve c k) => Curve M c k where+  point x y = let p = A x y in if def p then Just p else Nothing+  {-# INLINABLE point #-} -  data instance Point M c k = A k k -- ^ Affine point.-                            | O     -- ^ Infinite point.-    deriving (Eq, Generic, NFData, Read, Show)+  pointX x = A x <$> yX (witness :: MAPoint e q r) x+  {-# INLINABLE pointX #-} -  id = O-  {-# INLINE id #-}+  toA = identity+  {-# INLINABLE toA #-} -  inv O       = O-  inv (A x y) = A x (-y)-  {-# INLINE inv #-}+  yX _ x = sr ((((x + a) * x) + 1) * x / b)+    where+      a = a_ (witness :: MAPoint e q r)+      b = b_ (witness :: MAPoint e q r)+  {-# INLINABLE yX #-} -  add p O          = p-  add O q          = q-  add p@(A x1 y1) (A x2 y2)-    | x1 /= x2     = A x3 y3-    | y1 + y2 == 0 = O-    | otherwise    = double p+-- Montgomery affine points are groups.+instance MACurve e q r => Group (MAPoint e q r) where++  add p  O      = p+  add O q       = q+  add (A x1 y1) (A x2 y2)+    | x1 == x2  = O+    | otherwise = A x3 y3     where-      a  = a_ (witness :: c)-      b  = b_ (witness :: c)+      a  = a_ (witness :: MAPoint e q r)+      b  = b_ (witness :: MAPoint e q r)       l  = (y2 - y1) / (x2 - x1)       x3 = b * l * l - a - x1 - x2       y3 = l * (x1 - x3) - y1-  {-# INLINE add #-}+  {-# INLINABLE add #-} -  double O       = O-  double (A _ 0) = O-  double (A x y) = A x' y'+  dbl O         = O+  dbl (A x y)+    | y == 0    = O+    | otherwise = A x' y'     where-      a  = a_ (witness :: c)-      b  = b_ (witness :: c)+      a  = a_ (witness :: MAPoint e q r)+      b  = b_ (witness :: MAPoint e q r)       l  = (x * (3 * x + 2 * a) + 1) / (2 * b * y)       x' = b * l * l - a - 2 * x       y' = l * (x - x') - y-  {-# INLINE double #-}+  {-# INLINABLE dbl #-}    def O       = True   def (A x y) = b * y * y == (((x + a) * x) + 1) * x     where-      a = a_ (witness :: c)-      b = b_ (witness :: c)-  {-# INLINE def #-}+      a = a_ (witness :: MAPoint e q r)+      b = b_ (witness :: MAPoint e q r)+  {-# INLINABLE def #-} -  disc _ = b * (a * a - 4)-    where-      a = a_ (witness :: c)-      b = b_ (witness :: c)-  {-# INLINE disc #-}+  gen = gA_+  {-# INLINABLE gen #-} -  point x = A x <$> sr ((((x + a) * x) + 1) * x / b)-    where-      a  = a_ (witness :: c)-      b  = b_ (witness :: c)-  {-# INLINE point #-}+  id = O+  {-# INLINABLE id #-} -  rnd = getRandom-  {-# INLINE rnd #-}+  inv O       = O+  inv (A x y) = A x (-y)+  {-# INLINABLE inv #-}++  order = r_+  {-# INLINABLE order #-}++-- Montgomery affine points are pretty.+instance MACurve e q r => Pretty (MAPoint e q r) where++  pretty (A x y) = pretty (x, y)+  pretty O       = "O"

src/Curve/Montgomery/Curve25519.hs view

@@ -1,74 +1,92 @@ module Curve.Montgomery.Curve25519-  ( Fp-  , P-  , _a-  , _b-  , _g-  , _h-  , _n-  , _p+  ( module Curve.Montgomery+  , module Curve.Montgomery.Curve25519   ) where  import Protolude -import PrimeField (PrimeField)+import PrimeField -import Curve.Montgomery (Point(..), MCurve(..), MPoint)+import Curve.Montgomery  ------------------------------------------------------------------------------- -- Types ------------------------------------------------------------------------------- --- | Curve25519 curve+-- | Curve25519 curve. data Curve25519 --- | Field of Curve25519 curve-type Fp = PrimeField 0x7fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffed+-- | Field of points of Curve25519 curve.+type Fq = PrimeField 0x7fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffed --- | Curve25519 curve is a Montgomery curve-instance MCurve Curve25519 Fp where+-- | Field of coefficients of Curve25519 curve.+type Fr = PrimeField 0x1000000000000000000000000000000014def9dea2f79cd65812631a5cf5d3ed++-- | Curve25519 curve is a Montgomery curve.+instance Curve 'Montgomery c Curve25519 Fq Fr => MCurve c Curve25519 Fq Fr where   a_ = const _a-  {-# INLINE a_ #-}+  {-# INLINABLE a_ #-}   b_ = const _b-  {-# INLINE b_ #-}-  g_ = _g-  {-# INLINE g_ #-}+  {-# INLINABLE b_ #-}+  h_ = const _h+  {-# INLINABLE h_ #-}+  q_ = const _q+  {-# INLINABLE q_ #-}+  r_ = const _r+  {-# INLINABLE r_ #-}+  x_ = const _x+  {-# INLINABLE x_ #-}+  y_ = const _y+  {-# INLINABLE y_ #-} --- | Point of Curve25519 curve-type P = MPoint Curve25519 Fp+-- | Affine Curve25519 curve point.+type PA = MAPoint Curve25519 Fq Fr +-- | Affine Curve25519 curve is a Montgomery affine curve.+instance MACurve Curve25519 Fq Fr where+  gA_ = gA+  {-# INLINABLE gA_ #-}+ ------------------------------------------------------------------------------- -- Parameters ------------------------------------------------------------------------------- --- | Coefficient @A@ of Curve25519 curve-_a :: Fp+-- | Coefficient @A@ of Curve25519 curve.+_a :: Fq _a = 0x76d06-{-# INLINE _a #-}---- | Coefficient @B@ of Curve25519 curve-_b :: Fp-_b = 1-{-# INLINE _b #-}+{-# INLINABLE _a #-} --- | Generator of Curve25519 curve-_g :: P-_g = A-     9-     0x20ae19a1b8a086b4e01edd2c7748d14c923d4d7e6d7c61b229e9c5a27eced3d9-{-# INLINE _g #-}+-- | Coefficient @B@ of Curve25519 curve.+_b :: Fq+_b = 0x1+{-# INLINABLE _b #-} --- | Cofactor of Curve25519 curve+-- | Cofactor of Curve25519 curve. _h :: Integer-_h = 8-{-# INLINE _h #-}+_h = 0x8+{-# INLINABLE _h #-} --- | Order of Curve25519 curve-_n :: Integer-_n = 0x1000000000000000000000000000000014def9dea2f79cd65812631a5cf5d3ed-{-# INLINE _n #-}+-- | Characteristic of Curve25519 curve.+_q :: Integer+_q = 0x7fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffed+{-# INLINABLE _q #-} --- | Characteristic of Curve25519 curve-_p :: Integer-_p = 0x7fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffed-{-# INLINE _p #-}+-- | Order of Curve25519 curve.+_r :: Integer+_r = 0x1000000000000000000000000000000014def9dea2f79cd65812631a5cf5d3ed+{-# INLINABLE _r #-}++-- | Coordinate @X@ of Curve25519 curve.+_x :: Fq+_x = 0x9+{-# INLINABLE _x #-}++-- | Coordinate @Y@ of Curve25519 curve.+_y :: Fq+_y = 0x20ae19a1b8a086b4e01edd2c7748d14c923d4d7e6d7c61b229e9c5a27eced3d9+{-# INLINABLE _y #-}++-- | Generator of affine Curve25519 curve.+gA :: PA+gA = A _x _y+{-# INLINABLE gA #-}

src/Curve/Montgomery/Curve383187.hs view

@@ -1,74 +1,92 @@ module Curve.Montgomery.Curve383187-  ( Fp-  , P-  , _a-  , _b-  , _g-  , _h-  , _n-  , _p+  ( module Curve.Montgomery+  , module Curve.Montgomery.Curve383187   ) where  import Protolude -import PrimeField (PrimeField)+import PrimeField -import Curve.Montgomery (Point(..), MCurve(..), MPoint)+import Curve.Montgomery  ------------------------------------------------------------------------------- -- Types ------------------------------------------------------------------------------- --- | Curve383187 curve+-- | Curve383187 curve. data Curve383187 --- | Field of Curve383187 curve-type Fp = PrimeField 0x7fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff45+-- | Field of points of Curve383187 curve.+type Fq = PrimeField 0x7fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff45 --- | Curve383187 curve is a Montgomery curve-instance MCurve Curve383187 Fp where+-- | Field of coefficients of Curve383187 curve.+type Fr = PrimeField 0x1000000000000000000000000000000000000000000000000e85a85287a1488acd41ae84b2b7030446f72088b00a0e21++-- | Curve383187 curve is a Montgomery curve.+instance Curve 'Montgomery c Curve383187 Fq Fr => MCurve c Curve383187 Fq Fr where   a_ = const _a-  {-# INLINE a_ #-}+  {-# INLINABLE a_ #-}   b_ = const _b-  {-# INLINE b_ #-}-  g_ = _g-  {-# INLINE g_ #-}+  {-# INLINABLE b_ #-}+  h_ = const _h+  {-# INLINABLE h_ #-}+  q_ = const _q+  {-# INLINABLE q_ #-}+  r_ = const _r+  {-# INLINABLE r_ #-}+  x_ = const _x+  {-# INLINABLE x_ #-}+  y_ = const _y+  {-# INLINABLE y_ #-} --- | Point of Curve383187 curve-type P = MPoint Curve383187 Fp+-- | Affine Curve383187 curve point.+type PA = MAPoint Curve383187 Fq Fr +-- | Affine Curve383187 curve is a Montgomery affine curve.+instance MACurve Curve383187 Fq Fr where+  gA_ = gA+  {-# INLINABLE gA_ #-}+ ------------------------------------------------------------------------------- -- Parameters ------------------------------------------------------------------------------- --- | Coefficient @A@ of Curve383187 curve-_a :: Fp+-- | Coefficient @A@ of Curve383187 curve.+_a :: Fq _a = 0x38251-{-# INLINE _a #-}---- | Coefficient @B@ of Curve383187 curve-_b :: Fp-_b = 1-{-# INLINE _b #-}+{-# INLINABLE _a #-} --- | Generator of Curve383187 curve-_g :: P-_g = A-     5-     0x1eebe07dc1871896732b12d5504a32370471965c7a11f2c89865f855ab3cbd7c224e3620c31af3370788457dd5ce46df-{-# INLINE _g #-}+-- | Coefficient @B@ of Curve383187 curve.+_b :: Fq+_b = 0x1+{-# INLINABLE _b #-} --- | Cofactor of Curve383187 curve+-- | Cofactor of Curve383187 curve. _h :: Integer-_h = 8-{-# INLINE _h #-}+_h = 0x8+{-# INLINABLE _h #-} --- | Order of Curve383187 curve-_n :: Integer-_n = 0x1000000000000000000000000000000000000000000000000e85a85287a1488acd41ae84b2b7030446f72088b00a0e21-{-# INLINE _n #-}+-- | Characteristic of Curve383187 curve.+_q :: Integer+_q = 0x7fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff45+{-# INLINABLE _q #-} --- | Characteristic of Curve383187 curve-_p :: Integer-_p = 0x7fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff45-{-# INLINE _p #-}+-- | Order of Curve383187 curve.+_r :: Integer+_r = 0x1000000000000000000000000000000000000000000000000e85a85287a1488acd41ae84b2b7030446f72088b00a0e21+{-# INLINABLE _r #-}++-- | Coordinate @X@ of Curve383187 curve.+_x :: Fq+_x = 0x5+{-# INLINABLE _x #-}++-- | Coordinate @Y@ of Curve383187 curve.+_y :: Fq+_y = 0x1eebe07dc1871896732b12d5504a32370471965c7a11f2c89865f855ab3cbd7c224e3620c31af3370788457dd5ce46df+{-# INLINABLE _y #-}++-- | Generator of affine Curve383187 curve.+gA :: PA+gA = A _x _y+{-# INLINABLE gA #-}

src/Curve/Montgomery/Curve448.hs view

@@ -1,74 +1,92 @@ module Curve.Montgomery.Curve448-  ( Fp-  , P-  , _a-  , _b-  , _g-  , _h-  , _n-  , _p+  ( module Curve.Montgomery+  , module Curve.Montgomery.Curve448   ) where  import Protolude -import PrimeField (PrimeField)+import PrimeField -import Curve.Montgomery (Point(..), MCurve(..), MPoint)+import Curve.Montgomery  ------------------------------------------------------------------------------- -- Types ------------------------------------------------------------------------------- --- | Curve448 curve+-- | Curve448 curve. data Curve448 --- | Field of Curve448 curve-type Fp = PrimeField 0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffeffffffffffffffffffffffffffffffffffffffffffffffffffffffff+-- | Field of points of Curve448 curve.+type Fq = PrimeField 0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffeffffffffffffffffffffffffffffffffffffffffffffffffffffffff --- | Curve448 curve is a Montgomery curve-instance MCurve Curve448 Fp where+-- | Field of coefficients of Curve448 curve.+type Fr = PrimeField 0x3fffffffffffffffffffffffffffffffffffffffffffffffffffffff7cca23e9c44edb49aed63690216cc2728dc58f552378c292ab5844f3++-- | Curve448 curve is a Montgomery curve.+instance Curve 'Montgomery c Curve448 Fq Fr => MCurve c Curve448 Fq Fr where   a_ = const _a-  {-# INLINE a_ #-}+  {-# INLINABLE a_ #-}   b_ = const _b-  {-# INLINE b_ #-}-  g_ = _g-  {-# INLINE g_ #-}+  {-# INLINABLE b_ #-}+  h_ = const _h+  {-# INLINABLE h_ #-}+  q_ = const _q+  {-# INLINABLE q_ #-}+  r_ = const _r+  {-# INLINABLE r_ #-}+  x_ = const _x+  {-# INLINABLE x_ #-}+  y_ = const _y+  {-# INLINABLE y_ #-} --- | Point of Curve448 curve-type P = MPoint Curve448 Fp+-- | Affine Curve448 curve point.+type PA = MAPoint Curve448 Fq Fr +-- | Affine Curve448 curve is a Montgomery affine curve.+instance MACurve Curve448 Fq Fr where+  gA_ = gA+  {-# INLINABLE gA_ #-}+ ------------------------------------------------------------------------------- -- Parameters ------------------------------------------------------------------------------- --- | Coefficient @A@ of Curve448 curve-_a :: Fp+-- | Coefficient @A@ of Curve448 curve.+_a :: Fq _a = 0x262a6-{-# INLINE _a #-}---- | Coefficient @B@ of Curve448 curve-_b :: Fp-_b = 1-{-# INLINE _b #-}+{-# INLINABLE _a #-} --- | Generator of Curve448 curve-_g :: P-_g = A-     5-     0x7d235d1295f5b1f66c98ab6e58326fcecbae5d34f55545d060f75dc28df3f6edb8027e2346430d211312c4b150677af76fd7223d457b5b1a-{-# INLINE _g #-}+-- | Coefficient @B@ of Curve448 curve.+_b :: Fq+_b = 0x1+{-# INLINABLE _b #-} --- | Cofactor of Curve448 curve+-- | Cofactor of Curve448 curve. _h :: Integer-_h = 4-{-# INLINE _h #-}+_h = 0x4+{-# INLINABLE _h #-} --- | Order of Curve448 curve-_n :: Integer-_n = 0x3fffffffffffffffffffffffffffffffffffffffffffffffffffffff7cca23e9c44edb49aed63690216cc2728dc58f552378c292ab5844f3-{-# INLINE _n #-}+-- | Characteristic of Curve448 curve.+_q :: Integer+_q = 0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffeffffffffffffffffffffffffffffffffffffffffffffffffffffffff+{-# INLINABLE _q #-} --- | Characteristic of Curve448 curve-_p :: Integer-_p = 0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffeffffffffffffffffffffffffffffffffffffffffffffffffffffffff-{-# INLINE _p #-}+-- | Order of Curve448 curve.+_r :: Integer+_r = 0x3fffffffffffffffffffffffffffffffffffffffffffffffffffffff7cca23e9c44edb49aed63690216cc2728dc58f552378c292ab5844f3+{-# INLINABLE _r #-}++-- | Coordinate @X@ of Curve448 curve.+_x :: Fq+_x = 0x5+{-# INLINABLE _x #-}++-- | Coordinate @Y@ of Curve448 curve.+_y :: Fq+_y = 0x7d235d1295f5b1f66c98ab6e58326fcecbae5d34f55545d060f75dc28df3f6edb8027e2346430d211312c4b150677af76fd7223d457b5b1a+{-# INLINABLE _y #-}++-- | Generator of affine Curve448 curve.+gA :: PA+gA = A _x _y+{-# INLINABLE gA #-}

src/Curve/Montgomery/M221.hs view

@@ -1,74 +1,92 @@ module Curve.Montgomery.M221-  ( Fp-  , P-  , _a-  , _b-  , _g-  , _h-  , _n-  , _p+  ( module Curve.Montgomery+  , module Curve.Montgomery.M221   ) where  import Protolude -import PrimeField (PrimeField)+import PrimeField -import Curve.Montgomery (Point(..), MCurve(..), MPoint)+import Curve.Montgomery  ------------------------------------------------------------------------------- -- Types ------------------------------------------------------------------------------- --- | M-221 curve+-- | M221 curve. data M221 --- | Field of M-221 curve-type Fp = PrimeField 0x1ffffffffffffffffffffffffffffffffffffffffffffffffffffffd+-- | Field of points of M221 curve.+type Fq = PrimeField 0x1ffffffffffffffffffffffffffffffffffffffffffffffffffffffd --- | M-221 curve is a Montgomery curve-instance MCurve M221 Fp where+-- | Field of coefficients of M221 curve.+type Fr = PrimeField 0x40000000000000000000000000015a08ed730e8a2f77f005042605b++-- | M221 curve is a Montgomery curve.+instance Curve 'Montgomery c M221 Fq Fr => MCurve c M221 Fq Fr where   a_ = const _a-  {-# INLINE a_ #-}+  {-# INLINABLE a_ #-}   b_ = const _b-  {-# INLINE b_ #-}-  g_ = _g-  {-# INLINE g_ #-}+  {-# INLINABLE b_ #-}+  h_ = const _h+  {-# INLINABLE h_ #-}+  q_ = const _q+  {-# INLINABLE q_ #-}+  r_ = const _r+  {-# INLINABLE r_ #-}+  x_ = const _x+  {-# INLINABLE x_ #-}+  y_ = const _y+  {-# INLINABLE y_ #-} --- | Point of M-221 curve-type P = MPoint M221 Fp+-- | Affine M221 curve point.+type PA = MAPoint M221 Fq Fr +-- | Affine M221 curve is a Montgomery affine curve.+instance MACurve M221 Fq Fr where+  gA_ = gA+  {-# INLINABLE gA_ #-}+ ------------------------------------------------------------------------------- -- Parameters ------------------------------------------------------------------------------- --- | Coefficient @A@ of M-221 curve-_a :: Fp+-- | Coefficient @A@ of M221 curve.+_a :: Fq _a = 0x1c93a-{-# INLINE _a #-}---- | Coefficient @B@ of M-221 curve-_b :: Fp-_b = 1-{-# INLINE _b #-}+{-# INLINABLE _a #-} --- | Generator of M-221 curve-_g :: P-_g = A-     4-     0xf7acdd2a4939571d1cef14eca37c228e61dbff10707dc6c08c5056d-{-# INLINE _g #-}+-- | Coefficient @B@ of M221 curve.+_b :: Fq+_b = 0x1+{-# INLINABLE _b #-} --- | Cofactor of M-221 curve+-- | Cofactor of M221 curve. _h :: Integer-_h = 8-{-# INLINE _h #-}+_h = 0x8+{-# INLINABLE _h #-} --- | Order of M-221 curve-_n :: Integer-_n = 0x40000000000000000000000000015a08ed730e8a2f77f005042605b-{-# INLINE _n #-}+-- | Characteristic of M221 curve.+_q :: Integer+_q = 0x1ffffffffffffffffffffffffffffffffffffffffffffffffffffffd+{-# INLINABLE _q #-} --- | Characteristic of M-221 curve-_p :: Integer-_p = 0x1ffffffffffffffffffffffffffffffffffffffffffffffffffffffd-{-# INLINE _p #-}+-- | Order of M221 curve.+_r :: Integer+_r = 0x40000000000000000000000000015a08ed730e8a2f77f005042605b+{-# INLINABLE _r #-}++-- | Coordinate @X@ of M221 curve.+_x :: Fq+_x = 0x4+{-# INLINABLE _x #-}++-- | Coordinate @Y@ of M221 curve.+_y :: Fq+_y = 0xf7acdd2a4939571d1cef14eca37c228e61dbff10707dc6c08c5056d+{-# INLINABLE _y #-}++-- | Generator of affine M221 curve.+gA :: PA+gA = A _x _y+{-# INLINABLE gA #-}

src/Curve/Montgomery/M383.hs view

@@ -1,74 +1,92 @@ module Curve.Montgomery.M383-  ( Fp-  , P-  , _a-  , _b-  , _g-  , _h-  , _n-  , _p+  ( module Curve.Montgomery+  , module Curve.Montgomery.M383   ) where  import Protolude -import PrimeField (PrimeField)+import PrimeField -import Curve.Montgomery (Point(..), MCurve(..), MPoint)+import Curve.Montgomery  ------------------------------------------------------------------------------- -- Types ------------------------------------------------------------------------------- --- | M-383 curve+-- | M383 curve. data M383 --- | Field of M-383 curve-type Fp = PrimeField 0x7fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff45+-- | Field of points of M383 curve.+type Fq = PrimeField 0x7fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff45 --- | M-383 curve is a Montgomery curve-instance MCurve M383 Fp where+-- | Field of coefficients of M383 curve.+type Fr = PrimeField 0x10000000000000000000000000000000000000000000000006c79673ac36ba6e7a32576f7b1b249e46bbc225be9071d7++-- | M383 curve is a Montgomery curve.+instance Curve 'Montgomery c M383 Fq Fr => MCurve c M383 Fq Fr where   a_ = const _a-  {-# INLINE a_ #-}+  {-# INLINABLE a_ #-}   b_ = const _b-  {-# INLINE b_ #-}-  g_ = _g-  {-# INLINE g_ #-}+  {-# INLINABLE b_ #-}+  h_ = const _h+  {-# INLINABLE h_ #-}+  q_ = const _q+  {-# INLINABLE q_ #-}+  r_ = const _r+  {-# INLINABLE r_ #-}+  x_ = const _x+  {-# INLINABLE x_ #-}+  y_ = const _y+  {-# INLINABLE y_ #-} --- | Point of M-383 curve-type P = MPoint M383 Fp+-- | Affine M383 curve point.+type PA = MAPoint M383 Fq Fr +-- | Affine M383 curve is a Montgomery affine curve.+instance MACurve M383 Fq Fr where+  gA_ = gA+  {-# INLINABLE gA_ #-}+ ------------------------------------------------------------------------------- -- Parameters ------------------------------------------------------------------------------- --- | Coefficient @A@ of M-383 curve-_a :: Fp+-- | Coefficient @A@ of M383 curve.+_a :: Fq _a = 0x1f82fe-{-# INLINE _a #-}---- | Coefficient @B@ of M-383 curve-_b :: Fp-_b = 1-{-# INLINE _b #-}+{-# INLINABLE _a #-} --- | Generator of M-383 curve-_g :: P-_g = A-     0xc-     0x1ec7ed04aaf834af310e304b2da0f328e7c165f0e8988abd3992861290f617aa1f1b2e7d0b6e332e969991b62555e77e-{-# INLINE _g #-}+-- | Coefficient @B@ of M383 curve.+_b :: Fq+_b = 0x1+{-# INLINABLE _b #-} --- | Cofactor of M-383 curve+-- | Cofactor of M383 curve. _h :: Integer-_h = 8-{-# INLINE _h #-}+_h = 0x8+{-# INLINABLE _h #-} --- | Order of M-383 curve-_n :: Integer-_n = 0x10000000000000000000000000000000000000000000000006c79673ac36ba6e7a32576f7b1b249e46bbc225be9071d7-{-# INLINE _n #-}+-- | Characteristic of M383 curve.+_q :: Integer+_q = 0x7fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff45+{-# INLINABLE _q #-} --- | Characteristic of M-383 curve-_p :: Integer-_p = 0x7fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff45-{-# INLINE _p #-}+-- | Order of M383 curve.+_r :: Integer+_r = 0x10000000000000000000000000000000000000000000000006c79673ac36ba6e7a32576f7b1b249e46bbc225be9071d7+{-# INLINABLE _r #-}++-- | Coordinate @X@ of M383 curve.+_x :: Fq+_x = 0xc+{-# INLINABLE _x #-}++-- | Coordinate @Y@ of M383 curve.+_y :: Fq+_y = 0x1ec7ed04aaf834af310e304b2da0f328e7c165f0e8988abd3992861290f617aa1f1b2e7d0b6e332e969991b62555e77e+{-# INLINABLE _y #-}++-- | Generator of affine M383 curve.+gA :: PA+gA = A _x _y+{-# INLINABLE gA #-}

src/Curve/Montgomery/M511.hs view

@@ -1,74 +1,92 @@ module Curve.Montgomery.M511-  ( Fp-  , P-  , _a-  , _b-  , _g-  , _h-  , _n-  , _p+  ( module Curve.Montgomery+  , module Curve.Montgomery.M511   ) where  import Protolude -import PrimeField (PrimeField)+import PrimeField -import Curve.Montgomery (Point(..), MCurve(..), MPoint)+import Curve.Montgomery  ------------------------------------------------------------------------------- -- Types ------------------------------------------------------------------------------- --- | M-511 curve+-- | M511 curve. data M511 --- | Field of M-511 curve-type Fp = PrimeField 0x7fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff45+-- | Field of points of M511 curve.+type Fq = PrimeField 0x7fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff45 --- | M-511 curve is a Montgomery curve-instance MCurve M511 Fp where+-- | Field of coefficients of M511 curve.+type Fr = PrimeField 0x100000000000000000000000000000000000000000000000000000000000000017b5feff30c7f5677ab2aeebd13779a2ac125042a6aa10bfa54c15bab76baf1b++-- | M511 curve is a Montgomery curve.+instance Curve 'Montgomery c M511 Fq Fr => MCurve c M511 Fq Fr where   a_ = const _a-  {-# INLINE a_ #-}+  {-# INLINABLE a_ #-}   b_ = const _b-  {-# INLINE b_ #-}-  g_ = _g-  {-# INLINE g_ #-}+  {-# INLINABLE b_ #-}+  h_ = const _h+  {-# INLINABLE h_ #-}+  q_ = const _q+  {-# INLINABLE q_ #-}+  r_ = const _r+  {-# INLINABLE r_ #-}+  x_ = const _x+  {-# INLINABLE x_ #-}+  y_ = const _y+  {-# INLINABLE y_ #-} --- | Point of M-511 curve-type P = MPoint M511 Fp+-- | Affine M511 curve point.+type PA = MAPoint M511 Fq Fr +-- | Affine M511 curve is a Montgomery affine curve.+instance MACurve M511 Fq Fr where+  gA_ = gA+  {-# INLINABLE gA_ #-}+ ------------------------------------------------------------------------------- -- Parameters ------------------------------------------------------------------------------- --- | Coefficient @A@ of M-511 curve-_a :: Fp+-- | Coefficient @A@ of M511 curve.+_a :: Fq _a = 0x81806-{-# INLINE _a #-}---- | Coefficient @B@ of M-511 curve-_b :: Fp-_b = 1-{-# INLINE _b #-}+{-# INLINABLE _a #-} --- | Generator of M-511 curve-_g :: P-_g = A-     5-     0x2fbdc0ad8530803d28fdbad354bb488d32399ac1cf8f6e01ee3f96389b90c809422b9429e8a43dbf49308ac4455940abe9f1dbca542093a895e30a64af056fa5-{-# INLINE _g #-}+-- | Coefficient @B@ of M511 curve.+_b :: Fq+_b = 0x1+{-# INLINABLE _b #-} --- | Cofactor of M-511 curve+-- | Cofactor of M511 curve. _h :: Integer-_h = 8-{-# INLINE _h #-}+_h = 0x8+{-# INLINABLE _h #-} --- | Order of M-511 curve-_n :: Integer-_n = 0x100000000000000000000000000000000000000000000000000000000000000017b5feff30c7f5677ab2aeebd13779a2ac125042a6aa10bfa54c15bab76baf1b-{-# INLINE _n #-}+-- | Characteristic of M511 curve.+_q :: Integer+_q = 0x7fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff45+{-# INLINABLE _q #-} --- | Characteristic of M-511 curve-_p :: Integer-_p = 0x7fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff45-{-# INLINE _p #-}+-- | Order of M511 curve.+_r :: Integer+_r = 0x100000000000000000000000000000000000000000000000000000000000000017b5feff30c7f5677ab2aeebd13779a2ac125042a6aa10bfa54c15bab76baf1b+{-# INLINABLE _r #-}++-- | Coordinate @X@ of M511 curve.+_x :: Fq+_x = 0x5+{-# INLINABLE _x #-}++-- | Coordinate @Y@ of M511 curve.+_y :: Fq+_y = 0x2fbdc0ad8530803d28fdbad354bb488d32399ac1cf8f6e01ee3f96389b90c809422b9429e8a43dbf49308ac4455940abe9f1dbca542093a895e30a64af056fa5+{-# INLINABLE _y #-}++-- | Generator of affine M511 curve.+gA :: PA+gA = A _x _y+{-# INLINABLE gA #-}

src/Curve/Weierstrass.hs view

@@ -1,117 +1,384 @@+{-# OPTIONS -fno-warn-orphans #-}+ module Curve.Weierstrass-  ( Point(..)-  , WCurve(..)-  , WPoint+  ( module Curve+  , module Curve.Weierstrass+  , module Group   ) where  import Protolude -import Control.Monad.Random (Random(..), RandomGen, getRandom)-import ExtensionField (ExtensionField, IrreducibleMonic) import GaloisField (GaloisField(..))-import PrimeField (PrimeField)-import Test.Tasty.QuickCheck (Arbitrary(..), Gen, suchThatMap) import Text.PrettyPrint.Leijen.Text (Pretty(..)) -import Curve (Curve(..))+import Curve (Coordinates(..), Curve(..), Form(..))+import Group (Group(..))  ---------------------------------------------------------------------------------- Types+-- Weierstrass form ------------------------------------------------------------------------------- --- | Weierstrass curve representation.-data W+-- | Weierstrass points.+type WPoint = Point 'Weierstrass --- | Weierstrass curve points.-type WPoint = Point W+-- | Weierstrass curves.+class (GaloisField q, GaloisField r, Curve 'Weierstrass c e q r) => WCurve c e q r where+  {-# MINIMAL a_, b_, h_, q_, r_, x_, y_ #-}+  a_ :: WPoint c e q r -> q       -- ^ Coefficient @A@.+  b_ :: WPoint c e q r -> q       -- ^ Coefficient @B@.+  h_ :: WPoint c e q r -> Integer -- ^ Curve cofactor.+  q_ :: WPoint c e q r -> Integer -- ^ Curve characteristic.+  r_ :: WPoint c e q r -> Integer -- ^ Curve order.+  x_ :: WPoint c e q r -> q       -- ^ Coordinate @X@.+  y_ :: WPoint c e q r -> q       -- ^ Coordinate @Y@. --- | Weierstrass curves @y^2 = x^3 + Ax + B@.-class Curve W c k => WCurve c k where-  a_ :: c -> k     -- ^ Coefficient @A@.-  b_ :: c -> k     -- ^ Coefficient @B@.-  g_ :: WPoint c k -- ^ Curve generator.+-------------------------------------------------------------------------------+-- Affine coordinates+------------------------------------------------------------------------------- --- Weierstrass points are arbitrary.-instance (GaloisField k, IrreducibleMonic k im, WCurve c (ExtensionField k im))-  => Arbitrary (Point W c (ExtensionField k im)) where-  arbitrary = flip mul g_ <$> (arbitrary :: Gen Int) -- TODO-instance (KnownNat p, WCurve c (PrimeField p))-  => Arbitrary (Point W c (PrimeField p)) where-  arbitrary = suchThatMap arbitrary point+-- | Weierstrass affine points.+type WAPoint = WPoint 'Affine --- Weierstrass points are pretty.-instance (GaloisField k, WCurve c k) => Pretty (Point W c k) where-  pretty (A x y) = pretty (x, y)-  pretty O       = "O"+-- | Weierstrass affine curves @y^2 = x^3 + Ax + B@.+class WCurve 'Affine e q r => WACurve e q r where+  {-# MINIMAL gA_ #-}+  gA_ :: WAPoint e q r -- ^ Curve generator. --- Weierstrass points are random.-instance (GaloisField k, WCurve c k) => Random (Point W c k) where-  random = first (flip mul g_) . (random :: RandomGen g => g -> (Int, g)) -- TODO-  -- random g = case point x of-  --   Just p -> (p, g')-  --   _      -> random g'-  --   where-  --     (x, g') = random g-  {-# INLINE random #-}-  randomR  = panic "not implemented."+-- Weierstrass affine curves are elliptic curves.+instance WACurve e q r => Curve 'Weierstrass 'Affine e q r where ----------------------------------------------------------------------------------- Operations--------------------------------------------------------------------------------+  data instance Point 'Weierstrass 'Affine e q r = A q q -- ^ Affine point.+                                                 | O     -- ^ Infinite point.+    deriving (Eq, Generic, NFData, Read, Show) --- Weierstrass curves are elliptic curves.-instance (GaloisField k, WCurve c k) => Curve W c k where+  char = q_+  {-# INLINABLE char #-} -  data instance Point W c k = A k k -- ^ Affine point.-                            | O     -- ^ Infinite point.-    deriving (Eq, Generic, NFData, Read, Show)+  cof = h_+  {-# INLINABLE cof #-} -  id = O-  {-# INLINE id #-}+  disc _ = 4 * a * a * a + 27 * b * b+    where+      a = a_ (witness :: WAPoint e q r)+      b = b_ (witness :: WAPoint e q r)+  {-# INLINABLE disc #-} -  inv O       = O-  inv (A x y) = A x (-y)-  {-# INLINE inv #-}+  fromA = identity+  {-# INLINABLE fromA #-} -  add p O          = p-  add O q          = q-  add p@(A x1 y1) (A x2 y2)-    | x1 /= x2     = A x3 y3-    | y1 + y2 == 0 = O-    | otherwise    = double p+  point x y = let p = A x y in if def p then Just p else Nothing+  {-# INLINABLE point #-}++  pointX x = A x <$> yX (witness :: WAPoint e q r) x+  {-# INLINABLE pointX #-}++  toA = identity+  {-# INLINABLE toA #-}++  yX _ x = sr (((x * x + a) * x) + b)     where+      a = a_ (witness :: WAPoint e q r)+      b = b_ (witness :: WAPoint e q r)+  {-# INLINABLE yX #-}++-- Weierstrass affine points are groups.+instance WACurve e q r => Group (WAPoint e q r) where++  add p O       = p+  add O q       = q+  add (A x1 y1) (A x2 y2)+    | x1 == x2  = O+    | otherwise = A x3 y3+    where       l  = (y1 - y2) / (x1 - x2)       x3 = l * l - x1 - x2       y3 = l * (x1 - x3) - y1-  {-# INLINE add #-}+  {-# INLINABLE add #-} -  double O       = O-  double (A _ 0) = O-  double (A x y) = A x' y'+  dbl O         = O+  dbl (A x y)+    | y == 0    = O+    | otherwise = A x' y'     where-      l  = (3 * x * x + a_ (witness :: c)) / (2 * y)+      a  = a_ (witness :: WAPoint e q r)+      l  = (3 * x * x + a) / (2 * y)       x' = l * l - 2 * x       y' = l * (x - x') - y-  {-# INLINE double #-}+  {-# INLINABLE dbl #-}    def O       = True   def (A x y) = y * y == (x * x + a) * x + b     where-      a = a_ (witness :: c)-      b = b_ (witness :: c)-  {-# INLINE def #-}+      a = a_ (witness :: WAPoint e q r)+      b = b_ (witness :: WAPoint e q r)+  {-# INLINABLE def #-} +  gen = gA_+  {-# INLINABLE gen #-}++  id = O+  {-# INLINABLE id #-}++  inv O       = O+  inv (A x y) = A x (-y)+  {-# INLINABLE inv #-}++  order = r_+  {-# INLINABLE order #-}++-- Weierstrass affine points are pretty.+instance WACurve e q r => Pretty (WAPoint e q r) where++  pretty (A x y) = pretty (x, y)+  pretty O       = "O"++-------------------------------------------------------------------------------+-- Jacobian coordinates+-------------------------------------------------------------------------------++-- | Weierstrass Jacobian points.+type WJPoint = WPoint 'Jacobian++-- | Weierstrass Jacobian curves @y^2 = x^3 + Ax + B@.+class WCurve 'Jacobian e q r => WJCurve e q r where+  {-# MINIMAL gJ_ #-}+  gJ_ :: WJPoint e q r -- ^ Curve generator.++-- Weierstrass Jacobian curves are elliptic curves.+instance WJCurve e q r => Curve 'Weierstrass 'Jacobian e q r where++  data instance Point 'Weierstrass 'Jacobian e q r = J q q q -- ^ Jacobian point.+    deriving (Generic, NFData, Read, Show)++  char = q_+  {-# INLINABLE char #-}++  cof = h_+  {-# INLINABLE cof #-}+   disc _ = 4 * a * a * a + 27 * b * b     where-      a = a_ (witness :: c)-      b = b_ (witness :: c)-  {-# INLINE disc #-}+      a = a_ (witness :: WJPoint e q r)+      b = b_ (witness :: WJPoint e q r)+  {-# INLINABLE disc #-} -  point x = A x <$> sr (((x * x + a) * x) + b)+  fromA (A x y) = J x y 1+  fromA _       = J 1 1 0+  {-# INLINABLE fromA #-}++  point x y = let p = J x y 1 in if def p then Just p else Nothing+  {-# INLINABLE point #-}++  pointX x = flip (J x) 1 <$> yX (witness :: WJPoint e q r) x+  {-# INLINABLE pointX #-}++  toA (J _ _ 0) = O+  toA (J x y z) = let zz = z * z in A (x / zz) (y / (z * zz))+  {-# INLINABLE toA #-}++  yX _ x = sr (((x * x + a) * x) + b)     where-      a = a_ (witness :: c)-      b = b_ (witness :: c)-  {-# INLINE point #-}+      a = a_ (witness :: WJPoint e q r)+      b = b_ (witness :: WJPoint e q r)+  {-# INLINABLE yX #-} -  rnd = getRandom-  {-# INLINE rnd #-}+-- Weierstrass Jacobian points are groups.+instance WJCurve e q r => Group (WJPoint e q r) where++  -- Addition formula add-2007-bl+  add  p           (J  _  _  0) = p+  add (J  _  _  0)  q           = q+  add (J x1 y1 z1) (J x2 y2 z2) = J x3 y3 z3+    where+      z1z1 = z1 * z1+      z2z2 = z2 * z2+      z1z2 = z1 + z2+      u1   = x1 * z2z2+      u2   = x2 * z1z1+      s1   = y1 * z2 * z2z2+      s2   = y2 * z1 * z1z1+      h    = u2 - u1+      h2   = 2 * h+      i    = h2 * h2+      j    = h * i+      r    = 2 * (s2 - s1)+      v    = u1 * i+      x3   = r * r - j - 2 * v+      y3   = r * (v - x3) - 2 * s1 * j+      z3   = (z1z2 * z1z2 - z1z1 - z2z2) * h+  {-# INLINABLE add #-}++  -- Doubling formula dbl-2007-bl+  dbl (J  _  _  0) = J  1  1  0+  dbl (J x1 y1 z1) = J x3 y3 z3+    where+      a    = a_ (witness :: WJPoint e q r)+      xx   = x1 * x1+      yy   = y1 * y1+      yyyy = yy * yy+      zz   = z1 * z1+      xy   = x1 + yy+      yz   = y1 + z1+      s    = 2 * (xy * xy - xx - yyyy)+      m    = 3 * xx + a * zz * zz+      t    = m * m - 2 * s+      x3   = t+      y3   = m * (s - t) - 8 * yyyy+      z3   = yz * yz - yy - zz+  {-# INLINABLE dbl #-}++  def (J x y z) = y * y == x * x * x + zz * zz * (a * x + b * zz)+    where+      a  = a_ (witness :: WJPoint e q r)+      b  = b_ (witness :: WJPoint e q r)+      zz = z * z+  {-# INLINABLE def #-}++  gen = gJ_+  {-# INLINABLE gen #-}++  id = J 1 1 0+  {-# INLINABLE id #-}++  inv (J x y z) = J x (-y) z+  {-# INLINABLE inv #-}++  order = r_+  {-# INLINABLE order #-}++-- Weierstrass Jacobian points are equatable.+instance WJCurve e q r => Eq (WJPoint e q r) where++  J x1 y1 z1 == J x2 y2 z2 = z1 == 0 && z2 == 0+    || x1 * zz2 == x2 * zz1 && y1 * z2 * zz2 == y2 * z1 * zz1+    where+      zz1 = z1 * z1+      zz2 = z2 * z2++-- Weierstrass Jacobian points are pretty.+instance WJCurve e q r => Pretty (WJPoint e q r) where++  pretty (J x y z) = pretty (x, y, z)++-------------------------------------------------------------------------------+-- Projective coordinates+-------------------------------------------------------------------------------++-- | Weierstrass projective points.+type WPPoint = WPoint 'Projective++-- | Weierstrass projective curves @y^2 = x^3 + Ax + B@.+class WCurve 'Projective e q r => WPCurve e q r where+  {-# MINIMAL gP_ #-}+  gP_ :: WPPoint e q r -- ^ Curve generator.++-- Weierstrass projective curves are elliptic curves.+instance WPCurve e q r => Curve 'Weierstrass 'Projective e q r where++  data instance Point 'Weierstrass 'Projective e q r = P q q q -- ^ Projective point.+    deriving (Generic, NFData, Read, Show)++  char = q_+  {-# INLINABLE char #-}++  cof = h_+  {-# INLINABLE cof #-}++  disc _ = 4 * a * a * a + 27 * b * b+    where+      a = a_ (witness :: WPPoint e q r)+      b = b_ (witness :: WPPoint e q r)+  {-# INLINABLE disc #-}++  fromA (A x y) = P x y 1+  fromA _       = P 0 1 0+  {-# INLINABLE fromA #-}++  point x y = let p = P x y 1 in if def p then Just p else Nothing+  {-# INLINABLE point #-}++  pointX x = flip (P x) 1 <$> yX (witness :: WPPoint e q r) x+  {-# INLINABLE pointX #-}++  toA (P _ _ 0) = O+  toA (P x y z) = A (x / z) (y / z)+  {-# INLINABLE toA #-}++  yX _ x = sr (((x * x + a) * x) + b)+    where+      a = a_ (witness :: WPPoint e q r)+      b = b_ (witness :: WPPoint e q r)+  {-# INLINABLE yX #-}++-- Weierstrass projective points are groups.+instance WPCurve e q r => Group (WPPoint e q r) where++  -- Addition formula add-1998-cmo-2+  add  p           (P  _  _  0) = p+  add (P  _  _  0)  q           = q+  add (P x1 y1 z1) (P x2 y2 z2) = P x3 y3 z3+    where+      y1z2 = y1 * z2+      x1z2 = x1 * z2+      z1z2 = z1 * z2+      u    = y2 * z1 - y1z2+      uu   = u * u+      v    = x2 * z1 - x1z2+      vv   = v * v+      vvv  = v * vv+      r    = vv * x1z2+      a    = uu * z1z2 - vvv - 2 * r+      x3   = v * a+      y3   = u * (r - a) - vvv * y1z2+      z3   = vvv * z1z2+  {-# INLINABLE add #-}++  -- Doubling formula dbl-2007-bl+  dbl (P  _  _  0) = P  0  1  0+  dbl (P x1 y1 z1) = P x3 y3 z3+    where+      xx  = x1 * x1+      zz  = z1 * z1+      w   = a_ (witness :: WPPoint e q r) * zz + 3 * xx+      s   = 2 * y1 * z1+      ss  = s * s+      sss = s * ss+      r   = y1 * s+      rr  = r * r+      xr  = x1 + r+      b   = xr * xr - xx - rr+      h   = w * w - 2 * b+      x3  = h * s+      y3  = w * (b - h) - 2 * rr+      z3  = sss+  {-# INLINABLE dbl #-}++  def (P x y z) = (x * x + a * zz) * x == (y * y - b * zz) * z+    where+      a  = a_ (witness :: WPPoint e q r)+      b  = b_ (witness :: WPPoint e q r)+      zz = z * z+  {-# INLINABLE def #-}++  gen = gP_+  {-# INLINABLE gen #-}++  id = P 0 1 0+  {-# INLINABLE id #-}++  inv (P x y z) = P x (-y) z+  {-# INLINABLE inv #-}++  order = r_+  {-# INLINABLE order #-}++-- Weierstrass projective points are equatable.+instance WPCurve e q r => Eq (WPPoint e q r) where++  P x1 y1 z1 == P x2 y2 z2 = z1 == 0 && z2 == 0+    || x1 * z2 == x2 * z1 && y1 * z2 == y2 * z1++-- Weierstrass projective points are pretty.+instance WPCurve e q r => Pretty (WPPoint e q r) where++  pretty (P x y z) = pretty (x, y, z)

src/Curve/Weierstrass/ANSSIFRP256V1.hs view

@@ -1,74 +1,118 @@ module Curve.Weierstrass.ANSSIFRP256V1-  ( Fp-  , P-  , _a-  , _b-  , _g-  , _h-  , _n-  , _p+  ( module Curve.Weierstrass+  , module Curve.Weierstrass.ANSSIFRP256V1   ) where  import Protolude -import PrimeField (PrimeField)+import PrimeField -import Curve.Weierstrass (Point(..), WCurve(..), WPoint)+import Curve.Weierstrass  ------------------------------------------------------------------------------- -- Types ------------------------------------------------------------------------------- --- | ANSSI-FRP256V1 curve+-- | ANSSIFRP256V1 curve. data ANSSIFRP256V1 --- | Field of ANSSI-FRP256V1 curve-type Fp = PrimeField 0xf1fd178c0b3ad58f10126de8ce42435b3961adbcabc8ca6de8fcf353d86e9c03+-- | Field of points of ANSSIFRP256V1 curve.+type Fq = PrimeField 0xf1fd178c0b3ad58f10126de8ce42435b3961adbcabc8ca6de8fcf353d86e9c03 --- | ANSSI-FRP256V1 curve is a Weierstrass curve-instance WCurve ANSSIFRP256V1 Fp where+-- | Field of coefficients of ANSSIFRP256V1 curve.+type Fr = PrimeField 0xf1fd178c0b3ad58f10126de8ce42435b53dc67e140d2bf941ffdd459c6d655e1++-- | ANSSIFRP256V1 curve is a Weierstrass curve.+instance Curve 'Weierstrass c ANSSIFRP256V1 Fq Fr => WCurve c ANSSIFRP256V1 Fq Fr where   a_ = const _a-  {-# INLINE a_ #-}+  {-# INLINABLE a_ #-}   b_ = const _b-  {-# INLINE b_ #-}-  g_ = _g-  {-# INLINE g_ #-}+  {-# INLINABLE b_ #-}+  h_ = const _h+  {-# INLINABLE h_ #-}+  q_ = const _q+  {-# INLINABLE q_ #-}+  r_ = const _r+  {-# INLINABLE r_ #-}+  x_ = const _x+  {-# INLINABLE x_ #-}+  y_ = const _y+  {-# INLINABLE y_ #-} --- | Point of ANSSI-FRP256V1 curve-type P = WPoint ANSSIFRP256V1 Fp+-- | Affine ANSSIFRP256V1 curve point.+type PA = WAPoint ANSSIFRP256V1 Fq Fr +-- | Affine ANSSIFRP256V1 curve is a Weierstrass affine curve.+instance WACurve ANSSIFRP256V1 Fq Fr where+  gA_ = gA+  {-# INLINABLE gA_ #-}++-- | Jacobian ANSSIFRP256V1 point.+type PJ = WJPoint ANSSIFRP256V1 Fq Fr++-- | Jacobian ANSSIFRP256V1 curve is a Weierstrass Jacobian curve.+instance WJCurve ANSSIFRP256V1 Fq Fr where+  gJ_ = gJ+  {-# INLINABLE gJ_ #-}++-- | Projective ANSSIFRP256V1 point.+type PP = WPPoint ANSSIFRP256V1 Fq Fr++-- | Projective ANSSIFRP256V1 curve is a Weierstrass projective curve.+instance WPCurve ANSSIFRP256V1 Fq Fr where+  gP_ = gP+  {-# INLINABLE gP_ #-}+ ------------------------------------------------------------------------------- -- Parameters ------------------------------------------------------------------------------- --- | Coefficient @A@ of ANSSI-FRP256V1 curve-_a :: Fp+-- | Coefficient @A@ of ANSSIFRP256V1 curve.+_a :: Fq _a = 0xf1fd178c0b3ad58f10126de8ce42435b3961adbcabc8ca6de8fcf353d86e9c00-{-# INLINE _a #-}+{-# INLINABLE _a #-} --- | Coefficient @B@ of ANSSI-FRP256V1 curve-_b :: Fp+-- | Coefficient @B@ of ANSSIFRP256V1 curve.+_b :: Fq _b = 0xee353fca5428a9300d4aba754a44c00fdfec0c9ae4b1a1803075ed967b7bb73f-{-# INLINE _b #-}---- | Generator of ANSSI-FRP256V1 curve-_g :: P-_g = A-     0xb6b3d4c356c139eb31183d4749d423958c27d2dcaf98b70164c97a2dd98f5cff-     0x6142e0f7c8b204911f9271f0f3ecef8c2701c307e8e4c9e183115a1554062cfb-{-# INLINE _g #-}+{-# INLINABLE _b #-} --- | Cofactor of ANSSI-FRP256V1 curve+-- | Cofactor of ANSSIFRP256V1 curve. _h :: Integer-_h = 1-{-# INLINE _h #-}+_h = 0x1+{-# INLINABLE _h #-} --- | Order of ANSSI-FRP256V1 curve-_n :: Integer-_n = 0xf1fd178c0b3ad58f10126de8ce42435b53dc67e140d2bf941ffdd459c6d655e1-{-# INLINE _n #-}+-- | Characteristic of ANSSIFRP256V1 curve.+_q :: Integer+_q = 0xf1fd178c0b3ad58f10126de8ce42435b3961adbcabc8ca6de8fcf353d86e9c03+{-# INLINABLE _q #-} --- | Characteristic of ANSSI-FRP256V1 curve-_p :: Integer-_p = 0xf1fd178c0b3ad58f10126de8ce42435b3961adbcabc8ca6de8fcf353d86e9c03-{-# INLINE _p #-}+-- | Order of ANSSIFRP256V1 curve.+_r :: Integer+_r = 0xf1fd178c0b3ad58f10126de8ce42435b53dc67e140d2bf941ffdd459c6d655e1+{-# INLINABLE _r #-}++-- | Coordinate @X@ of ANSSIFRP256V1 curve.+_x :: Fq+_x = 0xb6b3d4c356c139eb31183d4749d423958c27d2dcaf98b70164c97a2dd98f5cff+{-# INLINABLE _x #-}++-- | Coordinate @Y@ of ANSSIFRP256V1 curve.+_y :: Fq+_y = 0x6142e0f7c8b204911f9271f0f3ecef8c2701c307e8e4c9e183115a1554062cfb+{-# INLINABLE _y #-}++-- | Generator of affine ANSSIFRP256V1 curve.+gA :: PA+gA = A _x _y+{-# INLINABLE gA #-}++-- | Generator of Jacobian ANSSIFRP256V1 curve.+gJ :: PJ+gJ = J _x _y 1+{-# INLINABLE gJ #-}++-- | Generator of projective ANSSIFRP256V1 curve.+gP :: PP+gP = P _x _y 1+{-# INLINABLE gP #-}

src/Curve/Weierstrass/Anomalous.hs view

@@ -1,74 +1,118 @@ module Curve.Weierstrass.Anomalous-  ( Fp-  , P-  , _a-  , _b-  , _g-  , _h-  , _n-  , _p+  ( module Curve.Weierstrass+  , module Curve.Weierstrass.Anomalous   ) where  import Protolude -import PrimeField (PrimeField)+import PrimeField -import Curve.Weierstrass (Point(..), WCurve(..), WPoint)+import Curve.Weierstrass  ------------------------------------------------------------------------------- -- Types ------------------------------------------------------------------------------- --- | Anomalous curve+-- | Anomalous curve. data Anomalous --- | Field of Anomalous curve-type Fp = PrimeField 0xb0000000000000000000000953000000000000000000001f9d7+-- | Field of points of Anomalous curve.+type Fq = PrimeField 0xb0000000000000000000000953000000000000000000001f9d7 --- | Anomalous curve is a Weierstrass curve-instance WCurve Anomalous Fp where+-- | Field of coefficients of Anomalous curve.+type Fr = PrimeField 0xb0000000000000000000000953000000000000000000001f9d7++-- | Anomalous curve is a Weierstrass curve.+instance Curve 'Weierstrass c Anomalous Fq Fr => WCurve c Anomalous Fq Fr where   a_ = const _a-  {-# INLINE a_ #-}+  {-# INLINABLE a_ #-}   b_ = const _b-  {-# INLINE b_ #-}-  g_ = _g-  {-# INLINE g_ #-}+  {-# INLINABLE b_ #-}+  h_ = const _h+  {-# INLINABLE h_ #-}+  q_ = const _q+  {-# INLINABLE q_ #-}+  r_ = const _r+  {-# INLINABLE r_ #-}+  x_ = const _x+  {-# INLINABLE x_ #-}+  y_ = const _y+  {-# INLINABLE y_ #-} --- | Point of Anomalous curve-type P = WPoint Anomalous Fp+-- | Affine Anomalous curve point.+type PA = WAPoint Anomalous Fq Fr +-- | Affine Anomalous curve is a Weierstrass affine curve.+instance WACurve Anomalous Fq Fr where+  gA_ = gA+  {-# INLINABLE gA_ #-}++-- | Jacobian Anomalous point.+type PJ = WJPoint Anomalous Fq Fr++-- | Jacobian Anomalous curve is a Weierstrass Jacobian curve.+instance WJCurve Anomalous Fq Fr where+  gJ_ = gJ+  {-# INLINABLE gJ_ #-}++-- | Projective Anomalous point.+type PP = WPPoint Anomalous Fq Fr++-- | Projective Anomalous curve is a Weierstrass projective curve.+instance WPCurve Anomalous Fq Fr where+  gP_ = gP+  {-# INLINABLE gP_ #-}+ ------------------------------------------------------------------------------- -- Parameters ------------------------------------------------------------------------------- --- | Coefficient @A@ of Anomalous curve-_a :: Fp+-- | Coefficient @A@ of Anomalous curve.+_a :: Fq _a = 0x98d0fac687d6343eb1a1f595283eb1a1f58d0fac687d635f5e4-{-# INLINE _a #-}+{-# INLINABLE _a #-} --- | Coefficient @B@ of Anomalous curve-_b :: Fp+-- | Coefficient @B@ of Anomalous curve.+_b :: Fq _b = 0x4a1f58d0fac687d6343eb1a5e2d6343eb1a1f58d0fac688ab3f-{-# INLINE _b #-}---- | Generator of Anomalous curve-_g :: P-_g = A-     0x101efb35fd1963c4871a2d17edaafa7e249807f58f8705126c6-     0x22389a3954375834304ba1d509a97de6c07148ea7f5951b20e7-{-# INLINE _g #-}+{-# INLINABLE _b #-} --- | Cofactor of Anomalous curve+-- | Cofactor of Anomalous curve. _h :: Integer-_h = 1-{-# INLINE _h #-}+_h = 0x1+{-# INLINABLE _h #-} --- | Order of Anomalous curve-_n :: Integer-_n = 0xb0000000000000000000000953000000000000000000001f9d7-{-# INLINE _n #-}+-- | Characteristic of Anomalous curve.+_q :: Integer+_q = 0xb0000000000000000000000953000000000000000000001f9d7+{-# INLINABLE _q #-} --- | Characteristic of Anomalous curve-_p :: Integer-_p = 0xb0000000000000000000000953000000000000000000001f9d7-{-# INLINE _p #-}+-- | Order of Anomalous curve.+_r :: Integer+_r = 0xb0000000000000000000000953000000000000000000001f9d7+{-# INLINABLE _r #-}++-- | Coordinate @X@ of Anomalous curve.+_x :: Fq+_x = 0x101efb35fd1963c4871a2d17edaafa7e249807f58f8705126c6+{-# INLINABLE _x #-}++-- | Coordinate @Y@ of Anomalous curve.+_y :: Fq+_y = 0x22389a3954375834304ba1d509a97de6c07148ea7f5951b20e7+{-# INLINABLE _y #-}++-- | Generator of affine Anomalous curve.+gA :: PA+gA = A _x _y+{-# INLINABLE gA #-}++-- | Generator of Jacobian Anomalous curve.+gJ :: PJ+gJ = J _x _y 1+{-# INLINABLE gJ #-}++-- | Generator of projective Anomalous curve.+gP :: PP+gP = P _x _y 1+{-# INLINABLE gP #-}

+ src/Curve/Weierstrass/BLS12381.hs view

@@ -0,0 +1,118 @@+module Curve.Weierstrass.BLS12381+  ( module Curve.Weierstrass+  , module Curve.Weierstrass.BLS12381+  ) where++import Protolude++import PrimeField++import Curve.Weierstrass++-------------------------------------------------------------------------------+-- Types+-------------------------------------------------------------------------------++-- | BLS12381 curve.+data BLS12381++-- | Field of points of BLS12381 curve.+type Fq = PrimeField 0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabfffeb153ffffb9feffffffffaaab++-- | Field of coefficients of BLS12381 curve.+type Fr = PrimeField 0x73eda753299d7d483339d80809a1d80553bda402fffe5bfeffffffff00000001++-- | BLS12381 curve is a Weierstrass curve.+instance Curve 'Weierstrass c BLS12381 Fq Fr => WCurve c BLS12381 Fq Fr where+  a_ = const _a+  {-# INLINABLE a_ #-}+  b_ = const _b+  {-# INLINABLE b_ #-}+  h_ = const _h+  {-# INLINABLE h_ #-}+  q_ = const _q+  {-# INLINABLE q_ #-}+  r_ = const _r+  {-# INLINABLE r_ #-}+  x_ = const _x+  {-# INLINABLE x_ #-}+  y_ = const _y+  {-# INLINABLE y_ #-}++-- | Affine BLS12381 curve point.+type PA = WAPoint BLS12381 Fq Fr++-- | Affine BLS12381 curve is a Weierstrass affine curve.+instance WACurve BLS12381 Fq Fr where+  gA_ = gA+  {-# INLINABLE gA_ #-}++-- | Jacobian BLS12381 point.+type PJ = WJPoint BLS12381 Fq Fr++-- | Jacobian BLS12381 curve is a Weierstrass Jacobian curve.+instance WJCurve BLS12381 Fq Fr where+  gJ_ = gJ+  {-# INLINABLE gJ_ #-}++-- | Projective BLS12381 point.+type PP = WPPoint BLS12381 Fq Fr++-- | Projective BLS12381 curve is a Weierstrass projective curve.+instance WPCurve BLS12381 Fq Fr where+  gP_ = gP+  {-# INLINABLE gP_ #-}++-------------------------------------------------------------------------------+-- Parameters+-------------------------------------------------------------------------------++-- | Coefficient @A@ of BLS12381 curve.+_a :: Fq+_a = 0x0+{-# INLINABLE _a #-}++-- | Coefficient @B@ of BLS12381 curve.+_b :: Fq+_b = 0x4+{-# INLINABLE _b #-}++-- | Cofactor of BLS12381 curve.+_h :: Integer+_h = 0x396c8c005555e1568c00aaab0000aaab+{-# INLINABLE _h #-}++-- | Characteristic of BLS12381 curve.+_q :: Integer+_q = 0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabfffeb153ffffb9feffffffffaaab+{-# INLINABLE _q #-}++-- | Order of BLS12381 curve.+_r :: Integer+_r = 0x73eda753299d7d483339d80809a1d80553bda402fffe5bfeffffffff00000001+{-# INLINABLE _r #-}++-- | Coordinate @X@ of BLS12381 curve.+_x :: Fq+_x = 0x17f1d3a73197d7942695638c4fa9ac0fc3688c4f9774b905a14e3a3f171bac586c55e83ff97a1aeffb3af00adb22c6bb+{-# INLINABLE _x #-}++-- | Coordinate @Y@ of BLS12381 curve.+_y :: Fq+_y = 0x8b3f481e3aaa0f1a09e30ed741d8ae4fcf5e095d5d00af600db18cb2c04b3edd03cc744a2888ae40caa232946c5e7e1+{-# INLINABLE _y #-}++-- | Generator of affine BLS12381 curve.+gA :: PA+gA = A _x _y+{-# INLINABLE gA #-}++-- | Generator of Jacobian BLS12381 curve.+gJ :: PJ+gJ = J _x _y 1+{-# INLINABLE gJ #-}++-- | Generator of projective BLS12381 curve.+gP :: PP+gP = P _x _y 1+{-# INLINABLE gP #-}

+ src/Curve/Weierstrass/BLS12381T.hs view

@@ -0,0 +1,130 @@+module Curve.Weierstrass.BLS12381T+  ( module Curve.Weierstrass+  , module Curve.Weierstrass.BLS12381T+  ) where++import Protolude++import ExtensionField+import PrimeField++import Curve.Weierstrass+import Curve.Weierstrass.BLS12381 (Fq)++-------------------------------------------------------------------------------+-- Types+-------------------------------------------------------------------------------++-- | BLS12381T curve.+data BLS12381T++-- | Field of points of BLS12381T curve.+data PolynomialU+instance IrreducibleMonic Fq PolynomialU where+  split _ = X2 + 1+type Fq2 = ExtensionField Fq PolynomialU++-- | Field of coefficients of BLS12381T curve.+type Fr = PrimeField 0x73eda753299d7d483339d80809a1d80553bda402fffe5bfeffffffff00000001++-- | BLS12381T curve is a Weierstrass curve.+instance Curve 'Weierstrass c BLS12381T Fq2 Fr => WCurve c BLS12381T Fq2 Fr where+  a_ = const _a+  {-# INLINABLE a_ #-}+  b_ = const _b+  {-# INLINABLE b_ #-}+  h_ = const _h+  {-# INLINABLE h_ #-}+  q_ = const _q+  {-# INLINABLE q_ #-}+  r_ = const _r+  {-# INLINABLE r_ #-}+  x_ = const _x+  {-# INLINABLE x_ #-}+  y_ = const _y+  {-# INLINABLE y_ #-}++-- | Affine BLS12381T curve point.+type PA = WAPoint BLS12381T Fq2 Fr++-- | Affine BLS12381T curve is a Weierstrass affine curve.+instance WACurve BLS12381T Fq2 Fr where+  gA_ = gA+  {-# INLINABLE gA_ #-}++-- | Jacobian BLS12381T point.+type PJ = WJPoint BLS12381T Fq2 Fr++-- | Jacobian BLS12381T curve is a Weierstrass Jacobian curve.+instance WJCurve BLS12381T Fq2 Fr where+  gJ_ = gJ+  {-# INLINABLE gJ_ #-}++-- | Projective BLS12381T point.+type PP = WPPoint BLS12381T Fq2 Fr++-- | Projective BLS12381T curve is a Weierstrass projective curve.+instance WPCurve BLS12381T Fq2 Fr where+  gP_ = gP+  {-# INLINABLE gP_ #-}++-------------------------------------------------------------------------------+-- Parameters+-------------------------------------------------------------------------------++-- | Coefficient @A@ of BLS12381T curve.+_a :: Fq2+_a = toField [+             ]+{-# INLINABLE _a #-}++-- | Coefficient @B@ of BLS12381T curve.+_b :: Fq2+_b = toField [ 0x4+             , 0x4+             ]+{-# INLINABLE _b #-}++-- | Cofactor of BLS12381T curve.+_h :: Integer+_h = 0x5d543a95414e7f1091d50792876a202cd91de4547085abaa68a205b2e5a7ddfa628f1cb4d9e82ef21537e293a6691ae1616ec6e786f0c70cf1c38e31c7238e5+{-# INLINABLE _h #-}++-- | Characteristic of BLS12381T curve.+_q :: Integer+_q = 0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabfffeb153ffffb9feffffffffaaab+{-# INLINABLE _q #-}++-- | Order of BLS12381T curve.+_r :: Integer+_r = 0x73eda753299d7d483339d80809a1d80553bda402fffe5bfeffffffff00000001+{-# INLINABLE _r #-}++-- | Coordinate @X@ of BLS12381T curve.+_x :: Fq2+_x = toField [ 0x24aa2b2f08f0a91260805272dc51051c6e47ad4fa403b02b4510b647ae3d1770bac0326a805bbefd48056c8c121bdb8+             , 0x13e02b6052719f607dacd3a088274f65596bd0d09920b61ab5da61bbdc7f5049334cf11213945d57e5ac7d055d042b7e+             ]+{-# INLINABLE _x #-}++-- | Coordinate @Y@ of BLS12381T curve.+_y :: Fq2+_y = toField [ 0xce5d527727d6e118cc9cdc6da2e351aadfd9baa8cbdd3a76d429a695160d12c923ac9cc3baca289e193548608b82801+             , 0x606c4a02ea734cc32acd2b02bc28b99cb3e287e85a763af267492ab572e99ab3f370d275cec1da1aaa9075ff05f79be+             ]+{-# INLINABLE _y #-}++-- | Generator of affine BLS12381T curve.+gA :: PA+gA = A _x _y+{-# INLINABLE gA #-}++-- | Generator of Jacobian BLS12381T curve.+gJ :: PJ+gJ = J _x _y 1+{-# INLINABLE gJ #-}++-- | Generator of projective BLS12381T curve.+gP :: PP+gP = P _x _y 1+{-# INLINABLE gP #-}

− src/Curve/Weierstrass/BLS12_381.hs

@@ -1,74 +0,0 @@-module Curve.Weierstrass.BLS12_381-  ( Fp-  , P-  , _a-  , _b-  , _g-  , _h-  , _n-  , _p-  ) where--import Protolude--import PrimeField (PrimeField)--import Curve.Weierstrass (Point(..), WCurve(..), WPoint)------------------------------------------------------------------------------------ Types------------------------------------------------------------------------------------ | BLS12-381 curve-data BLS12_381---- | Field of BLS12-381 curve-type Fp = PrimeField 0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabfffeb153ffffb9feffffffffaaab---- | BLS12-381 curve is a Weierstrass curve-instance WCurve BLS12_381 Fp where-  a_ = const _a-  {-# INLINE a_ #-}-  b_ = const _b-  {-# INLINE b_ #-}-  g_ = _g-  {-# INLINE g_ #-}---- | Point of BLS12-381 curve-type P = WPoint BLS12_381 Fp------------------------------------------------------------------------------------ Parameters------------------------------------------------------------------------------------ | Coefficient @A@ of BLS12-381 curve-_a :: Fp-_a = 0-{-# INLINE _a #-}---- | Coefficient @B@ of BLS12-381 curve-_b :: Fp-_b = 4-{-# INLINE _b #-}---- | Generator of BLS12-381 curve-_g :: P-_g = A-     0x17f1d3a73197d7942695638c4fa9ac0fc3688c4f9774b905a14e3a3f171bac586c55e83ff97a1aeffb3af00adb22c6bb-     0x8b3f481e3aaa0f1a09e30ed741d8ae4fcf5e095d5d00af600db18cb2c04b3edd03cc744a2888ae40caa232946c5e7e1-{-# INLINE _g #-}---- | Cofactor of BLS12-381 curve-_h :: Integer-_h = 0x396c8c005555e1568c00aaab0000aaab-{-# INLINE _h #-}---- | Order of BLS12-381 curve-_n :: Integer-_n = 0x73eda753299d7d483339d80809a1d80553bda402fffe5bfeffffffff00000001-{-# INLINE _n #-}---- | Characteristic of BLS12-381 curve-_p :: Integer-_p = 0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabfffeb153ffffb9feffffffffaaab-{-# INLINE _p #-}

− src/Curve/Weierstrass/BLS12_381T.hs

@@ -1,86 +0,0 @@-module Curve.Weierstrass.BLS12_381T-  ( Fp2-  , P-  , _a-  , _b-  , _g-  , _h-  , _n-  , _p-  ) where--import Protolude--import ExtensionField (ExtensionField, IrreducibleMonic(..), fromList, x)--import Curve.Weierstrass (Point(..), WCurve(..), WPoint)-import Curve.Weierstrass.BLS12_381 (Fp)------------------------------------------------------------------------------------ Types------------------------------------------------------------------------------------ | BLS12-381T curve-data BLS12_381T---- | Field of BLS12-381T curve-data PolynomialU-instance IrreducibleMonic Fp PolynomialU where-  split _ = x ^ (2 :: Int) + 1-type Fp2 = ExtensionField Fp PolynomialU---- | BLS12-381T curve is a Weierstrass curve-instance WCurve BLS12_381T Fp2 where-  a_ = const _a-  {-# INLINE a_ #-}-  b_ = const _b-  {-# INLINE b_ #-}-  g_ = _g-  {-# INLINE g_ #-}---- | Point of BLS12-381T curve-type P = WPoint BLS12_381T Fp2------------------------------------------------------------------------------------ Parameters------------------------------------------------------------------------------------ | Coefficient @A@ of BLS12-381T curve-_a :: Fp2-_a = 0-{-# INLINE _a #-}---- | Coefficient @B@ of BLS12-381T curve-_b :: Fp2-_b = fromList [4, 4]-{-# INLINE _b #-}---- | Generator of BLS12-381T curve-_g :: P-_g = A-  ( fromList-   [ 0x24aa2b2f08f0a91260805272dc51051c6e47ad4fa403b02b4510b647ae3d1770bac0326a805bbefd48056c8c121bdb8-   , 0x13e02b6052719f607dacd3a088274f65596bd0d09920b61ab5da61bbdc7f5049334cf11213945d57e5ac7d055d042b7e-   ]-  )-  ( fromList-   [ 0xce5d527727d6e118cc9cdc6da2e351aadfd9baa8cbdd3a76d429a695160d12c923ac9cc3baca289e193548608b82801-   , 0x606c4a02ea734cc32acd2b02bc28b99cb3e287e85a763af267492ab572e99ab3f370d275cec1da1aaa9075ff05f79be-   ]-  )-{-# INLINE _g #-}---- | Cofactor of BLS12-381T curve-_h :: Integer-_h = 0x5d543a95414e7f1091d50792876a202cd91de4547085abaa68a205b2e5a7ddfa628f1cb4d9e82ef21537e293a6691ae1616ec6e786f0c70cf1c38e31c7238e5-{-# INLINE _h #-}---- | Order of BLS12-381T curve-_n :: Integer-_n = 0x73eda753299d7d483339d80809a1d80553bda402fffe5bfeffffffff00000001-{-# INLINE _n #-}---- | Characteristic of BLS12-381T curve-_p :: Integer-_p = 0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabfffeb153ffffb9feffffffffaaab-{-# INLINE _p #-}

+ src/Curve/Weierstrass/BLS48581.hs view

@@ -0,0 +1,118 @@+module Curve.Weierstrass.BLS48581+  ( module Curve.Weierstrass+  , module Curve.Weierstrass.BLS48581+  ) where++import Protolude++import PrimeField++import Curve.Weierstrass++-------------------------------------------------------------------------------+-- Types+-------------------------------------------------------------------------------++-- | BLS48581 curve.+data BLS48581++-- | Field of points of BLS48581 curve.+type Fq = PrimeField 0x1280f73ff3476f313824e31d47012a0056e84f8d122131bb3be6c0f1f3975444a48ae43af6e082acd9cd30394f4736daf68367a5513170ee0a578fdf721a4a48ac3edc154e6565912b++-- | Field of coefficients of BLS48581 curve.+type Fr = PrimeField 0x2386f8a925e2885e233a9ccc1615c0d6c635387a3f0b3cbe003fad6bc972c2e6e741969d34c4c92016a85c7cd0562303c4ccbe599467c24da118a5fe6fcd671c01++-- | BLS48581 curve is a Weierstrass curve.+instance Curve 'Weierstrass c BLS48581 Fq Fr => WCurve c BLS48581 Fq Fr where+  a_ = const _a+  {-# INLINABLE a_ #-}+  b_ = const _b+  {-# INLINABLE b_ #-}+  h_ = const _h+  {-# INLINABLE h_ #-}+  q_ = const _q+  {-# INLINABLE q_ #-}+  r_ = const _r+  {-# INLINABLE r_ #-}+  x_ = const _x+  {-# INLINABLE x_ #-}+  y_ = const _y+  {-# INLINABLE y_ #-}++-- | Affine BLS48581 curve point.+type PA = WAPoint BLS48581 Fq Fr++-- | Affine BLS48581 curve is a Weierstrass affine curve.+instance WACurve BLS48581 Fq Fr where+  gA_ = gA+  {-# INLINABLE gA_ #-}++-- | Jacobian BLS48581 point.+type PJ = WJPoint BLS48581 Fq Fr++-- | Jacobian BLS48581 curve is a Weierstrass Jacobian curve.+instance WJCurve BLS48581 Fq Fr where+  gJ_ = gJ+  {-# INLINABLE gJ_ #-}++-- | Projective BLS48581 point.+type PP = WPPoint BLS48581 Fq Fr++-- | Projective BLS48581 curve is a Weierstrass projective curve.+instance WPCurve BLS48581 Fq Fr where+  gP_ = gP+  {-# INLINABLE gP_ #-}++-------------------------------------------------------------------------------+-- Parameters+-------------------------------------------------------------------------------++-- | Coefficient @A@ of BLS48581 curve.+_a :: Fq+_a = 0x0+{-# INLINABLE _a #-}++-- | Coefficient @B@ of BLS48581 curve.+_b :: Fq+_b = 0x1+{-# INLINABLE _b #-}++-- | Cofactor of BLS48581 curve.+_h :: Integer+_h = 0x85555841aaaec4ac+{-# INLINABLE _h #-}++-- | Characteristic of BLS48581 curve.+_q :: Integer+_q = 0x1280f73ff3476f313824e31d47012a0056e84f8d122131bb3be6c0f1f3975444a48ae43af6e082acd9cd30394f4736daf68367a5513170ee0a578fdf721a4a48ac3edc154e6565912b+{-# INLINABLE _q #-}++-- | Order of BLS48581 curve.+_r :: Integer+_r = 0x2386f8a925e2885e233a9ccc1615c0d6c635387a3f0b3cbe003fad6bc972c2e6e741969d34c4c92016a85c7cd0562303c4ccbe599467c24da118a5fe6fcd671c01+{-# INLINABLE _r #-}++-- | Coordinate @X@ of BLS48581 curve.+_x :: Fq+_x = 0x2af59b7ac340f2baf2b73df1e93f860de3f257e0e86868cf61abdbaedffb9f7544550546a9df6f9645847665d859236ebdbc57db368b11786cb74da5d3a1e6d8c3bce8732315af640+{-# INLINABLE _x #-}++-- | Coordinate @Y@ of BLS48581 curve.+_y :: Fq+_y = 0xcefda44f6531f91f86b3a2d1fb398a488a553c9efeb8a52e991279dd41b720ef7bb7beffb98aee53e80f678584c3ef22f487f77c2876d1b2e35f37aef7b926b576dbb5de3e2587a70+{-# INLINABLE _y #-}++-- | Generator of affine BLS48581 curve.+gA :: PA+gA = A _x _y+{-# INLINABLE gA #-}++-- | Generator of Jacobian BLS48581 curve.+gJ :: PJ+gJ = J _x _y 1+{-# INLINABLE gJ #-}++-- | Generator of projective BLS48581 curve.+gP :: PP+gP = P _x _y 1+{-# INLINABLE gP #-}

+ src/Curve/Weierstrass/BLS48581T.hs view

@@ -0,0 +1,168 @@+module Curve.Weierstrass.BLS48581T+  ( module Curve.Weierstrass+  , module Curve.Weierstrass.BLS48581T+  ) where++import Protolude++import ExtensionField+import PrimeField++import Curve.Weierstrass+import Curve.Weierstrass.BLS48581 (Fq)++-------------------------------------------------------------------------------+-- Types+-------------------------------------------------------------------------------++-- | BLS48581T curve.+data BLS48581T++-- | Field of points of BLS48581T curve.+data PolynomialU+instance IrreducibleMonic Fq PolynomialU where+  split _ = X2 + 1+type Fq2 = ExtensionField Fq PolynomialU+data PolynomialV+instance IrreducibleMonic Fq2 PolynomialV where+  split _ = X2 + 1 + Y X+type Fq4 = ExtensionField Fq2 PolynomialV+data PolynomialW+instance IrreducibleMonic Fq4 PolynomialW where+  split _ = X2 + Y X+type Fq8 = ExtensionField Fq4 PolynomialW++-- | Field of coefficients of BLS48581T curve.+type Fr = PrimeField 0x2386f8a925e2885e233a9ccc1615c0d6c635387a3f0b3cbe003fad6bc972c2e6e741969d34c4c92016a85c7cd0562303c4ccbe599467c24da118a5fe6fcd671c01++-- | BLS48581T curve is a Weierstrass curve.+instance Curve 'Weierstrass c BLS48581T Fq8 Fr => WCurve c BLS48581T Fq8 Fr where+  a_ = const _a+  {-# INLINABLE a_ #-}+  b_ = const _b+  {-# INLINABLE b_ #-}+  h_ = const _h+  {-# INLINABLE h_ #-}+  q_ = const _q+  {-# INLINABLE q_ #-}+  r_ = const _r+  {-# INLINABLE r_ #-}+  x_ = const _x+  {-# INLINABLE x_ #-}+  y_ = const _y+  {-# INLINABLE y_ #-}++-- | Affine BLS48581T curve point.+type PA = WAPoint BLS48581T Fq8 Fr++-- | Affine BLS48581T curve is a Weierstrass affine curve.+instance WACurve BLS48581T Fq8 Fr where+  gA_ = gA+  {-# INLINABLE gA_ #-}++-- | Jacobian BLS48581T point.+type PJ = WJPoint BLS48581T Fq8 Fr++-- | Jacobian BLS48581T curve is a Weierstrass Jacobian curve.+instance WJCurve BLS48581T Fq8 Fr where+  gJ_ = gJ+  {-# INLINABLE gJ_ #-}++-- | Projective BLS48581T point.+type PP = WPPoint BLS48581T Fq8 Fr++-- | Projective BLS48581T curve is a Weierstrass projective curve.+instance WPCurve BLS48581T Fq8 Fr where+  gP_ = gP+  {-# INLINABLE gP_ #-}++-------------------------------------------------------------------------------+-- Parameters+-------------------------------------------------------------------------------++-- | Coefficient @A@ of BLS48581T curve.+_a :: Fq8+_a = toField [+             ]+{-# INLINABLE _a #-}++-- | Coefficient @B@ of BLS48581T curve.+_b :: Fq8+_b = toField [ toField [+                       ]+             , toField [ toField [+                                 ]+                       , toField [ 0x9407b9ff9a3b7989c12718ea38095002b7427c6891098dd9df36078f9cbaa225245721d7b7041566ce6981ca7a39b6d7b41b3d2a898b877052bc7efb90d2524561f6e0aa732b2c895+                                 , 0x9407b9ff9a3b7989c12718ea38095002b7427c6891098dd9df36078f9cbaa225245721d7b7041566ce6981ca7a39b6d7b41b3d2a898b877052bc7efb90d2524561f6e0aa732b2c896+                                 ]+                       ]+             ]+{-# INLINABLE _b #-}++-- | Cofactor of BLS48581T curve.+_h :: Integer+_h = 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{-# INLINABLE _h #-}++-- | Characteristic of BLS48581T curve.+_q :: Integer+_q = 0x1280f73ff3476f313824e31d47012a0056e84f8d122131bb3be6c0f1f3975444a48ae43af6e082acd9cd30394f4736daf68367a5513170ee0a578fdf721a4a48ac3edc154e6565912b+{-# INLINABLE _q #-}++-- | Order of BLS48581T curve.+_r :: Integer+_r = 0x2386f8a925e2885e233a9ccc1615c0d6c635387a3f0b3cbe003fad6bc972c2e6e741969d34c4c92016a85c7cd0562303c4ccbe599467c24da118a5fe6fcd671c01+{-# INLINABLE _r #-}++-- | Coordinate @X@ of BLS48581T curve.+_x :: Fq8+_x = toField [ toField [ toField [ 0x5d615d9a7871e4a38237fa45a2775debabbefc70344dbccb7de64db3a2ef156c46ff79baad1a8c42281a63ca0612f400503004d80491f510317b79766322154dec34fd0b4ace8bfab+                                 , 0x7c4973ece2258512069b0e86abc07e8b22bb6d980e1623e9526f6da12307f4e1c3943a00abfedf16214a76affa62504f0c3c7630d979630ffd75556a01afa143f1669b36676b47c57+                                 ]+                       , toField [ 0x1fccc70198f1334e1b2ea1853ad83bc73a8a6ca9ae237ca7a6d6957ccbab5ab6860161c1dbd19242ffae766f0d2a6d55f028cbdfbb879d5fea8ef4cded6b3f0b46488156ca55a3e6a+                                 , 0xbe2218c25ceb6185c78d8012954d4bfe8f5985ac62f3e5821b7b92a393f8be0cc218a95f63e1c776e6ec143b1b279b9468c31c5257c200ca52310b8cb4e80bc3f09a7033cbb7feafe+                                 ]+                       ]+             , toField [ toField [ 0x38b91c600b35913a3c598e4caa9dd63007c675d0b1642b5675ff0e7c5805386699981f9e48199d5ac10b2ef492ae589274fad55fc1889aa80c65b5f746c9d4cbb739c3a1c53f8cce5+                                 , 0xc96c7797eb0738603f1311e4ecda088f7b8f35dcef0977a3d1a58677bb037418181df63835d28997eb57b40b9c0b15dd7595a9f177612f097fc7960910fce3370f2004d914a3c093a+                                 ]+                       , toField [ 0xb9b7951c6061ee3f0197a498908aee660dea41b39d13852b6db908ba2c0b7a449cef11f293b13ced0fd0caa5efcf3432aad1cbe4324c22d63334b5b0e205c3354e41607e60750e057+                                 , 0x827d5c22fb2bdec5282624c4f4aaa2b1e5d7a9defaf47b5211cf741719728a7f9f8cfca93f29cff364a7190b7e2b0d4585479bd6aebf9fc44e56af2fc9e97c3f84e19da00fbc6ae34+                                 ]+                       ]+             ]+{-# INLINABLE _x #-}++-- | Coordinate @Y@ of BLS48581T curve.+_y :: Fq8+_y = toField [ toField [ toField [ 0xeb53356c375b5dfa497216452f3024b918b4238059a577e6f3b39ebfc435faab0906235afa27748d90f7336d8ae5163c1599abf77eea6d659045012ab12c0ff323edd3fe4d2d7971+                                 , 0x284dc75979e0ff144da6531815fcadc2b75a422ba325e6fba01d72964732fcbf3afb096b243b1f192c5c3d1892ab24e1dd212fa097d760e2e588b423525ffc7b111471db936cd5665+                                 ]+                       , toField [ 0xb36a201dd008523e421efb70367669ef2c2fc5030216d5b119d3a480d370514475f7d5c99d0e90411515536ca3295e5e2f0c1d35d51a652269cbc7c46fc3b8fde68332a526a2a8474+                                 , 0xaec25a4621edc0688223fbbd478762b1c2cded3360dcee23dd8b0e710e122d2742c89b224333fa40dced2817742770ba10d67bda503ee5e578fb3d8b8a1e5337316213da92841589d+                                 ]+                       ]+             , toField [ toField [ 0xd209d5a223a9c46916503fa5a88325a2554dc541b43dd93b5a959805f1129857ed85c77fa238cdce8a1e2ca4e512b64f59f430135945d137b08857fdddfcf7a43f47831f982e50137+                                 , 0x7d0d03745736b7a513d339d5ad537b90421ad66eb16722b589d82e2055ab7504fa83420e8c270841f6824f47c180d139e3aafc198caa72b679da59ed8226cf3a594eedc58cf90bee4+                                 ]+                       , toField [ 0x896767811be65ea25c2d05dfdd17af8a006f364fc0841b064155f14e4c819a6df98f425ae3a2864f22c1fab8c74b2618b5bb40fa639f53dccc9e884017d9aa62b3d41faeafeb23986+                                 , 0x35e2524ff89029d393a5c07e84f981b5e068f1406be8e50c87549b6ef8eca9a9533a3f8e69c31e97e1ad0333ec719205417300d8c4ab33f748e5ac66e84069c55d667ffcb732718b6+                                 ]+                       ]+             ]+{-# INLINABLE _y #-}++-- | Generator of affine BLS48581T curve.+gA :: PA+gA = A _x _y+{-# INLINABLE gA #-}++-- | Generator of Jacobian BLS48581T curve.+gJ :: PJ+gJ = J _x _y 1+{-# INLINABLE gJ #-}++-- | Generator of projective BLS48581T curve.+gP :: PP+gP = P _x _y 1+{-# INLINABLE gP #-}

− src/Curve/Weierstrass/BLS48_581.hs

@@ -1,74 +0,0 @@-module Curve.Weierstrass.BLS48_581-  ( Fp-  , P-  , _a-  , _b-  , _g-  , _h-  , _n-  , _p-  ) where--import Protolude--import PrimeField (PrimeField)--import Curve.Weierstrass (Point(..), WCurve(..), WPoint)------------------------------------------------------------------------------------ Types------------------------------------------------------------------------------------ | BLS48-581 curve-data BLS48_581---- | Field of BLS48-581 curve-type Fp = PrimeField 0x1280f73ff3476f313824e31d47012a0056e84f8d122131bb3be6c0f1f3975444a48ae43af6e082acd9cd30394f4736daf68367a5513170ee0a578fdf721a4a48ac3edc154e6565912b---- | BLS48-581 curve is a Weierstrass curve-instance WCurve BLS48_581 Fp where-  a_ = const _a-  {-# INLINE a_ #-}-  b_ = const _b-  {-# INLINE b_ #-}-  g_ = _g-  {-# INLINE g_ #-}---- | Point of BLS48-581 curve-type P = WPoint BLS48_581 Fp------------------------------------------------------------------------------------ Parameters------------------------------------------------------------------------------------ | Coefficient @A@ of BLS48-581 curve-_a :: Fp-_a = 0-{-# INLINE _a #-}---- | Coefficient @B@ of BLS48-581 curve-_b :: Fp-_b = 1-{-# INLINE _b #-}---- | Generator of BLS48-581 curve-_g :: P-_g = A-     0x2af59b7ac340f2baf2b73df1e93f860de3f257e0e86868cf61abdbaedffb9f7544550546a9df6f9645847665d859236ebdbc57db368b11786cb74da5d3a1e6d8c3bce8732315af640-     0xcefda44f6531f91f86b3a2d1fb398a488a553c9efeb8a52e991279dd41b720ef7bb7beffb98aee53e80f678584c3ef22f487f77c2876d1b2e35f37aef7b926b576dbb5de3e2587a70-{-# INLINE _g #-}---- | Cofactor of BLS48-581 curve-_h :: Integer-_h = 0x85555841aaaec4ac-{-# INLINE _h #-}---- | Order of BLS48-581 curve-_n :: Integer-_n = 0x2386f8a925e2885e233a9ccc1615c0d6c635387a3f0b3cbe003fad6bc972c2e6e741969d34c4c92016a85c7cd0562303c4ccbe599467c24da118a5fe6fcd671c01-{-# INLINE _n #-}---- | Characteristic of BLS48-581 curve-_p :: Integer-_p = 0x1280f73ff3476f313824e31d47012a0056e84f8d122131bb3be6c0f1f3975444a48ae43af6e082acd9cd30394f4736daf68367a5513170ee0a578fdf721a4a48ac3edc154e6565912b-{-# INLINE _p #-}

− src/Curve/Weierstrass/BLS48_581T.hs

@@ -1,130 +0,0 @@-module Curve.Weierstrass.BLS48_581T-  ( Fp8-  , P-  , _a-  , _b-  , _g-  , _h-  , _n-  , _p-  ) where--import Protolude--import ExtensionField (ExtensionField, IrreducibleMonic(..), fromList, t, x)--import Curve.Weierstrass (Point(..), WCurve(..), WPoint)-import Curve.Weierstrass.BLS48_581 (Fp)------------------------------------------------------------------------------------ Types------------------------------------------------------------------------------------ | BLS48-581T curve-data BLS48_581T---- | Field of BLS48-581T curve-data PolynomialU-instance IrreducibleMonic Fp PolynomialU where-  split _ = x ^ (2 :: Int) + 1-type Fp2 = ExtensionField Fp PolynomialU-data PolynomialV-instance IrreducibleMonic Fp2 PolynomialV where-  split _ = x ^ (2 :: Int) + 1 + t x-type Fp4 = ExtensionField Fp2 PolynomialV-data PolynomialW-instance IrreducibleMonic Fp4 PolynomialW where-  split _ = x ^ (2 :: Int) + t x-type Fp8 = ExtensionField Fp4 PolynomialW---- | BLS48-581T curve is a Weierstrass curve-instance WCurve BLS48_581T Fp8 where-  a_ = const _a-  {-# INLINE a_ #-}-  b_ = const _b-  {-# INLINE b_ #-}-  g_ = _g-  {-# INLINE g_ #-}---- | Point of BLS48-581T curve-type P = WPoint BLS48_581T Fp8------------------------------------------------------------------------------------ Parameters------------------------------------------------------------------------------------ | Coefficient @A@ of BLS48-581T curve-_a :: Fp8-_a = 0-{-# INLINE _a #-}---- | Coefficient @B@ of BLS48-581T curve-_b :: Fp8-_b = -1 / fromList [0, 1]-{-# INLINE _b #-}---- | Generator of BLS48-581T curve-_g :: P-_g = A-  ( fromList-   [ fromList-    [ fromList-     [ 0x5d615d9a7871e4a38237fa45a2775debabbefc70344dbccb7de64db3a2ef156c46ff79baad1a8c42281a63ca0612f400503004d80491f510317b79766322154dec34fd0b4ace8bfab-     , 0x7c4973ece2258512069b0e86abc07e8b22bb6d980e1623e9526f6da12307f4e1c3943a00abfedf16214a76affa62504f0c3c7630d979630ffd75556a01afa143f1669b36676b47c57-     ]-    , fromList-     [ 0x1fccc70198f1334e1b2ea1853ad83bc73a8a6ca9ae237ca7a6d6957ccbab5ab6860161c1dbd19242ffae766f0d2a6d55f028cbdfbb879d5fea8ef4cded6b3f0b46488156ca55a3e6a-     , 0xbe2218c25ceb6185c78d8012954d4bfe8f5985ac62f3e5821b7b92a393f8be0cc218a95f63e1c776e6ec143b1b279b9468c31c5257c200ca52310b8cb4e80bc3f09a7033cbb7feafe-     ]-    ]-   , fromList-    [ fromList-     [ 0x38b91c600b35913a3c598e4caa9dd63007c675d0b1642b5675ff0e7c5805386699981f9e48199d5ac10b2ef492ae589274fad55fc1889aa80c65b5f746c9d4cbb739c3a1c53f8cce5-     , 0xc96c7797eb0738603f1311e4ecda088f7b8f35dcef0977a3d1a58677bb037418181df63835d28997eb57b40b9c0b15dd7595a9f177612f097fc7960910fce3370f2004d914a3c093a-     ]-    , fromList-     [ 0xb9b7951c6061ee3f0197a498908aee660dea41b39d13852b6db908ba2c0b7a449cef11f293b13ced0fd0caa5efcf3432aad1cbe4324c22d63334b5b0e205c3354e41607e60750e057-     , 0x827d5c22fb2bdec5282624c4f4aaa2b1e5d7a9defaf47b5211cf741719728a7f9f8cfca93f29cff364a7190b7e2b0d4585479bd6aebf9fc44e56af2fc9e97c3f84e19da00fbc6ae34-     ]-    ]-   ]-  )-  ( fromList-   [ fromList-    [ fromList-     [ 0xeb53356c375b5dfa497216452f3024b918b4238059a577e6f3b39ebfc435faab0906235afa27748d90f7336d8ae5163c1599abf77eea6d659045012ab12c0ff323edd3fe4d2d7971-     , 0x284dc75979e0ff144da6531815fcadc2b75a422ba325e6fba01d72964732fcbf3afb096b243b1f192c5c3d1892ab24e1dd212fa097d760e2e588b423525ffc7b111471db936cd5665-     ]-    , fromList-     [ 0xb36a201dd008523e421efb70367669ef2c2fc5030216d5b119d3a480d370514475f7d5c99d0e90411515536ca3295e5e2f0c1d35d51a652269cbc7c46fc3b8fde68332a526a2a8474-     , 0xaec25a4621edc0688223fbbd478762b1c2cded3360dcee23dd8b0e710e122d2742c89b224333fa40dced2817742770ba10d67bda503ee5e578fb3d8b8a1e5337316213da92841589d-     ]-    ]-   , fromList-    [ fromList-     [ 0xd209d5a223a9c46916503fa5a88325a2554dc541b43dd93b5a959805f1129857ed85c77fa238cdce8a1e2ca4e512b64f59f430135945d137b08857fdddfcf7a43f47831f982e50137-     , 0x7d0d03745736b7a513d339d5ad537b90421ad66eb16722b589d82e2055ab7504fa83420e8c270841f6824f47c180d139e3aafc198caa72b679da59ed8226cf3a594eedc58cf90bee4-     ]-    , fromList-     [ 0x896767811be65ea25c2d05dfdd17af8a006f364fc0841b064155f14e4c819a6df98f425ae3a2864f22c1fab8c74b2618b5bb40fa639f53dccc9e884017d9aa62b3d41faeafeb23986-     , 0x35e2524ff89029d393a5c07e84f981b5e068f1406be8e50c87549b6ef8eca9a9533a3f8e69c31e97e1ad0333ec719205417300d8c4ab33f748e5ac66e84069c55d667ffcb732718b6-     ]-    ]-   ]-  )-{-# INLINE _g #-}---- | Cofactor of BLS48-581T curve-_h :: Integer-_h = 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-{-# INLINE _h #-}---- | Order of BLS48-581T curve-_n :: Integer-_n = 0x2386f8a925e2885e233a9ccc1615c0d6c635387a3f0b3cbe003fad6bc972c2e6e741969d34c4c92016a85c7cd0562303c4ccbe599467c24da118a5fe6fcd671c01-{-# INLINE _n #-}---- | Characteristic of BLS48-581T curve-_p :: Integer-_p = 0x1280f73ff3476f313824e31d47012a0056e84f8d122131bb3be6c0f1f3975444a48ae43af6e082acd9cd30394f4736daf68367a5513170ee0a578fdf721a4a48ac3edc154e6565912b-{-# INLINE _p #-}

src/Curve/Weierstrass/BN224.hs view

@@ -1,74 +1,118 @@ module Curve.Weierstrass.BN224-  ( Fp-  , P-  , _a-  , _b-  , _g-  , _h-  , _n-  , _p+  ( module Curve.Weierstrass+  , module Curve.Weierstrass.BN224   ) where  import Protolude -import PrimeField (PrimeField)+import PrimeField -import Curve.Weierstrass (Point(..), WCurve(..), WPoint)+import Curve.Weierstrass  ------------------------------------------------------------------------------- -- Types ------------------------------------------------------------------------------- --- | BN224 curve+-- | BN224 curve. data BN224 --- | Field of BN224 curve-type Fp = PrimeField 0xfffffffffff107288ec29e602c4520db42180823bb907d1287127833+-- | Field of points of BN224 curve.+type Fq = PrimeField 0xfffffffffff107288ec29e602c4520db42180823bb907d1287127833 --- | BN224 curve is a Weierstrass curve-instance WCurve BN224 Fp where+-- | Field of coefficients of BN224 curve.+type Fr = PrimeField 0xfffffffffff107288ec29e602c4420db4218082b36c2accff76c58ed++-- | BN224 curve is a Weierstrass curve.+instance Curve 'Weierstrass c BN224 Fq Fr => WCurve c BN224 Fq Fr where   a_ = const _a-  {-# INLINE a_ #-}+  {-# INLINABLE a_ #-}   b_ = const _b-  {-# INLINE b_ #-}-  g_ = _g-  {-# INLINE g_ #-}+  {-# INLINABLE b_ #-}+  h_ = const _h+  {-# INLINABLE h_ #-}+  q_ = const _q+  {-# INLINABLE q_ #-}+  r_ = const _r+  {-# INLINABLE r_ #-}+  x_ = const _x+  {-# INLINABLE x_ #-}+  y_ = const _y+  {-# INLINABLE y_ #-} --- | Point of BN224 curve-type P = WPoint BN224 Fp+-- | Affine BN224 curve point.+type PA = WAPoint BN224 Fq Fr +-- | Affine BN224 curve is a Weierstrass affine curve.+instance WACurve BN224 Fq Fr where+  gA_ = gA+  {-# INLINABLE gA_ #-}++-- | Jacobian BN224 point.+type PJ = WJPoint BN224 Fq Fr++-- | Jacobian BN224 curve is a Weierstrass Jacobian curve.+instance WJCurve BN224 Fq Fr where+  gJ_ = gJ+  {-# INLINABLE gJ_ #-}++-- | Projective BN224 point.+type PP = WPPoint BN224 Fq Fr++-- | Projective BN224 curve is a Weierstrass projective curve.+instance WPCurve BN224 Fq Fr where+  gP_ = gP+  {-# INLINABLE gP_ #-}+ ------------------------------------------------------------------------------- -- Parameters ------------------------------------------------------------------------------- --- | Coefficient @A@ of BN224 curve-_a :: Fp-_a = 0-{-# INLINE _a #-}---- | Coefficient @B@ of BN224 curve-_b :: Fp-_b = 3-{-# INLINE _b #-}+-- | Coefficient @A@ of BN224 curve.+_a :: Fq+_a = 0x0+{-# INLINABLE _a #-} --- | Generator of BN224 curve-_g :: P-_g = A-     1-     2-{-# INLINE _g #-}+-- | Coefficient @B@ of BN224 curve.+_b :: Fq+_b = 0x3+{-# INLINABLE _b #-} --- | Cofactor of BN224 curve+-- | Cofactor of BN224 curve. _h :: Integer-_h = 1-{-# INLINE _h #-}+_h = 0x1+{-# INLINABLE _h #-} --- | Order of BN224 curve-_n :: Integer-_n = 0xfffffffffff107288ec29e602c4420db4218082b36c2accff76c58ed-{-# INLINE _n #-}+-- | Characteristic of BN224 curve.+_q :: Integer+_q = 0xfffffffffff107288ec29e602c4520db42180823bb907d1287127833+{-# INLINABLE _q #-} --- | Characteristic of BN224 curve-_p :: Integer-_p = 0xfffffffffff107288ec29e602c4520db42180823bb907d1287127833-{-# INLINE _p #-}+-- | Order of BN224 curve.+_r :: Integer+_r = 0xfffffffffff107288ec29e602c4420db4218082b36c2accff76c58ed+{-# INLINABLE _r #-}++-- | Coordinate @X@ of BN224 curve.+_x :: Fq+_x = 0x1+{-# INLINABLE _x #-}++-- | Coordinate @Y@ of BN224 curve.+_y :: Fq+_y = 0x2+{-# INLINABLE _y #-}++-- | Generator of affine BN224 curve.+gA :: PA+gA = A _x _y+{-# INLINABLE gA #-}++-- | Generator of Jacobian BN224 curve.+gJ :: PJ+gJ = J _x _y 1+{-# INLINABLE gJ #-}++-- | Generator of projective BN224 curve.+gP :: PP+gP = P _x _y 1+{-# INLINABLE gP #-}

src/Curve/Weierstrass/BN254.hs view

@@ -1,74 +1,118 @@ module Curve.Weierstrass.BN254-  ( Fp-  , P-  , _a-  , _b-  , _g-  , _h-  , _n-  , _p+  ( module Curve.Weierstrass+  , module Curve.Weierstrass.BN254   ) where  import Protolude -import PrimeField (PrimeField)+import PrimeField -import Curve.Weierstrass (Point(..), WCurve(..), WPoint)+import Curve.Weierstrass  ------------------------------------------------------------------------------- -- Types ------------------------------------------------------------------------------- --- | BN254 curve+-- | BN254 curve. data BN254 --- | Field of BN254 curve-type Fp = PrimeField 0x30644e72e131a029b85045b68181585d97816a916871ca8d3c208c16d87cfd47+-- | Field of points of BN254 curve.+type Fq = PrimeField 0x30644e72e131a029b85045b68181585d97816a916871ca8d3c208c16d87cfd47 --- | BN254 curve is a Weierstrass curve-instance WCurve BN254 Fp where+-- | Field of coefficients of BN254 curve.+type Fr = PrimeField 0x30644e72e131a029b85045b68181585d2833e84879b9709143e1f593f0000001++-- | BN254 curve is a Weierstrass curve.+instance Curve 'Weierstrass c BN254 Fq Fr => WCurve c BN254 Fq Fr where   a_ = const _a-  {-# INLINE a_ #-}+  {-# INLINABLE a_ #-}   b_ = const _b-  {-# INLINE b_ #-}-  g_ = _g-  {-# INLINE g_ #-}+  {-# INLINABLE b_ #-}+  h_ = const _h+  {-# INLINABLE h_ #-}+  q_ = const _q+  {-# INLINABLE q_ #-}+  r_ = const _r+  {-# INLINABLE r_ #-}+  x_ = const _x+  {-# INLINABLE x_ #-}+  y_ = const _y+  {-# INLINABLE y_ #-} --- | Point of BN254 curve-type P = WPoint BN254 Fp+-- | Affine BN254 curve point.+type PA = WAPoint BN254 Fq Fr +-- | Affine BN254 curve is a Weierstrass affine curve.+instance WACurve BN254 Fq Fr where+  gA_ = gA+  {-# INLINABLE gA_ #-}++-- | Jacobian BN254 point.+type PJ = WJPoint BN254 Fq Fr++-- | Jacobian BN254 curve is a Weierstrass Jacobian curve.+instance WJCurve BN254 Fq Fr where+  gJ_ = gJ+  {-# INLINABLE gJ_ #-}++-- | Projective BN254 point.+type PP = WPPoint BN254 Fq Fr++-- | Projective BN254 curve is a Weierstrass projective curve.+instance WPCurve BN254 Fq Fr where+  gP_ = gP+  {-# INLINABLE gP_ #-}+ ------------------------------------------------------------------------------- -- Parameters ------------------------------------------------------------------------------- --- | Coefficient @A@ of BN254 curve-_a :: Fp-_a = 0-{-# INLINE _a #-}---- | Coefficient @B@ of BN254 curve-_b :: Fp-_b = 3-{-# INLINE _b #-}+-- | Coefficient @A@ of BN254 curve.+_a :: Fq+_a = 0x0+{-# INLINABLE _a #-} --- | Generator of BN254 curve-_g :: P-_g = A-     1-     2-{-# INLINE _g #-}+-- | Coefficient @B@ of BN254 curve.+_b :: Fq+_b = 0x3+{-# INLINABLE _b #-} --- | Cofactor of BN254 curve+-- | Cofactor of BN254 curve. _h :: Integer-_h = 1-{-# INLINE _h #-}+_h = 0x1+{-# INLINABLE _h #-} --- | Order of BN254 curve-_n :: Integer-_n = 0x30644e72e131a029b85045b68181585d2833e84879b9709143e1f593f0000001-{-# INLINE _n #-}+-- | Characteristic of BN254 curve.+_q :: Integer+_q = 0x30644e72e131a029b85045b68181585d97816a916871ca8d3c208c16d87cfd47+{-# INLINABLE _q #-} --- | Characteristic of BN254 curve-_p :: Integer-_p = 0x30644e72e131a029b85045b68181585d97816a916871ca8d3c208c16d87cfd47-{-# INLINE _p #-}+-- | Order of BN254 curve.+_r :: Integer+_r = 0x30644e72e131a029b85045b68181585d2833e84879b9709143e1f593f0000001+{-# INLINABLE _r #-}++-- | Coordinate @X@ of BN254 curve.+_x :: Fq+_x = 0x1+{-# INLINABLE _x #-}++-- | Coordinate @Y@ of BN254 curve.+_y :: Fq+_y = 0x2+{-# INLINABLE _y #-}++-- | Generator of affine BN254 curve.+gA :: PA+gA = A _x _y+{-# INLINABLE gA #-}++-- | Generator of Jacobian BN254 curve.+gJ :: PJ+gJ = J _x _y 1+{-# INLINABLE gJ #-}++-- | Generator of projective BN254 curve.+gP :: PP+gP = P _x _y 1+{-# INLINABLE gP #-}

src/Curve/Weierstrass/BN254A.hs view

@@ -1,74 +1,118 @@ module Curve.Weierstrass.BN254A-  ( Fp-  , P-  , _a-  , _b-  , _g-  , _h-  , _n-  , _p+  ( module Curve.Weierstrass+  , module Curve.Weierstrass.BN254A   ) where  import Protolude -import PrimeField (PrimeField)+import PrimeField -import Curve.Weierstrass (Point(..), WCurve(..), WPoint)+import Curve.Weierstrass  ------------------------------------------------------------------------------- -- Types ------------------------------------------------------------------------------- --- | BN254A curve+-- | BN254A curve. data BN254A --- | Field of BN254A curve-type Fp = PrimeField 0x2370fb049d410fbe4e761a9886e502417d023f40180000017e80600000000001+-- | Field of points of BN254A curve.+type Fq = PrimeField 0x2370fb049d410fbe4e761a9886e502417d023f40180000017e80600000000001 --- | BN254A curve is a Weierstrass curve-instance WCurve BN254A Fp where+-- | Field of coefficients of BN254A curve.+type Fr = PrimeField 0x2370fb049d410fbe4e761a9886e502411dc1af70120000017e80600000000001++-- | BN254A curve is a Weierstrass curve.+instance Curve 'Weierstrass c BN254A Fq Fr => WCurve c BN254A Fq Fr where   a_ = const _a-  {-# INLINE a_ #-}+  {-# INLINABLE a_ #-}   b_ = const _b-  {-# INLINE b_ #-}-  g_ = _g-  {-# INLINE g_ #-}+  {-# INLINABLE b_ #-}+  h_ = const _h+  {-# INLINABLE h_ #-}+  q_ = const _q+  {-# INLINABLE q_ #-}+  r_ = const _r+  {-# INLINABLE r_ #-}+  x_ = const _x+  {-# INLINABLE x_ #-}+  y_ = const _y+  {-# INLINABLE y_ #-} --- | Point of BN254A curve-type P = WPoint BN254A Fp+-- | Affine BN254A curve point.+type PA = WAPoint BN254A Fq Fr +-- | Affine BN254A curve is a Weierstrass affine curve.+instance WACurve BN254A Fq Fr where+  gA_ = gA+  {-# INLINABLE gA_ #-}++-- | Jacobian BN254A point.+type PJ = WJPoint BN254A Fq Fr++-- | Jacobian BN254A curve is a Weierstrass Jacobian curve.+instance WJCurve BN254A Fq Fr where+  gJ_ = gJ+  {-# INLINABLE gJ_ #-}++-- | Projective BN254A point.+type PP = WPPoint BN254A Fq Fr++-- | Projective BN254A curve is a Weierstrass projective curve.+instance WPCurve BN254A Fq Fr where+  gP_ = gP+  {-# INLINABLE gP_ #-}+ ------------------------------------------------------------------------------- -- Parameters ------------------------------------------------------------------------------- --- | Coefficient @A@ of BN254A curve-_a :: Fp-_a = 0-{-# INLINE _a #-}---- | Coefficient @B@ of BN254A curve-_b :: Fp-_b = 5-{-# INLINE _b #-}+-- | Coefficient @A@ of BN254A curve.+_a :: Fq+_a = 0x0+{-# INLINABLE _a #-} --- | Generator of BN254A curve-_g :: P-_g = A-     1-     0xd45589b158faaf6ab0e4ad38d998e9982e7ff63964ee1460342a592677cccb0-{-# INLINE _g #-}+-- | Coefficient @B@ of BN254A curve.+_b :: Fq+_b = 0x5+{-# INLINABLE _b #-} --- | Cofactor of BN254A curve+-- | Cofactor of BN254A curve. _h :: Integer-_h = 1-{-# INLINE _h #-}+_h = 0x1+{-# INLINABLE _h #-} --- | Order of BN254A curve-_n :: Integer-_n = 0x2370fb049d410fbe4e761a9886e502411dc1af70120000017e80600000000001-{-# INLINE _n #-}+-- | Characteristic of BN254A curve.+_q :: Integer+_q = 0x2370fb049d410fbe4e761a9886e502417d023f40180000017e80600000000001+{-# INLINABLE _q #-} --- | Characteristic of BN254A curve-_p :: Integer-_p = 0x2370fb049d410fbe4e761a9886e502417d023f40180000017e80600000000001-{-# INLINE _p #-}+-- | Order of BN254A curve.+_r :: Integer+_r = 0x2370fb049d410fbe4e761a9886e502411dc1af70120000017e80600000000001+{-# INLINABLE _r #-}++-- | Coordinate @X@ of BN254A curve.+_x :: Fq+_x = 0x1+{-# INLINABLE _x #-}++-- | Coordinate @Y@ of BN254A curve.+_y :: Fq+_y = 0xd45589b158faaf6ab0e4ad38d998e9982e7ff63964ee1460342a592677cccb0+{-# INLINABLE _y #-}++-- | Generator of affine BN254A curve.+gA :: PA+gA = A _x _y+{-# INLINABLE gA #-}++-- | Generator of Jacobian BN254A curve.+gJ :: PJ+gJ = J _x _y 1+{-# INLINABLE gJ #-}++-- | Generator of projective BN254A curve.+gP :: PP+gP = P _x _y 1+{-# INLINABLE gP #-}

src/Curve/Weierstrass/BN254AT.hs view

@@ -1,86 +1,130 @@ module Curve.Weierstrass.BN254AT-  ( Fp2-  , P-  , _a-  , _b-  , _g-  , _h-  , _n-  , _p+  ( module Curve.Weierstrass+  , module Curve.Weierstrass.BN254AT   ) where  import Protolude -import ExtensionField (ExtensionField, IrreducibleMonic(..), fromList, x)+import ExtensionField+import PrimeField -import Curve.Weierstrass (Point(..), WCurve(..), WPoint)-import Curve.Weierstrass.BN254A (Fp)+import Curve.Weierstrass+import Curve.Weierstrass.BN254A (Fq)  ------------------------------------------------------------------------------- -- Types ------------------------------------------------------------------------------- --- | BN254AT curve+-- | BN254AT curve. data BN254AT --- | Field of BN254AT curve+-- | Field of points of BN254AT curve. data PolynomialU-instance IrreducibleMonic Fp PolynomialU where-  split _ = x ^ (2 :: Int) + 5-type Fp2 = ExtensionField Fp PolynomialU+instance IrreducibleMonic Fq PolynomialU where+  split _ = X2 + 5+type Fq2 = ExtensionField Fq PolynomialU --- | BN254AT curve is a Weierstrass curve-instance WCurve BN254AT Fp2 where+-- | Field of coefficients of BN254AT curve.+type Fr = PrimeField 0x2370fb049d410fbe4e761a9886e502411dc1af70120000017e80600000000001++-- | BN254AT curve is a Weierstrass curve.+instance Curve 'Weierstrass c BN254AT Fq2 Fr => WCurve c BN254AT Fq2 Fr where   a_ = const _a-  {-# INLINE a_ #-}+  {-# INLINABLE a_ #-}   b_ = const _b-  {-# INLINE b_ #-}-  g_ = _g-  {-# INLINE g_ #-}+  {-# INLINABLE b_ #-}+  h_ = const _h+  {-# INLINABLE h_ #-}+  q_ = const _q+  {-# INLINABLE q_ #-}+  r_ = const _r+  {-# INLINABLE r_ #-}+  x_ = const _x+  {-# INLINABLE x_ #-}+  y_ = const _y+  {-# INLINABLE y_ #-} --- | Point of BN254AT curve-type P = WPoint BN254AT Fp2+-- | Affine BN254AT curve point.+type PA = WAPoint BN254AT Fq2 Fr +-- | Affine BN254AT curve is a Weierstrass affine curve.+instance WACurve BN254AT Fq2 Fr where+  gA_ = gA+  {-# INLINABLE gA_ #-}++-- | Jacobian BN254AT point.+type PJ = WJPoint BN254AT Fq2 Fr++-- | Jacobian BN254AT curve is a Weierstrass Jacobian curve.+instance WJCurve BN254AT Fq2 Fr where+  gJ_ = gJ+  {-# INLINABLE gJ_ #-}++-- | Projective BN254AT point.+type PP = WPPoint BN254AT Fq2 Fr++-- | Projective BN254AT curve is a Weierstrass projective curve.+instance WPCurve BN254AT Fq2 Fr where+  gP_ = gP+  {-# INLINABLE gP_ #-}+ ------------------------------------------------------------------------------- -- Parameters ------------------------------------------------------------------------------- --- | Coefficient @A@ of BN254AT curve-_a :: Fp2-_a = 0-{-# INLINE _a #-}---- | Coefficient @B@ of BN254AT curve-_b :: Fp2-_b = fromList [0, -1]-{-# INLINE _b #-}+-- | Coefficient @A@ of BN254AT curve.+_a :: Fq2+_a = toField [+             ]+{-# INLINABLE _a #-} --- | Generator of BN254AT curve-_g :: P-_g = A-  ( fromList-   [ 0x19b0bea4afe4c330da93cc3533da38a9f430b471c6f8a536e81962ed967909b5-   , 0xa1cf585585a61c6e9880b1f2a5c539f7d906fff238fa6341e1de1a2e45c3f72-   ]-  )-  ( fromList-   [ 0x17abd366ebbd65333e49c711a80a0cf6d24adf1b9b3990eedcc91731384d2627-   , 0xee97d6de9902a27d00e952232a78700863bc9aa9be960C32f5bf9fd0a32d345-   ]-  )-{-# INLINE _g #-}+-- | Coefficient @B@ of BN254AT curve.+_b :: Fq2+_b = toField [ 0x0+             , 0x2370fb049d410fbe4e761a9886e502417d023f40180000017e80600000000000+             ]+{-# INLINABLE _b #-} --- | Cofactor of BN254AT curve+-- | Cofactor of BN254AT curve. _h :: Integer _h = 0x2370fb049d410fbe4e761a9886e50241dc42cf101e0000017e80600000000001-{-# INLINE _h #-}+{-# INLINABLE _h #-} --- | Order of BN254AT curve-_n :: Integer-_n = 0x2370fb049d410fbe4e761a9886e502411dc1af70120000017e80600000000001-{-# INLINE _n #-}+-- | Characteristic of BN254AT curve.+_q :: Integer+_q = 0x2370fb049d410fbe4e761a9886e502417d023f40180000017e80600000000001+{-# INLINABLE _q #-} --- | Characteristic of BN254AT curve-_p :: Integer-_p = 0x2370fb049d410fbe4e761a9886e502417d023f40180000017e80600000000001-{-# INLINE _p #-}+-- | Order of BN254AT curve.+_r :: Integer+_r = 0x2370fb049d410fbe4e761a9886e502411dc1af70120000017e80600000000001+{-# INLINABLE _r #-}++-- | Coordinate @X@ of BN254AT curve.+_x :: Fq2+_x = toField [ 0x19b0bea4afe4c330da93cc3533da38a9f430b471c6f8a536e81962ed967909b5+             , 0xa1cf585585a61c6e9880b1f2a5c539f7d906fff238fa6341e1de1a2e45c3f72+             ]+{-# INLINABLE _x #-}++-- | Coordinate @Y@ of BN254AT curve.+_y :: Fq2+_y = toField [ 0x17abd366ebbd65333e49c711a80a0cf6d24adf1b9b3990eedcc91731384d2627+             , 0xee97d6de9902a27d00e952232a78700863bc9aa9be960c32f5bf9fd0a32d345+             ]+{-# INLINABLE _y #-}++-- | Generator of affine BN254AT curve.+gA :: PA+gA = A _x _y+{-# INLINABLE gA #-}++-- | Generator of Jacobian BN254AT curve.+gJ :: PJ+gJ = J _x _y 1+{-# INLINABLE gJ #-}++-- | Generator of projective BN254AT curve.+gP :: PP+gP = P _x _y 1+{-# INLINABLE gP #-}

src/Curve/Weierstrass/BN254B.hs view

@@ -1,74 +1,118 @@ module Curve.Weierstrass.BN254B-  ( Fp-  , P-  , _a-  , _b-  , _g-  , _h-  , _n-  , _p+  ( module Curve.Weierstrass+  , module Curve.Weierstrass.BN254B   ) where  import Protolude -import PrimeField (PrimeField)+import PrimeField -import Curve.Weierstrass (Point(..), WCurve(..), WPoint)+import Curve.Weierstrass  ------------------------------------------------------------------------------- -- Types ------------------------------------------------------------------------------- --- | BN254B curve+-- | BN254B curve. data BN254B --- | Field of BN254B curve-type Fp = PrimeField 0x2523648240000001ba344d80000000086121000000000013a700000000000013+-- | Field of points of BN254B curve.+type Fq = PrimeField 0x2523648240000001ba344d80000000086121000000000013a700000000000013 --- | BN254B curve is a Weierstrass curve-instance WCurve BN254B Fp where+-- | Field of coefficients of BN254B curve.+type Fr = PrimeField 0x2523648240000001ba344d8000000007ff9f800000000010a10000000000000d++-- | BN254B curve is a Weierstrass curve.+instance Curve 'Weierstrass c BN254B Fq Fr => WCurve c BN254B Fq Fr where   a_ = const _a-  {-# INLINE a_ #-}+  {-# INLINABLE a_ #-}   b_ = const _b-  {-# INLINE b_ #-}-  g_ = _g-  {-# INLINE g_ #-}+  {-# INLINABLE b_ #-}+  h_ = const _h+  {-# INLINABLE h_ #-}+  q_ = const _q+  {-# INLINABLE q_ #-}+  r_ = const _r+  {-# INLINABLE r_ #-}+  x_ = const _x+  {-# INLINABLE x_ #-}+  y_ = const _y+  {-# INLINABLE y_ #-} --- | Point of BN254B curve-type P = WPoint BN254B Fp+-- | Affine BN254B curve point.+type PA = WAPoint BN254B Fq Fr +-- | Affine BN254B curve is a Weierstrass affine curve.+instance WACurve BN254B Fq Fr where+  gA_ = gA+  {-# INLINABLE gA_ #-}++-- | Jacobian BN254B point.+type PJ = WJPoint BN254B Fq Fr++-- | Jacobian BN254B curve is a Weierstrass Jacobian curve.+instance WJCurve BN254B Fq Fr where+  gJ_ = gJ+  {-# INLINABLE gJ_ #-}++-- | Projective BN254B point.+type PP = WPPoint BN254B Fq Fr++-- | Projective BN254B curve is a Weierstrass projective curve.+instance WPCurve BN254B Fq Fr where+  gP_ = gP+  {-# INLINABLE gP_ #-}+ ------------------------------------------------------------------------------- -- Parameters ------------------------------------------------------------------------------- --- | Coefficient @A@ of BN254B curve-_a :: Fp-_a = 0-{-# INLINE _a #-}---- | Coefficient @B@ of BN254B curve-_b :: Fp-_b = 2-{-# INLINE _b #-}+-- | Coefficient @A@ of BN254B curve.+_a :: Fq+_a = 0x0+{-# INLINABLE _a #-} --- | Generator of BN254B curve-_g :: P-_g = A-     0x2523648240000001ba344d80000000086121000000000013a700000000000012-     1-{-# INLINE _g #-}+-- | Coefficient @B@ of BN254B curve.+_b :: Fq+_b = 0x2+{-# INLINABLE _b #-} --- | Cofactor of BN254B curve+-- | Cofactor of BN254B curve. _h :: Integer-_h = 1-{-# INLINE _h #-}+_h = 0x1+{-# INLINABLE _h #-} --- | Order of BN254B curve-_n :: Integer-_n = 0x2523648240000001ba344d8000000007ff9f800000000010a10000000000000d-{-# INLINE _n #-}+-- | Characteristic of BN254B curve.+_q :: Integer+_q = 0x2523648240000001ba344d80000000086121000000000013a700000000000013+{-# INLINABLE _q #-} --- | Characteristic of BN254B curve-_p :: Integer-_p = 0x2523648240000001ba344d80000000086121000000000013a700000000000013-{-# INLINE _p #-}+-- | Order of BN254B curve.+_r :: Integer+_r = 0x2523648240000001ba344d8000000007ff9f800000000010a10000000000000d+{-# INLINABLE _r #-}++-- | Coordinate @X@ of BN254B curve.+_x :: Fq+_x = 0x2523648240000001ba344d80000000086121000000000013a700000000000012+{-# INLINABLE _x #-}++-- | Coordinate @Y@ of BN254B curve.+_y :: Fq+_y = 0x1+{-# INLINABLE _y #-}++-- | Generator of affine BN254B curve.+gA :: PA+gA = A _x _y+{-# INLINABLE gA #-}++-- | Generator of Jacobian BN254B curve.+gJ :: PJ+gJ = J _x _y 1+{-# INLINABLE gJ #-}++-- | Generator of projective BN254B curve.+gP :: PP+gP = P _x _y 1+{-# INLINABLE gP #-}

src/Curve/Weierstrass/BN254BT.hs view

@@ -1,86 +1,130 @@ module Curve.Weierstrass.BN254BT-  ( Fp2-  , P-  , _a-  , _b-  , _g-  , _h-  , _n-  , _p+  ( module Curve.Weierstrass+  , module Curve.Weierstrass.BN254BT   ) where  import Protolude -import ExtensionField (ExtensionField, IrreducibleMonic(..), fromList, x)+import ExtensionField+import PrimeField -import Curve.Weierstrass (Point(..), WCurve(..), WPoint)-import Curve.Weierstrass.BN254B (Fp)+import Curve.Weierstrass+import Curve.Weierstrass.BN254B (Fq)  ------------------------------------------------------------------------------- -- Types ------------------------------------------------------------------------------- --- | BN254BT curve+-- | BN254BT curve. data BN254BT --- | Field of BN254BT curve+-- | Field of points of BN254BT curve. data PolynomialU-instance IrreducibleMonic Fp PolynomialU where-  split _ = x ^ (2 :: Int) + 1-type Fp2 = ExtensionField Fp PolynomialU+instance IrreducibleMonic Fq PolynomialU where+  split _ = X2 + 1+type Fq2 = ExtensionField Fq PolynomialU --- | BN254BT curve is a Weierstrass curve-instance WCurve BN254BT Fp2 where+-- | Field of coefficients of BN254BT curve.+type Fr = PrimeField 0x2523648240000001ba344d8000000007ff9f800000000010a10000000000000d++-- | BN254BT curve is a Weierstrass curve.+instance Curve 'Weierstrass c BN254BT Fq2 Fr => WCurve c BN254BT Fq2 Fr where   a_ = const _a-  {-# INLINE a_ #-}+  {-# INLINABLE a_ #-}   b_ = const _b-  {-# INLINE b_ #-}-  g_ = _g-  {-# INLINE g_ #-}+  {-# INLINABLE b_ #-}+  h_ = const _h+  {-# INLINABLE h_ #-}+  q_ = const _q+  {-# INLINABLE q_ #-}+  r_ = const _r+  {-# INLINABLE r_ #-}+  x_ = const _x+  {-# INLINABLE x_ #-}+  y_ = const _y+  {-# INLINABLE y_ #-} --- | Point of BN254BT curve-type P = WPoint BN254BT Fp2+-- | Affine BN254BT curve point.+type PA = WAPoint BN254BT Fq2 Fr +-- | Affine BN254BT curve is a Weierstrass affine curve.+instance WACurve BN254BT Fq2 Fr where+  gA_ = gA+  {-# INLINABLE gA_ #-}++-- | Jacobian BN254BT point.+type PJ = WJPoint BN254BT Fq2 Fr++-- | Jacobian BN254BT curve is a Weierstrass Jacobian curve.+instance WJCurve BN254BT Fq2 Fr where+  gJ_ = gJ+  {-# INLINABLE gJ_ #-}++-- | Projective BN254BT point.+type PP = WPPoint BN254BT Fq2 Fr++-- | Projective BN254BT curve is a Weierstrass projective curve.+instance WPCurve BN254BT Fq2 Fr where+  gP_ = gP+  {-# INLINABLE gP_ #-}+ ------------------------------------------------------------------------------- -- Parameters ------------------------------------------------------------------------------- --- | Coefficient @A@ of BN254BT curve-_a :: Fp2-_a = 0-{-# INLINE _a #-}---- | Coefficient @B@ of BN254BT curve-_b :: Fp2-_b = fromList [1, -1]-{-# INLINE _b #-}+-- | Coefficient @A@ of BN254BT curve.+_a :: Fq2+_a = toField [+             ]+{-# INLINABLE _a #-} --- | Generator of BN254BT curve-_g :: P-_g = A-  ( fromList-   [ 0x61a10bb519eb62feb8d8c7e8c61edb6a4648bbb4898bf0d91ee4224c803fb2b-   , 0x516aaf9ba737833310aa78c5982aa5b1f4d746bae3784b70d8c34c1e7d54cf3-   ]-  )-  ( fromList-   [ 0x21897a06baf93439a90e096698c822329bd0ae6bdbe09bd19f0e07891cd2b9a-   , 0xebb2b0e7c8b15268f6d4456f5f38d37b09006ffd739c9578a2d1aec6b3ace9b-   ]-  )-{-# INLINE _g #-}+-- | Coefficient @B@ of BN254BT curve.+_b :: Fq2+_b = toField [ 0x1+             , 0x2523648240000001ba344d80000000086121000000000013a700000000000012+             ]+{-# INLINABLE _b #-} --- | Cofactor of BN254BT curve+-- | Cofactor of BN254BT curve. _h :: Integer _h = 0x2523648240000001ba344d8000000008c2a2800000000016ad00000000000019-{-# INLINE _h #-}+{-# INLINABLE _h #-} --- | Order of BN254BT curve-_n :: Integer-_n = 0x2523648240000001ba344d8000000007ff9f800000000010a10000000000000d-{-# INLINE _n #-}+-- | Characteristic of BN254BT curve.+_q :: Integer+_q = 0x2523648240000001ba344d80000000086121000000000013a700000000000013+{-# INLINABLE _q #-} --- | Characteristic of BN254BT curve-_p :: Integer-_p = 0x2523648240000001ba344d80000000086121000000000013a700000000000013-{-# INLINE _p #-}+-- | Order of BN254BT curve.+_r :: Integer+_r = 0x2523648240000001ba344d8000000007ff9f800000000010a10000000000000d+{-# INLINABLE _r #-}++-- | Coordinate @X@ of BN254BT curve.+_x :: Fq2+_x = toField [ 0x61a10bb519eb62feb8d8c7e8c61edb6a4648bbb4898bf0d91ee4224c803fb2b+             , 0x516aaf9ba737833310aa78c5982aa5b1f4d746bae3784b70d8c34c1e7d54cf3+             ]+{-# INLINABLE _x #-}++-- | Coordinate @Y@ of BN254BT curve.+_y :: Fq2+_y = toField [ 0x21897a06baf93439a90e096698c822329bd0ae6bdbe09bd19f0e07891cd2b9a+             , 0xebb2b0e7c8b15268f6d4456f5f38d37b09006ffd739c9578a2d1aec6b3ace9b+             ]+{-# INLINABLE _y #-}++-- | Generator of affine BN254BT curve.+gA :: PA+gA = A _x _y+{-# INLINABLE gA #-}++-- | Generator of Jacobian BN254BT curve.+gJ :: PJ+gJ = J _x _y 1+{-# INLINABLE gJ #-}++-- | Generator of projective BN254BT curve.+gP :: PP+gP = P _x _y 1+{-# INLINABLE gP #-}

src/Curve/Weierstrass/BN254T.hs view

@@ -1,86 +1,130 @@ module Curve.Weierstrass.BN254T-  ( Fp2-  , P-  , _a-  , _b-  , _g-  , _h-  , _n-  , _p+  ( module Curve.Weierstrass+  , module Curve.Weierstrass.BN254T   ) where  import Protolude -import ExtensionField (ExtensionField, IrreducibleMonic(..), fromList, x)+import ExtensionField+import PrimeField -import Curve.Weierstrass (Point(..), WCurve(..), WPoint)-import Curve.Weierstrass.BN254 (Fp)+import Curve.Weierstrass+import Curve.Weierstrass.BN254 (Fq)  ------------------------------------------------------------------------------- -- Types ------------------------------------------------------------------------------- --- | BN254T curve+-- | BN254T curve. data BN254T --- | Field of BN254T curve+-- | Field of points of BN254T curve. data PolynomialU-instance IrreducibleMonic Fp PolynomialU where-  split _ = x ^ (2 :: Int) + 1-type Fp2 = ExtensionField Fp PolynomialU+instance IrreducibleMonic Fq PolynomialU where+  split _ = X2 + 1+type Fq2 = ExtensionField Fq PolynomialU --- | BN254T curve is a Weierstrass curve-instance WCurve BN254T Fp2 where+-- | Field of coefficients of BN254T curve.+type Fr = PrimeField 0x30644e72e131a029b85045b68181585d2833e84879b9709143e1f593f0000001++-- | BN254T curve is a Weierstrass curve.+instance Curve 'Weierstrass c BN254T Fq2 Fr => WCurve c BN254T Fq2 Fr where   a_ = const _a-  {-# INLINE a_ #-}+  {-# INLINABLE a_ #-}   b_ = const _b-  {-# INLINE b_ #-}-  g_ = _g-  {-# INLINE g_ #-}+  {-# INLINABLE b_ #-}+  h_ = const _h+  {-# INLINABLE h_ #-}+  q_ = const _q+  {-# INLINABLE q_ #-}+  r_ = const _r+  {-# INLINABLE r_ #-}+  x_ = const _x+  {-# INLINABLE x_ #-}+  y_ = const _y+  {-# INLINABLE y_ #-} --- | Point of BN254T curve-type P = WPoint BN254T Fp2+-- | Affine BN254T curve point.+type PA = WAPoint BN254T Fq2 Fr +-- | Affine BN254T curve is a Weierstrass affine curve.+instance WACurve BN254T Fq2 Fr where+  gA_ = gA+  {-# INLINABLE gA_ #-}++-- | Jacobian BN254T point.+type PJ = WJPoint BN254T Fq2 Fr++-- | Jacobian BN254T curve is a Weierstrass Jacobian curve.+instance WJCurve BN254T Fq2 Fr where+  gJ_ = gJ+  {-# INLINABLE gJ_ #-}++-- | Projective BN254T point.+type PP = WPPoint BN254T Fq2 Fr++-- | Projective BN254T curve is a Weierstrass projective curve.+instance WPCurve BN254T Fq2 Fr where+  gP_ = gP+  {-# INLINABLE gP_ #-}+ ------------------------------------------------------------------------------- -- Parameters ------------------------------------------------------------------------------- --- | Coefficient @A@ of BN254T curve-_a :: Fp2-_a = 0-{-# INLINE _a #-}---- | Coefficient @B@ of BN254T curve-_b :: Fp2-_b = 3 / fromList [9, 1]-{-# INLINE _b #-}+-- | Coefficient @A@ of BN254T curve.+_a :: Fq2+_a = toField [+             ]+{-# INLINABLE _a #-} --- | Generator of BN254T curve-_g :: P-_g = A-  ( fromList-   [ 0x1800deef121f1e76426a00665e5c4479674322d4f75edadd46debd5cd992f6ed-   , 0x198e9393920d483a7260bfb731fb5d25f1aa493335a9e71297e485b7aef312c2-   ]-  )-  ( fromList-   [ 0x12c85ea5db8c6deb4aab71808dcb408fe3d1e7690c43d37b4ce6cc0166fa7daa-   , 0x90689d0585ff075ec9e99ad690c3395bc4b313370b38ef355acdadcd122975b-   ]-  )-{-# INLINE _g #-}+-- | Coefficient @B@ of BN254T curve.+_b :: Fq2+_b = toField [ 0x2b149d40ceb8aaae81be18991be06ac3b5b4c5e559dbefa33267e6dc24a138e5+             , 0x9713b03af0fed4cd2cafadeed8fdf4a74fa084e52d1852e4a2bd0685c315d2+             ]+{-# INLINABLE _b #-} --- | Cofactor of BN254T curve+-- | Cofactor of BN254T curve. _h :: Integer _h = 0x30644e72e131a029b85045b68181585e06ceecda572a2489345f2299c0f9fa8d-{-# INLINE _h #-}+{-# INLINABLE _h #-} --- | Order of BN254T curve-_n :: Integer-_n = 0x30644e72e131a029b85045b68181585d2833e84879b9709143e1f593f0000001-{-# INLINE _n #-}+-- | Characteristic of BN254T curve.+_q :: Integer+_q = 0x30644e72e131a029b85045b68181585d97816a916871ca8d3c208c16d87cfd47+{-# INLINABLE _q #-} --- | Characteristic of BN254T curve-_p :: Integer-_p = 0x30644e72e131a029b85045b68181585d97816a916871ca8d3c208c16d87cfd47-{-# INLINE _p #-}+-- | Order of BN254T curve.+_r :: Integer+_r = 0x30644e72e131a029b85045b68181585d2833e84879b9709143e1f593f0000001+{-# INLINABLE _r #-}++-- | Coordinate @X@ of BN254T curve.+_x :: Fq2+_x = toField [ 0x1800deef121f1e76426a00665e5c4479674322d4f75edadd46debd5cd992f6ed+             , 0x198e9393920d483a7260bfb731fb5d25f1aa493335a9e71297e485b7aef312c2+             ]+{-# INLINABLE _x #-}++-- | Coordinate @Y@ of BN254T curve.+_y :: Fq2+_y = toField [ 0x12c85ea5db8c6deb4aab71808dcb408fe3d1e7690c43d37b4ce6cc0166fa7daa+             , 0x90689d0585ff075ec9e99ad690c3395bc4b313370b38ef355acdadcd122975b+             ]+{-# INLINABLE _y #-}++-- | Generator of affine BN254T curve.+gA :: PA+gA = A _x _y+{-# INLINABLE gA #-}++-- | Generator of Jacobian BN254T curve.+gJ :: PJ+gJ = J _x _y 1+{-# INLINABLE gJ #-}++-- | Generator of projective BN254T curve.+gP :: PP+gP = P _x _y 1+{-# INLINABLE gP #-}

src/Curve/Weierstrass/BN256.hs view

@@ -1,74 +1,118 @@ module Curve.Weierstrass.BN256-  ( Fp-  , P-  , _a-  , _b-  , _g-  , _h-  , _n-  , _p+  ( module Curve.Weierstrass+  , module Curve.Weierstrass.BN256   ) where  import Protolude -import PrimeField (PrimeField)+import PrimeField -import Curve.Weierstrass (Point(..), WCurve(..), WPoint)+import Curve.Weierstrass  ------------------------------------------------------------------------------- -- Types ------------------------------------------------------------------------------- --- | BN256 curve+-- | BN256 curve. data BN256 --- | Field of BN256 curve-type Fp = PrimeField 0xfffffffffffcf0cd46e5f25eee71a49f0cdc65fb12980a82d3292ddbaed33013+-- | Field of points of BN256 curve.+type Fq = PrimeField 0xfffffffffffcf0cd46e5f25eee71a49f0cdc65fb12980a82d3292ddbaed33013 --- | BN256 curve is a Weierstrass curve-instance WCurve BN256 Fp where+-- | Field of coefficients of BN256 curve.+type Fr = PrimeField 0xfffffffffffcf0cd46e5f25eee71a49e0cdc65fb1299921af62d536cd10b500d++-- | BN256 curve is a Weierstrass curve.+instance Curve 'Weierstrass c BN256 Fq Fr => WCurve c BN256 Fq Fr where   a_ = const _a-  {-# INLINE a_ #-}+  {-# INLINABLE a_ #-}   b_ = const _b-  {-# INLINE b_ #-}-  g_ = _g-  {-# INLINE g_ #-}+  {-# INLINABLE b_ #-}+  h_ = const _h+  {-# INLINABLE h_ #-}+  q_ = const _q+  {-# INLINABLE q_ #-}+  r_ = const _r+  {-# INLINABLE r_ #-}+  x_ = const _x+  {-# INLINABLE x_ #-}+  y_ = const _y+  {-# INLINABLE y_ #-} --- | Point of BN256 curve-type P = WPoint BN256 Fp+-- | Affine BN256 curve point.+type PA = WAPoint BN256 Fq Fr +-- | Affine BN256 curve is a Weierstrass affine curve.+instance WACurve BN256 Fq Fr where+  gA_ = gA+  {-# INLINABLE gA_ #-}++-- | Jacobian BN256 point.+type PJ = WJPoint BN256 Fq Fr++-- | Jacobian BN256 curve is a Weierstrass Jacobian curve.+instance WJCurve BN256 Fq Fr where+  gJ_ = gJ+  {-# INLINABLE gJ_ #-}++-- | Projective BN256 point.+type PP = WPPoint BN256 Fq Fr++-- | Projective BN256 curve is a Weierstrass projective curve.+instance WPCurve BN256 Fq Fr where+  gP_ = gP+  {-# INLINABLE gP_ #-}+ ------------------------------------------------------------------------------- -- Parameters ------------------------------------------------------------------------------- --- | Coefficient @A@ of BN256 curve-_a :: Fp-_a = 0-{-# INLINE _a #-}---- | Coefficient @B@ of BN256 curve-_b :: Fp-_b = 3-{-# INLINE _b #-}+-- | Coefficient @A@ of BN256 curve.+_a :: Fq+_a = 0x0+{-# INLINABLE _a #-} --- | Generator of BN256 curve-_g :: P-_g = A-     1-     2-{-# INLINE _g #-}+-- | Coefficient @B@ of BN256 curve.+_b :: Fq+_b = 0x3+{-# INLINABLE _b #-} --- | Cofactor of BN256 curve+-- | Cofactor of BN256 curve. _h :: Integer-_h = 1-{-# INLINE _h #-}+_h = 0x1+{-# INLINABLE _h #-} --- | Order of BN256 curve-_n :: Integer-_n = 0xfffffffffffcf0cd46e5f25eee71a49e0cdc65fb1299921af62d536cd10b500d-{-# INLINE _n #-}+-- | Characteristic of BN256 curve.+_q :: Integer+_q = 0xfffffffffffcf0cd46e5f25eee71a49f0cdc65fb12980a82d3292ddbaed33013+{-# INLINABLE _q #-} --- | Characteristic of BN256 curve-_p :: Integer-_p = 0xfffffffffffcf0cd46e5f25eee71a49f0cdc65fb12980a82d3292ddbaed33013-{-# INLINE _p #-}+-- | Order of BN256 curve.+_r :: Integer+_r = 0xfffffffffffcf0cd46e5f25eee71a49e0cdc65fb1299921af62d536cd10b500d+{-# INLINABLE _r #-}++-- | Coordinate @X@ of BN256 curve.+_x :: Fq+_x = 0x1+{-# INLINABLE _x #-}++-- | Coordinate @Y@ of BN256 curve.+_y :: Fq+_y = 0x2+{-# INLINABLE _y #-}++-- | Generator of affine BN256 curve.+gA :: PA+gA = A _x _y+{-# INLINABLE gA #-}++-- | Generator of Jacobian BN256 curve.+gJ :: PJ+gJ = J _x _y 1+{-# INLINABLE gJ #-}++-- | Generator of projective BN256 curve.+gP :: PP+gP = P _x _y 1+{-# INLINABLE gP #-}

src/Curve/Weierstrass/BN384.hs view

@@ -1,74 +1,118 @@ module Curve.Weierstrass.BN384-  ( Fp-  , P-  , _a-  , _b-  , _g-  , _h-  , _n-  , _p+  ( module Curve.Weierstrass+  , module Curve.Weierstrass.BN384   ) where  import Protolude -import PrimeField (PrimeField)+import PrimeField -import Curve.Weierstrass (Point(..), WCurve(..), WPoint)+import Curve.Weierstrass  ------------------------------------------------------------------------------- -- Types ------------------------------------------------------------------------------- --- | BN384 curve+-- | BN384 curve. data BN384 --- | Field of BN384 curve-type Fp = PrimeField 0xfffffffffffffffffff2a96823d5920d2a127e3f6fbca024c8fbe29531892c79534f9d306328261550a7cabd7cccd10b+-- | Field of points of BN384 curve.+type Fq = PrimeField 0xfffffffffffffffffff2a96823d5920d2a127e3f6fbca024c8fbe29531892c79534f9d306328261550a7cabd7cccd10b --- | BN384 curve is a Weierstrass curve-instance WCurve BN384 Fp where+-- | Field of coefficients of BN384 curve.+type Fr = PrimeField 0xfffffffffffffffffff2a96823d5920d2a127e3f6fbca023c8fbe29531892c795356487d8ac63e4f4db17384341a5775++-- | BN384 curve is a Weierstrass curve.+instance Curve 'Weierstrass c BN384 Fq Fr => WCurve c BN384 Fq Fr where   a_ = const _a-  {-# INLINE a_ #-}+  {-# INLINABLE a_ #-}   b_ = const _b-  {-# INLINE b_ #-}-  g_ = _g-  {-# INLINE g_ #-}+  {-# INLINABLE b_ #-}+  h_ = const _h+  {-# INLINABLE h_ #-}+  q_ = const _q+  {-# INLINABLE q_ #-}+  r_ = const _r+  {-# INLINABLE r_ #-}+  x_ = const _x+  {-# INLINABLE x_ #-}+  y_ = const _y+  {-# INLINABLE y_ #-} --- | Point of BN384 curve-type P = WPoint BN384 Fp+-- | Affine BN384 curve point.+type PA = WAPoint BN384 Fq Fr +-- | Affine BN384 curve is a Weierstrass affine curve.+instance WACurve BN384 Fq Fr where+  gA_ = gA+  {-# INLINABLE gA_ #-}++-- | Jacobian BN384 point.+type PJ = WJPoint BN384 Fq Fr++-- | Jacobian BN384 curve is a Weierstrass Jacobian curve.+instance WJCurve BN384 Fq Fr where+  gJ_ = gJ+  {-# INLINABLE gJ_ #-}++-- | Projective BN384 point.+type PP = WPPoint BN384 Fq Fr++-- | Projective BN384 curve is a Weierstrass projective curve.+instance WPCurve BN384 Fq Fr where+  gP_ = gP+  {-# INLINABLE gP_ #-}+ ------------------------------------------------------------------------------- -- Parameters ------------------------------------------------------------------------------- --- | Coefficient @A@ of BN384 curve-_a :: Fp-_a = 0-{-# INLINE _a #-}---- | Coefficient @B@ of BN384 curve-_b :: Fp-_b = 3-{-# INLINE _b #-}+-- | Coefficient @A@ of BN384 curve.+_a :: Fq+_a = 0x0+{-# INLINABLE _a #-} --- | Generator of BN384 curve-_g :: P-_g = A-     1-     2-{-# INLINE _g #-}+-- | Coefficient @B@ of BN384 curve.+_b :: Fq+_b = 0x3+{-# INLINABLE _b #-} --- | Cofactor of BN384 curve+-- | Cofactor of BN384 curve. _h :: Integer-_h = 1-{-# INLINE _h #-}+_h = 0x1+{-# INLINABLE _h #-} --- | Order of BN384 curve-_n :: Integer-_n = 0xfffffffffffffffffff2a96823d5920d2a127e3f6fbca023c8fbe29531892c795356487d8ac63e4f4db17384341a5775-{-# INLINE _n #-}+-- | Characteristic of BN384 curve.+_q :: Integer+_q = 0xfffffffffffffffffff2a96823d5920d2a127e3f6fbca024c8fbe29531892c79534f9d306328261550a7cabd7cccd10b+{-# INLINABLE _q #-} --- | Characteristic of BN384 curve-_p :: Integer-_p = 0xfffffffffffffffffff2a96823d5920d2a127e3f6fbca024c8fbe29531892c79534f9d306328261550a7cabd7cccd10b-{-# INLINE _p #-}+-- | Order of BN384 curve.+_r :: Integer+_r = 0xfffffffffffffffffff2a96823d5920d2a127e3f6fbca023c8fbe29531892c795356487d8ac63e4f4db17384341a5775+{-# INLINABLE _r #-}++-- | Coordinate @X@ of BN384 curve.+_x :: Fq+_x = 0x1+{-# INLINABLE _x #-}++-- | Coordinate @Y@ of BN384 curve.+_y :: Fq+_y = 0x2+{-# INLINABLE _y #-}++-- | Generator of affine BN384 curve.+gA :: PA+gA = A _x _y+{-# INLINABLE gA #-}++-- | Generator of Jacobian BN384 curve.+gJ :: PJ+gJ = J _x _y 1+{-# INLINABLE gJ #-}++-- | Generator of projective BN384 curve.+gP :: PP+gP = P _x _y 1+{-# INLINABLE gP #-}

src/Curve/Weierstrass/BN462.hs view

@@ -1,74 +1,118 @@ module Curve.Weierstrass.BN462-  ( Fp-  , P-  , _a-  , _b-  , _g-  , _h-  , _n-  , _p+  ( module Curve.Weierstrass+  , module Curve.Weierstrass.BN462   ) where  import Protolude -import PrimeField (PrimeField)+import PrimeField -import Curve.Weierstrass (Point(..), WCurve(..), WPoint)+import Curve.Weierstrass  ------------------------------------------------------------------------------- -- Types ------------------------------------------------------------------------------- --- | BN462 curve+-- | BN462 curve. data BN462 --- | Field of BN462 curve-type Fp = PrimeField 0x240480360120023ffffffffff6ff0cf6b7d9bfca0000000000d812908f41c8020ffffffffff6ff66fc6ff687f640000000002401b00840138013+-- | Field of points of BN462 curve.+type Fq = PrimeField 0x240480360120023ffffffffff6ff0cf6b7d9bfca0000000000d812908f41c8020ffffffffff6ff66fc6ff687f640000000002401b00840138013 --- | BN462 curve is a Weierstrass curve-instance WCurve BN462 Fp where+-- | Field of coefficients of BN462 curve.+type Fr = PrimeField 0x240480360120023ffffffffff6ff0cf6b7d9bfca0000000000d812908ee1c201f7fffffffff6ff66fc7bf717f7c0000000002401b007e010800d++-- | BN462 curve is a Weierstrass curve.+instance Curve 'Weierstrass c BN462 Fq Fr => WCurve c BN462 Fq Fr where   a_ = const _a-  {-# INLINE a_ #-}+  {-# INLINABLE a_ #-}   b_ = const _b-  {-# INLINE b_ #-}-  g_ = _g-  {-# INLINE g_ #-}+  {-# INLINABLE b_ #-}+  h_ = const _h+  {-# INLINABLE h_ #-}+  q_ = const _q+  {-# INLINABLE q_ #-}+  r_ = const _r+  {-# INLINABLE r_ #-}+  x_ = const _x+  {-# INLINABLE x_ #-}+  y_ = const _y+  {-# INLINABLE y_ #-} --- | Point of BN462 curve-type P = WPoint BN462 Fp+-- | Affine BN462 curve point.+type PA = WAPoint BN462 Fq Fr +-- | Affine BN462 curve is a Weierstrass affine curve.+instance WACurve BN462 Fq Fr where+  gA_ = gA+  {-# INLINABLE gA_ #-}++-- | Jacobian BN462 point.+type PJ = WJPoint BN462 Fq Fr++-- | Jacobian BN462 curve is a Weierstrass Jacobian curve.+instance WJCurve BN462 Fq Fr where+  gJ_ = gJ+  {-# INLINABLE gJ_ #-}++-- | Projective BN462 point.+type PP = WPPoint BN462 Fq Fr++-- | Projective BN462 curve is a Weierstrass projective curve.+instance WPCurve BN462 Fq Fr where+  gP_ = gP+  {-# INLINABLE gP_ #-}+ ------------------------------------------------------------------------------- -- Parameters ------------------------------------------------------------------------------- --- | Coefficient @A@ of BN462 curve-_a :: Fp-_a = 0-{-# INLINE _a #-}---- | Coefficient @B@ of BN462 curve-_b :: Fp-_b = 5-{-# INLINE _b #-}+-- | Coefficient @A@ of BN462 curve.+_a :: Fq+_a = 0x0+{-# INLINABLE _a #-} --- | Generator of BN462 curve-_g :: P-_g = A-     0x21a6d67ef250191fadba34a0a30160b9ac9264b6f95f63b3edbec3cf4b2e689db1bbb4e69a416a0b1e79239c0372e5cd70113c98d91f36b6980d-     0x118ea0460f7f7abb82b33676a7432a490eeda842cccfa7d788c659650426e6af77df11b8ae40eb80f475432c66600622ecaa8a5734d36fb03de-{-# INLINE _g #-}+-- | Coefficient @B@ of BN462 curve.+_b :: Fq+_b = 0x5+{-# INLINABLE _b #-} --- | Cofactor of BN462 curve+-- | Cofactor of BN462 curve. _h :: Integer-_h = 1-{-# INLINE _h #-}+_h = 0x1+{-# INLINABLE _h #-} --- | Order of BN462 curve-_n :: Integer-_n = 0x240480360120023ffffffffff6ff0cf6b7d9bfca0000000000d812908ee1c201f7fffffffff6ff66fc7bf717f7c0000000002401b007e010800d-{-# INLINE _n #-}+-- | Characteristic of BN462 curve.+_q :: Integer+_q = 0x240480360120023ffffffffff6ff0cf6b7d9bfca0000000000d812908f41c8020ffffffffff6ff66fc6ff687f640000000002401b00840138013+{-# INLINABLE _q #-} --- | Characteristic of BN462 curve-_p :: Integer-_p = 0x240480360120023ffffffffff6ff0cf6b7d9bfca0000000000d812908f41c8020ffffffffff6ff66fc6ff687f640000000002401b00840138013-{-# INLINE _p #-}+-- | Order of BN462 curve.+_r :: Integer+_r = 0x240480360120023ffffffffff6ff0cf6b7d9bfca0000000000d812908ee1c201f7fffffffff6ff66fc7bf717f7c0000000002401b007e010800d+{-# INLINABLE _r #-}++-- | Coordinate @X@ of BN462 curve.+_x :: Fq+_x = 0x21a6d67ef250191fadba34a0a30160b9ac9264b6f95f63b3edbec3cf4b2e689db1bbb4e69a416a0b1e79239c0372e5cd70113c98d91f36b6980d+{-# INLINABLE _x #-}++-- | Coordinate @Y@ of BN462 curve.+_y :: Fq+_y = 0x118ea0460f7f7abb82b33676a7432a490eeda842cccfa7d788c659650426e6af77df11b8ae40eb80f475432c66600622ecaa8a5734d36fb03de+{-# INLINABLE _y #-}++-- | Generator of affine BN462 curve.+gA :: PA+gA = A _x _y+{-# INLINABLE gA #-}++-- | Generator of Jacobian BN462 curve.+gJ :: PJ+gJ = J _x _y 1+{-# INLINABLE gJ #-}++-- | Generator of projective BN462 curve.+gP :: PP+gP = P _x _y 1+{-# INLINABLE gP #-}

src/Curve/Weierstrass/BN462T.hs view

@@ -1,86 +1,130 @@ module Curve.Weierstrass.BN462T-  ( Fp2-  , P-  , _a-  , _b-  , _g-  , _h-  , _n-  , _p+  ( module Curve.Weierstrass+  , module Curve.Weierstrass.BN462T   ) where  import Protolude -import ExtensionField (ExtensionField, IrreducibleMonic(..), fromList, x)+import ExtensionField+import PrimeField -import Curve.Weierstrass (Point(..), WCurve(..), WPoint)-import Curve.Weierstrass.BN462 (Fp)+import Curve.Weierstrass+import Curve.Weierstrass.BN462 (Fq)  ------------------------------------------------------------------------------- -- Types ------------------------------------------------------------------------------- --- | BN462T curve+-- | BN462T curve. data BN462T --- | Field of BN462T curve+-- | Field of points of BN462T curve. data PolynomialU-instance IrreducibleMonic Fp PolynomialU where-  split _ = x ^ (2 :: Int) + 1-type Fp2 = ExtensionField Fp PolynomialU+instance IrreducibleMonic Fq PolynomialU where+  split _ = X2 + 1+type Fq2 = ExtensionField Fq PolynomialU --- | BN462T curve is a Weierstrass curve-instance WCurve BN462T Fp2 where+-- | Field of coefficients of BN462T curve.+type Fr = PrimeField 0x240480360120023ffffffffff6ff0cf6b7d9bfca0000000000d812908ee1c201f7fffffffff6ff66fc7bf717f7c0000000002401b007e010800d++-- | BN462T curve is a Weierstrass curve.+instance Curve 'Weierstrass c BN462T Fq2 Fr => WCurve c BN462T Fq2 Fr where   a_ = const _a-  {-# INLINE a_ #-}+  {-# INLINABLE a_ #-}   b_ = const _b-  {-# INLINE b_ #-}-  g_ = _g-  {-# INLINE g_ #-}+  {-# INLINABLE b_ #-}+  h_ = const _h+  {-# INLINABLE h_ #-}+  q_ = const _q+  {-# INLINABLE q_ #-}+  r_ = const _r+  {-# INLINABLE r_ #-}+  x_ = const _x+  {-# INLINABLE x_ #-}+  y_ = const _y+  {-# INLINABLE y_ #-} --- | Point of BN462T curve-type P = WPoint BN462T Fp2+-- | Affine BN462T curve point.+type PA = WAPoint BN462T Fq2 Fr +-- | Affine BN462T curve is a Weierstrass affine curve.+instance WACurve BN462T Fq2 Fr where+  gA_ = gA+  {-# INLINABLE gA_ #-}++-- | Jacobian BN462T point.+type PJ = WJPoint BN462T Fq2 Fr++-- | Jacobian BN462T curve is a Weierstrass Jacobian curve.+instance WJCurve BN462T Fq2 Fr where+  gJ_ = gJ+  {-# INLINABLE gJ_ #-}++-- | Projective BN462T point.+type PP = WPPoint BN462T Fq2 Fr++-- | Projective BN462T curve is a Weierstrass projective curve.+instance WPCurve BN462T Fq2 Fr where+  gP_ = gP+  {-# INLINABLE gP_ #-}+ ------------------------------------------------------------------------------- -- Parameters ------------------------------------------------------------------------------- --- | Coefficient @A@ of BN462T curve-_a :: Fp2-_a = 0-{-# INLINE _a #-}---- | Coefficient @B@ of BN462T curve-_b :: Fp2-_b = fromList [2, -1]-{-# INLINE _b #-}+-- | Coefficient @A@ of BN462T curve.+_a :: Fq2+_a = toField [+             ]+{-# INLINABLE _a #-} --- | Generator of BN462T curve-_g :: P-_g = A-  ( fromList-   [ 0x257ccc85b58dda0dfb38e3a8cbdc5482e0337e7c1cd96ed61c913820408208f9ad2699bad92e0032ae1f0aa6a8b48807695468e3d934ae1e4df-   , 0x1d2e4343e8599102af8edca849566ba3c98e2a354730cbed9176884058b18134dd86bae555b783718f50af8b59bf7e850e9b73108ba6aa8cd283-   ]-  )-  ( fromList-   [ 0xa0650439da22c1979517427a20809eca035634706e23c3fa7a6bb42fe810f1399a1f41c9ddae32e03695a140e7b11d7c3376e5b68df0db7154e-   , 0x73ef0cbd438cbe0172c8ae37306324d44d5e6b0c69ac57b393f1ab370fd725cc647692444a04ef87387aa68d53743493b9eba14cc552ca2a93a-   ]-  )-{-# INLINE _g #-}+-- | Coefficient @B@ of BN462T curve.+_b :: Fq2+_b = toField [ 0x2+             , 0x240480360120023ffffffffff6ff0cf6b7d9bfca0000000000d812908f41c8020ffffffffff6ff66fc6ff687f640000000002401b00840138012+             ]+{-# INLINABLE _b #-} --- | Cofactor of BN462T curve+-- | Cofactor of BN462T curve. _h :: Integer _h = 0x240480360120023ffffffffff6ff0cf6b7d9bfca0000000000d812908fa1ce0227fffffffff6ff66fc63f5f7f4c0000000002401b008a0168019-{-# INLINE _h #-}+{-# INLINABLE _h #-} --- | Order of BN462T curve-_n :: Integer-_n = 0x240480360120023ffffffffff6ff0cf6b7d9bfca0000000000d812908ee1c201f7fffffffff6ff66fc7bf717f7c0000000002401b007e010800d-{-# INLINE _n #-}+-- | Characteristic of BN462T curve.+_q :: Integer+_q = 0x240480360120023ffffffffff6ff0cf6b7d9bfca0000000000d812908f41c8020ffffffffff6ff66fc6ff687f640000000002401b00840138013+{-# INLINABLE _q #-} --- | Characteristic of BN462T curve-_p :: Integer-_p = 0x240480360120023ffffffffff6ff0cf6b7d9bfca0000000000d812908f41c8020ffffffffff6ff66fc6ff687f640000000002401b00840138013-{-# INLINE _p #-}+-- | Order of BN462T curve.+_r :: Integer+_r = 0x240480360120023ffffffffff6ff0cf6b7d9bfca0000000000d812908ee1c201f7fffffffff6ff66fc7bf717f7c0000000002401b007e010800d+{-# INLINABLE _r #-}++-- | Coordinate @X@ of BN462T curve.+_x :: Fq2+_x = toField [ 0x257ccc85b58dda0dfb38e3a8cbdc5482e0337e7c1cd96ed61c913820408208f9ad2699bad92e0032ae1f0aa6a8b48807695468e3d934ae1e4df+             , 0x1d2e4343e8599102af8edca849566ba3c98e2a354730cbed9176884058b18134dd86bae555b783718f50af8b59bf7e850e9b73108ba6aa8cd283+             ]+{-# INLINABLE _x #-}++-- | Coordinate @Y@ of BN462T curve.+_y :: Fq2+_y = toField [ 0xa0650439da22c1979517427a20809eca035634706e23c3fa7a6bb42fe810f1399a1f41c9ddae32e03695a140e7b11d7c3376e5b68df0db7154e+             , 0x73ef0cbd438cbe0172c8ae37306324d44d5e6b0c69ac57b393f1ab370fd725cc647692444a04ef87387aa68d53743493b9eba14cc552ca2a93a+             ]+{-# INLINABLE _y #-}++-- | Generator of affine BN462T curve.+gA :: PA+gA = A _x _y+{-# INLINABLE gA #-}++-- | Generator of Jacobian BN462T curve.+gJ :: PJ+gJ = J _x _y 1+{-# INLINABLE gJ #-}++-- | Generator of projective BN462T curve.+gP :: PP+gP = P _x _y 1+{-# INLINABLE gP #-}

src/Curve/Weierstrass/BN512.hs view

@@ -1,74 +1,118 @@ module Curve.Weierstrass.BN512-  ( Fp-  , P-  , _a-  , _b-  , _g-  , _h-  , _n-  , _p+  ( module Curve.Weierstrass+  , module Curve.Weierstrass.BN512   ) where  import Protolude -import PrimeField (PrimeField)+import PrimeField -import Curve.Weierstrass (Point(..), WCurve(..), WPoint)+import Curve.Weierstrass  ------------------------------------------------------------------------------- -- Types ------------------------------------------------------------------------------- --- | BN512 curve+-- | BN512 curve. data BN512 --- | Field of BN512 curve-type Fp = PrimeField 0xfffffffffffffffffffffffffff9ec7f01c60ba1d8cb5307c0bbe3c111b0ef455146cf1eacbe98b8e48c65deab236fe1916a55ce5f4c6467b4eb280922adef33+-- | Field of points of BN512 curve.+type Fq = PrimeField 0xfffffffffffffffffffffffffff9ec7f01c60ba1d8cb5307c0bbe3c111b0ef455146cf1eacbe98b8e48c65deab236fe1916a55ce5f4c6467b4eb280922adef33 --- | BN512 curve is a Weierstrass curve-instance WCurve BN512 Fp where+-- | Field of coefficients of BN512 curve.+type Fr = PrimeField 0xfffffffffffffffffffffffffff9ec7f01c60ba1d8cb5307c0bbe3c111b0ef445146cf1eacbe98b8e48c65deab2679a34a10313e04f9a2b406a64a5f519a09ed++-- | BN512 curve is a Weierstrass curve.+instance Curve 'Weierstrass c BN512 Fq Fr => WCurve c BN512 Fq Fr where   a_ = const _a-  {-# INLINE a_ #-}+  {-# INLINABLE a_ #-}   b_ = const _b-  {-# INLINE b_ #-}-  g_ = _g-  {-# INLINE g_ #-}+  {-# INLINABLE b_ #-}+  h_ = const _h+  {-# INLINABLE h_ #-}+  q_ = const _q+  {-# INLINABLE q_ #-}+  r_ = const _r+  {-# INLINABLE r_ #-}+  x_ = const _x+  {-# INLINABLE x_ #-}+  y_ = const _y+  {-# INLINABLE y_ #-} --- | Point of BN512 curve-type P = WPoint BN512 Fp+-- | Affine BN512 curve point.+type PA = WAPoint BN512 Fq Fr +-- | Affine BN512 curve is a Weierstrass affine curve.+instance WACurve BN512 Fq Fr where+  gA_ = gA+  {-# INLINABLE gA_ #-}++-- | Jacobian BN512 point.+type PJ = WJPoint BN512 Fq Fr++-- | Jacobian BN512 curve is a Weierstrass Jacobian curve.+instance WJCurve BN512 Fq Fr where+  gJ_ = gJ+  {-# INLINABLE gJ_ #-}++-- | Projective BN512 point.+type PP = WPPoint BN512 Fq Fr++-- | Projective BN512 curve is a Weierstrass projective curve.+instance WPCurve BN512 Fq Fr where+  gP_ = gP+  {-# INLINABLE gP_ #-}+ ------------------------------------------------------------------------------- -- Parameters ------------------------------------------------------------------------------- --- | Coefficient @A@ of BN512 curve-_a :: Fp-_a = 0-{-# INLINE _a #-}---- | Coefficient @B@ of BN512 curve-_b :: Fp-_b = 3-{-# INLINE _b #-}+-- | Coefficient @A@ of BN512 curve.+_a :: Fq+_a = 0x0+{-# INLINABLE _a #-} --- | Generator of BN512 curve-_g :: P-_g = A-     1-     2-{-# INLINE _g #-}+-- | Coefficient @B@ of BN512 curve.+_b :: Fq+_b = 0x3+{-# INLINABLE _b #-} --- | Cofactor of BN512 curve+-- | Cofactor of BN512 curve. _h :: Integer-_h = 1-{-# INLINE _h #-}+_h = 0x1+{-# INLINABLE _h #-} --- | Order of BN512 curve-_n :: Integer-_n = 0xfffffffffffffffffffffffffff9ec7f01c60ba1d8cb5307c0bbe3c111b0ef445146cf1eacbe98b8e48c65deab2679a34a10313e04f9a2b406a64a5f519a09ed-{-# INLINE _n #-}+-- | Characteristic of BN512 curve.+_q :: Integer+_q = 0xfffffffffffffffffffffffffff9ec7f01c60ba1d8cb5307c0bbe3c111b0ef455146cf1eacbe98b8e48c65deab236fe1916a55ce5f4c6467b4eb280922adef33+{-# INLINABLE _q #-} --- | Characteristic of BN512 curve-_p :: Integer-_p = 0xfffffffffffffffffffffffffff9ec7f01c60ba1d8cb5307c0bbe3c111b0ef455146cf1eacbe98b8e48c65deab236fe1916a55ce5f4c6467b4eb280922adef33-{-# INLINE _p #-}+-- | Order of BN512 curve.+_r :: Integer+_r = 0xfffffffffffffffffffffffffff9ec7f01c60ba1d8cb5307c0bbe3c111b0ef445146cf1eacbe98b8e48c65deab2679a34a10313e04f9a2b406a64a5f519a09ed+{-# INLINABLE _r #-}++-- | Coordinate @X@ of BN512 curve.+_x :: Fq+_x = 0x1+{-# INLINABLE _x #-}++-- | Coordinate @Y@ of BN512 curve.+_y :: Fq+_y = 0x2+{-# INLINABLE _y #-}++-- | Generator of affine BN512 curve.+gA :: PA+gA = A _x _y+{-# INLINABLE gA #-}++-- | Generator of Jacobian BN512 curve.+gJ :: PJ+gJ = J _x _y 1+{-# INLINABLE gJ #-}++-- | Generator of projective BN512 curve.+gP :: PP+gP = P _x _y 1+{-# INLINABLE gP #-}

src/Curve/Weierstrass/BrainpoolP160R1.hs view

@@ -1,74 +1,118 @@ module Curve.Weierstrass.BrainpoolP160R1-  ( Fp-  , P-  , _a-  , _b-  , _g-  , _h-  , _n-  , _p+  ( module Curve.Weierstrass+  , module Curve.Weierstrass.BrainpoolP160R1   ) where  import Protolude -import PrimeField (PrimeField)+import PrimeField -import Curve.Weierstrass (Point(..), WCurve(..), WPoint)+import Curve.Weierstrass  ------------------------------------------------------------------------------- -- Types ------------------------------------------------------------------------------- --- | Brainpool-P160R1 curve+-- | BrainpoolP160R1 curve. data BrainpoolP160R1 --- | Field of Brainpool-P160R1 curve-type Fp = PrimeField 0xe95e4a5f737059dc60dfc7ad95b3d8139515620f+-- | Field of points of BrainpoolP160R1 curve.+type Fq = PrimeField 0xe95e4a5f737059dc60dfc7ad95b3d8139515620f --- | Brainpool-P160R1 curve is a Weierstrass curve-instance WCurve BrainpoolP160R1 Fp where+-- | Field of coefficients of BrainpoolP160R1 curve.+type Fr = PrimeField 0xe95e4a5f737059dc60df5991d45029409e60fc09++-- | BrainpoolP160R1 curve is a Weierstrass curve.+instance Curve 'Weierstrass c BrainpoolP160R1 Fq Fr => WCurve c BrainpoolP160R1 Fq Fr where   a_ = const _a-  {-# INLINE a_ #-}+  {-# INLINABLE a_ #-}   b_ = const _b-  {-# INLINE b_ #-}-  g_ = _g-  {-# INLINE g_ #-}+  {-# INLINABLE b_ #-}+  h_ = const _h+  {-# INLINABLE h_ #-}+  q_ = const _q+  {-# INLINABLE q_ #-}+  r_ = const _r+  {-# INLINABLE r_ #-}+  x_ = const _x+  {-# INLINABLE x_ #-}+  y_ = const _y+  {-# INLINABLE y_ #-} --- | Point of Brainpool-P160R1 curve-type P = WPoint BrainpoolP160R1 Fp+-- | Affine BrainpoolP160R1 curve point.+type PA = WAPoint BrainpoolP160R1 Fq Fr +-- | Affine BrainpoolP160R1 curve is a Weierstrass affine curve.+instance WACurve BrainpoolP160R1 Fq Fr where+  gA_ = gA+  {-# INLINABLE gA_ #-}++-- | Jacobian BrainpoolP160R1 point.+type PJ = WJPoint BrainpoolP160R1 Fq Fr++-- | Jacobian BrainpoolP160R1 curve is a Weierstrass Jacobian curve.+instance WJCurve BrainpoolP160R1 Fq Fr where+  gJ_ = gJ+  {-# INLINABLE gJ_ #-}++-- | Projective BrainpoolP160R1 point.+type PP = WPPoint BrainpoolP160R1 Fq Fr++-- | Projective BrainpoolP160R1 curve is a Weierstrass projective curve.+instance WPCurve BrainpoolP160R1 Fq Fr where+  gP_ = gP+  {-# INLINABLE gP_ #-}+ ------------------------------------------------------------------------------- -- Parameters ------------------------------------------------------------------------------- --- | Coefficient @A@ of Brainpool-P160R1 curve-_a :: Fp+-- | Coefficient @A@ of BrainpoolP160R1 curve.+_a :: Fq _a = 0x340e7be2a280eb74e2be61bada745d97e8f7c300-{-# INLINE _a #-}+{-# INLINABLE _a #-} --- | Coefficient @B@ of Brainpool-P160R1 curve-_b :: Fp+-- | Coefficient @B@ of BrainpoolP160R1 curve.+_b :: Fq _b = 0x1e589a8595423412134faa2dbdec95c8d8675e58-{-# INLINE _b #-}---- | Generator of Brainpool-P160R1 curve-_g :: P-_g = A-     0xbed5af16ea3f6a4f62938c4631eb5af7bdbcdbc3-     0x1667cb477a1a8ec338f94741669c976316da6321-{-# INLINE _g #-}+{-# INLINABLE _b #-} --- | Cofactor of Brainpool-P160R1 curve+-- | Cofactor of BrainpoolP160R1 curve. _h :: Integer-_h = 1-{-# INLINE _h #-}+_h = 0x1+{-# INLINABLE _h #-} --- | Order of Brainpool-P160R1 curve-_n :: Integer-_n = 0xe95e4a5f737059dc60df5991d45029409e60fc09-{-# INLINE _n #-}+-- | Characteristic of BrainpoolP160R1 curve.+_q :: Integer+_q = 0xe95e4a5f737059dc60dfc7ad95b3d8139515620f+{-# INLINABLE _q #-} --- | Characteristic of Brainpool-P160R1 curve-_p :: Integer-_p = 0xe95e4a5f737059dc60dfc7ad95b3d8139515620f-{-# INLINE _p #-}+-- | Order of BrainpoolP160R1 curve.+_r :: Integer+_r = 0xe95e4a5f737059dc60df5991d45029409e60fc09+{-# INLINABLE _r #-}++-- | Coordinate @X@ of BrainpoolP160R1 curve.+_x :: Fq+_x = 0xbed5af16ea3f6a4f62938c4631eb5af7bdbcdbc3+{-# INLINABLE _x #-}++-- | Coordinate @Y@ of BrainpoolP160R1 curve.+_y :: Fq+_y = 0x1667cb477a1a8ec338f94741669c976316da6321+{-# INLINABLE _y #-}++-- | Generator of affine BrainpoolP160R1 curve.+gA :: PA+gA = A _x _y+{-# INLINABLE gA #-}++-- | Generator of Jacobian BrainpoolP160R1 curve.+gJ :: PJ+gJ = J _x _y 1+{-# INLINABLE gJ #-}++-- | Generator of projective BrainpoolP160R1 curve.+gP :: PP+gP = P _x _y 1+{-# INLINABLE gP #-}

src/Curve/Weierstrass/BrainpoolP160T1.hs view

@@ -1,74 +1,118 @@ module Curve.Weierstrass.BrainpoolP160T1-  ( Fp-  , P-  , _a-  , _b-  , _g-  , _h-  , _n-  , _p+  ( module Curve.Weierstrass+  , module Curve.Weierstrass.BrainpoolP160T1   ) where  import Protolude -import PrimeField (PrimeField)+import PrimeField -import Curve.Weierstrass (Point(..), WCurve(..), WPoint)+import Curve.Weierstrass  ------------------------------------------------------------------------------- -- Types ------------------------------------------------------------------------------- --- | Brainpool-P160T1 curve+-- | BrainpoolP160T1 curve. data BrainpoolP160T1 --- | Field of Brainpool-P160T1 curve-type Fp = PrimeField 0xe95e4a5f737059dc60dfc7ad95b3d8139515620f+-- | Field of points of BrainpoolP160T1 curve.+type Fq = PrimeField 0xe95e4a5f737059dc60dfc7ad95b3d8139515620f --- | Brainpool-P160T1 curve is a Weierstrass curve-instance WCurve BrainpoolP160T1 Fp where+-- | Field of coefficients of BrainpoolP160T1 curve.+type Fr = PrimeField 0xe95e4a5f737059dc60df5991d45029409e60fc09++-- | BrainpoolP160T1 curve is a Weierstrass curve.+instance Curve 'Weierstrass c BrainpoolP160T1 Fq Fr => WCurve c BrainpoolP160T1 Fq Fr where   a_ = const _a-  {-# INLINE a_ #-}+  {-# INLINABLE a_ #-}   b_ = const _b-  {-# INLINE b_ #-}-  g_ = _g-  {-# INLINE g_ #-}+  {-# INLINABLE b_ #-}+  h_ = const _h+  {-# INLINABLE h_ #-}+  q_ = const _q+  {-# INLINABLE q_ #-}+  r_ = const _r+  {-# INLINABLE r_ #-}+  x_ = const _x+  {-# INLINABLE x_ #-}+  y_ = const _y+  {-# INLINABLE y_ #-} --- | Point of Brainpool-P160T1 curve-type P = WPoint BrainpoolP160T1 Fp+-- | Affine BrainpoolP160T1 curve point.+type PA = WAPoint BrainpoolP160T1 Fq Fr +-- | Affine BrainpoolP160T1 curve is a Weierstrass affine curve.+instance WACurve BrainpoolP160T1 Fq Fr where+  gA_ = gA+  {-# INLINABLE gA_ #-}++-- | Jacobian BrainpoolP160T1 point.+type PJ = WJPoint BrainpoolP160T1 Fq Fr++-- | Jacobian BrainpoolP160T1 curve is a Weierstrass Jacobian curve.+instance WJCurve BrainpoolP160T1 Fq Fr where+  gJ_ = gJ+  {-# INLINABLE gJ_ #-}++-- | Projective BrainpoolP160T1 point.+type PP = WPPoint BrainpoolP160T1 Fq Fr++-- | Projective BrainpoolP160T1 curve is a Weierstrass projective curve.+instance WPCurve BrainpoolP160T1 Fq Fr where+  gP_ = gP+  {-# INLINABLE gP_ #-}+ ------------------------------------------------------------------------------- -- Parameters ------------------------------------------------------------------------------- --- | Coefficient @A@ of Brainpool-P160T1 curve-_a :: Fp+-- | Coefficient @A@ of BrainpoolP160T1 curve.+_a :: Fq _a = 0xe95e4a5f737059dc60dfc7ad95b3d8139515620c-{-# INLINE _a #-}+{-# INLINABLE _a #-} --- | Coefficient @B@ of Brainpool-P160T1 curve-_b :: Fp+-- | Coefficient @B@ of BrainpoolP160T1 curve.+_b :: Fq _b = 0x7a556b6dae535b7b51ed2c4d7daa7a0b5c55f380-{-# INLINE _b #-}---- | Generator of Brainpool-P160T1 curve-_g :: P-_g = A-     0xb199b13b9b34efc1397e64baeb05acc265ff2378-     0xadd6718b7c7c1961f0991b842443772152c9e0ad-{-# INLINE _g #-}+{-# INLINABLE _b #-} --- | Cofactor of Brainpool-P160T1 curve+-- | Cofactor of BrainpoolP160T1 curve. _h :: Integer-_h = 1-{-# INLINE _h #-}+_h = 0x1+{-# INLINABLE _h #-} --- | Order of Brainpool-P160T1 curve-_n :: Integer-_n = 0xe95e4a5f737059dc60df5991d45029409e60fc09-{-# INLINE _n #-}+-- | Characteristic of BrainpoolP160T1 curve.+_q :: Integer+_q = 0xe95e4a5f737059dc60dfc7ad95b3d8139515620f+{-# INLINABLE _q #-} --- | Characteristic of Brainpool-P160T1 curve-_p :: Integer-_p = 0xe95e4a5f737059dc60dfc7ad95b3d8139515620f-{-# INLINE _p #-}+-- | Order of BrainpoolP160T1 curve.+_r :: Integer+_r = 0xe95e4a5f737059dc60df5991d45029409e60fc09+{-# INLINABLE _r #-}++-- | Coordinate @X@ of BrainpoolP160T1 curve.+_x :: Fq+_x = 0xb199b13b9b34efc1397e64baeb05acc265ff2378+{-# INLINABLE _x #-}++-- | Coordinate @Y@ of BrainpoolP160T1 curve.+_y :: Fq+_y = 0xadd6718b7c7c1961f0991b842443772152c9e0ad+{-# INLINABLE _y #-}++-- | Generator of affine BrainpoolP160T1 curve.+gA :: PA+gA = A _x _y+{-# INLINABLE gA #-}++-- | Generator of Jacobian BrainpoolP160T1 curve.+gJ :: PJ+gJ = J _x _y 1+{-# INLINABLE gJ #-}++-- | Generator of projective BrainpoolP160T1 curve.+gP :: PP+gP = P _x _y 1+{-# INLINABLE gP #-}

src/Curve/Weierstrass/BrainpoolP192R1.hs view

@@ -1,74 +1,118 @@ module Curve.Weierstrass.BrainpoolP192R1-  ( Fp-  , P-  , _a-  , _b-  , _g-  , _h-  , _n-  , _p+  ( module Curve.Weierstrass+  , module Curve.Weierstrass.BrainpoolP192R1   ) where  import Protolude -import PrimeField (PrimeField)+import PrimeField -import Curve.Weierstrass (Point(..), WCurve(..), WPoint)+import Curve.Weierstrass  ------------------------------------------------------------------------------- -- Types ------------------------------------------------------------------------------- --- | Brainpool-P192R1 curve+-- | BrainpoolP192R1 curve. data BrainpoolP192R1 --- | Field of Brainpool-P192R1 curve-type Fp = PrimeField 0xc302f41d932a36cda7a3463093d18db78fce476de1a86297+-- | Field of points of BrainpoolP192R1 curve.+type Fq = PrimeField 0xc302f41d932a36cda7a3463093d18db78fce476de1a86297 --- | Brainpool-P192R1 curve is a Weierstrass curve-instance WCurve BrainpoolP192R1 Fp where+-- | Field of coefficients of BrainpoolP192R1 curve.+type Fr = PrimeField 0xc302f41d932a36cda7a3462f9e9e916b5be8f1029ac4acc1++-- | BrainpoolP192R1 curve is a Weierstrass curve.+instance Curve 'Weierstrass c BrainpoolP192R1 Fq Fr => WCurve c BrainpoolP192R1 Fq Fr where   a_ = const _a-  {-# INLINE a_ #-}+  {-# INLINABLE a_ #-}   b_ = const _b-  {-# INLINE b_ #-}-  g_ = _g-  {-# INLINE g_ #-}+  {-# INLINABLE b_ #-}+  h_ = const _h+  {-# INLINABLE h_ #-}+  q_ = const _q+  {-# INLINABLE q_ #-}+  r_ = const _r+  {-# INLINABLE r_ #-}+  x_ = const _x+  {-# INLINABLE x_ #-}+  y_ = const _y+  {-# INLINABLE y_ #-} --- | Point of Brainpool-P192R1 curve-type P = WPoint BrainpoolP192R1 Fp+-- | Affine BrainpoolP192R1 curve point.+type PA = WAPoint BrainpoolP192R1 Fq Fr +-- | Affine BrainpoolP192R1 curve is a Weierstrass affine curve.+instance WACurve BrainpoolP192R1 Fq Fr where+  gA_ = gA+  {-# INLINABLE gA_ #-}++-- | Jacobian BrainpoolP192R1 point.+type PJ = WJPoint BrainpoolP192R1 Fq Fr++-- | Jacobian BrainpoolP192R1 curve is a Weierstrass Jacobian curve.+instance WJCurve BrainpoolP192R1 Fq Fr where+  gJ_ = gJ+  {-# INLINABLE gJ_ #-}++-- | Projective BrainpoolP192R1 point.+type PP = WPPoint BrainpoolP192R1 Fq Fr++-- | Projective BrainpoolP192R1 curve is a Weierstrass projective curve.+instance WPCurve BrainpoolP192R1 Fq Fr where+  gP_ = gP+  {-# INLINABLE gP_ #-}+ ------------------------------------------------------------------------------- -- Parameters ------------------------------------------------------------------------------- --- | Coefficient @A@ of Brainpool-P192R1 curve-_a :: Fp+-- | Coefficient @A@ of BrainpoolP192R1 curve.+_a :: Fq _a = 0x6a91174076b1e0e19c39c031fe8685c1cae040e5c69a28ef-{-# INLINE _a #-}+{-# INLINABLE _a #-} --- | Coefficient @B@ of Brainpool-P192R1 curve-_b :: Fp+-- | Coefficient @B@ of BrainpoolP192R1 curve.+_b :: Fq _b = 0x469a28ef7c28cca3dc721d044f4496bcca7ef4146fbf25c9-{-# INLINE _b #-}---- | Generator of Brainpool-P192R1 curve-_g :: P-_g = A-     0xc0a0647eaab6a48753b033c56cb0f0900a2f5c4853375fd6-     0x14b690866abd5bb88b5f4828c1490002e6773fa2fa299b8f-{-# INLINE _g #-}+{-# INLINABLE _b #-} --- | Cofactor of Brainpool-P192R1 curve+-- | Cofactor of BrainpoolP192R1 curve. _h :: Integer-_h = 1-{-# INLINE _h #-}+_h = 0x1+{-# INLINABLE _h #-} --- | Order of Brainpool-P192R1 curve-_n :: Integer-_n = 0xc302f41d932a36cda7a3462f9e9e916b5be8f1029ac4acc1-{-# INLINE _n #-}+-- | Characteristic of BrainpoolP192R1 curve.+_q :: Integer+_q = 0xc302f41d932a36cda7a3463093d18db78fce476de1a86297+{-# INLINABLE _q #-} --- | Characteristic of Brainpool-P192R1 curve-_p :: Integer-_p = 0xc302f41d932a36cda7a3463093d18db78fce476de1a86297-{-# INLINE _p #-}+-- | Order of BrainpoolP192R1 curve.+_r :: Integer+_r = 0xc302f41d932a36cda7a3462f9e9e916b5be8f1029ac4acc1+{-# INLINABLE _r #-}++-- | Coordinate @X@ of BrainpoolP192R1 curve.+_x :: Fq+_x = 0xc0a0647eaab6a48753b033c56cb0f0900a2f5c4853375fd6+{-# INLINABLE _x #-}++-- | Coordinate @Y@ of BrainpoolP192R1 curve.+_y :: Fq+_y = 0x14b690866abd5bb88b5f4828c1490002e6773fa2fa299b8f+{-# INLINABLE _y #-}++-- | Generator of affine BrainpoolP192R1 curve.+gA :: PA+gA = A _x _y+{-# INLINABLE gA #-}++-- | Generator of Jacobian BrainpoolP192R1 curve.+gJ :: PJ+gJ = J _x _y 1+{-# INLINABLE gJ #-}++-- | Generator of projective BrainpoolP192R1 curve.+gP :: PP+gP = P _x _y 1+{-# INLINABLE gP #-}

src/Curve/Weierstrass/BrainpoolP192T1.hs view

@@ -1,74 +1,118 @@ module Curve.Weierstrass.BrainpoolP192T1-  ( Fp-  , P-  , _a-  , _b-  , _g-  , _h-  , _n-  , _p+  ( module Curve.Weierstrass+  , module Curve.Weierstrass.BrainpoolP192T1   ) where  import Protolude -import PrimeField (PrimeField)+import PrimeField -import Curve.Weierstrass (Point(..), WCurve(..), WPoint)+import Curve.Weierstrass  ------------------------------------------------------------------------------- -- Types ------------------------------------------------------------------------------- --- | Brainpool-P192T1 curve+-- | BrainpoolP192T1 curve. data BrainpoolP192T1 --- | Field of Brainpool-P192T1 curve-type Fp = PrimeField 0xc302f41d932a36cda7a3463093d18db78fce476de1a86297+-- | Field of points of BrainpoolP192T1 curve.+type Fq = PrimeField 0xc302f41d932a36cda7a3463093d18db78fce476de1a86297 --- | Brainpool-P192T1 curve is a Weierstrass curve-instance WCurve BrainpoolP192T1 Fp where+-- | Field of coefficients of BrainpoolP192T1 curve.+type Fr = PrimeField 0xc302f41d932a36cda7a3462f9e9e916b5be8f1029ac4acc1++-- | BrainpoolP192T1 curve is a Weierstrass curve.+instance Curve 'Weierstrass c BrainpoolP192T1 Fq Fr => WCurve c BrainpoolP192T1 Fq Fr where   a_ = const _a-  {-# INLINE a_ #-}+  {-# INLINABLE a_ #-}   b_ = const _b-  {-# INLINE b_ #-}-  g_ = _g-  {-# INLINE g_ #-}+  {-# INLINABLE b_ #-}+  h_ = const _h+  {-# INLINABLE h_ #-}+  q_ = const _q+  {-# INLINABLE q_ #-}+  r_ = const _r+  {-# INLINABLE r_ #-}+  x_ = const _x+  {-# INLINABLE x_ #-}+  y_ = const _y+  {-# INLINABLE y_ #-} --- | Point of Brainpool-P192T1 curve-type P = WPoint BrainpoolP192T1 Fp+-- | Affine BrainpoolP192T1 curve point.+type PA = WAPoint BrainpoolP192T1 Fq Fr +-- | Affine BrainpoolP192T1 curve is a Weierstrass affine curve.+instance WACurve BrainpoolP192T1 Fq Fr where+  gA_ = gA+  {-# INLINABLE gA_ #-}++-- | Jacobian BrainpoolP192T1 point.+type PJ = WJPoint BrainpoolP192T1 Fq Fr++-- | Jacobian BrainpoolP192T1 curve is a Weierstrass Jacobian curve.+instance WJCurve BrainpoolP192T1 Fq Fr where+  gJ_ = gJ+  {-# INLINABLE gJ_ #-}++-- | Projective BrainpoolP192T1 point.+type PP = WPPoint BrainpoolP192T1 Fq Fr++-- | Projective BrainpoolP192T1 curve is a Weierstrass projective curve.+instance WPCurve BrainpoolP192T1 Fq Fr where+  gP_ = gP+  {-# INLINABLE gP_ #-}+ ------------------------------------------------------------------------------- -- Parameters ------------------------------------------------------------------------------- --- | Coefficient @A@ of Brainpool-P192T1 curve-_a :: Fp+-- | Coefficient @A@ of BrainpoolP192T1 curve.+_a :: Fq _a = 0xc302f41d932a36cda7a3463093d18db78fce476de1a86294-{-# INLINE _a #-}+{-# INLINABLE _a #-} --- | Coefficient @B@ of Brainpool-P192T1 curve-_b :: Fp+-- | Coefficient @B@ of BrainpoolP192T1 curve.+_b :: Fq _b = 0x13d56ffaec78681e68f9deb43b35bec2fb68542e27897b79-{-# INLINE _b #-}---- | Generator of Brainpool-P192T1 curve-_g :: P-_g = A-     0x3ae9e58c82f63c30282e1fe7bbf43fa72c446af6f4618129-     0x97e2c5667c2223a902ab5ca449d0084b7e5b3de7ccc01c9-{-# INLINE _g #-}+{-# INLINABLE _b #-} --- | Cofactor of Brainpool-P192T1 curve+-- | Cofactor of BrainpoolP192T1 curve. _h :: Integer-_h = 1-{-# INLINE _h #-}+_h = 0x1+{-# INLINABLE _h #-} --- | Order of Brainpool-P192T1 curve-_n :: Integer-_n = 0xc302f41d932a36cda7a3462f9e9e916b5be8f1029ac4acc1-{-# INLINE _n #-}+-- | Characteristic of BrainpoolP192T1 curve.+_q :: Integer+_q = 0xc302f41d932a36cda7a3463093d18db78fce476de1a86297+{-# INLINABLE _q #-} --- | Characteristic of Brainpool-P192T1 curve-_p :: Integer-_p = 0xc302f41d932a36cda7a3463093d18db78fce476de1a86297-{-# INLINE _p #-}+-- | Order of BrainpoolP192T1 curve.+_r :: Integer+_r = 0xc302f41d932a36cda7a3462f9e9e916b5be8f1029ac4acc1+{-# INLINABLE _r #-}++-- | Coordinate @X@ of BrainpoolP192T1 curve.+_x :: Fq+_x = 0x3ae9e58c82f63c30282e1fe7bbf43fa72c446af6f4618129+{-# INLINABLE _x #-}++-- | Coordinate @Y@ of BrainpoolP192T1 curve.+_y :: Fq+_y = 0x97e2c5667c2223a902ab5ca449d0084b7e5b3de7ccc01c9+{-# INLINABLE _y #-}++-- | Generator of affine BrainpoolP192T1 curve.+gA :: PA+gA = A _x _y+{-# INLINABLE gA #-}++-- | Generator of Jacobian BrainpoolP192T1 curve.+gJ :: PJ+gJ = J _x _y 1+{-# INLINABLE gJ #-}++-- | Generator of projective BrainpoolP192T1 curve.+gP :: PP+gP = P _x _y 1+{-# INLINABLE gP #-}

src/Curve/Weierstrass/BrainpoolP224R1.hs view

@@ -1,74 +1,118 @@ module Curve.Weierstrass.BrainpoolP224R1-  ( Fp-  , P-  , _a-  , _b-  , _g-  , _h-  , _n-  , _p+  ( module Curve.Weierstrass+  , module Curve.Weierstrass.BrainpoolP224R1   ) where  import Protolude -import PrimeField (PrimeField)+import PrimeField -import Curve.Weierstrass (Point(..), WCurve(..), WPoint)+import Curve.Weierstrass  ------------------------------------------------------------------------------- -- Types ------------------------------------------------------------------------------- --- | Brainpool-P224R1 curve+-- | BrainpoolP224R1 curve. data BrainpoolP224R1 --- | Field of Brainpool-P224R1 curve-type Fp = PrimeField 0xd7c134aa264366862a18302575d1d787b09f075797da89f57ec8c0ff+-- | Field of points of BrainpoolP224R1 curve.+type Fq = PrimeField 0xd7c134aa264366862a18302575d1d787b09f075797da89f57ec8c0ff --- | Brainpool-P224R1 curve is a Weierstrass curve-instance WCurve BrainpoolP224R1 Fp where+-- | Field of coefficients of BrainpoolP224R1 curve.+type Fr = PrimeField 0xd7c134aa264366862a18302575d0fb98d116bc4b6ddebca3a5a7939f++-- | BrainpoolP224R1 curve is a Weierstrass curve.+instance Curve 'Weierstrass c BrainpoolP224R1 Fq Fr => WCurve c BrainpoolP224R1 Fq Fr where   a_ = const _a-  {-# INLINE a_ #-}+  {-# INLINABLE a_ #-}   b_ = const _b-  {-# INLINE b_ #-}-  g_ = _g-  {-# INLINE g_ #-}+  {-# INLINABLE b_ #-}+  h_ = const _h+  {-# INLINABLE h_ #-}+  q_ = const _q+  {-# INLINABLE q_ #-}+  r_ = const _r+  {-# INLINABLE r_ #-}+  x_ = const _x+  {-# INLINABLE x_ #-}+  y_ = const _y+  {-# INLINABLE y_ #-} --- | Point of Brainpool-P224R1 curve-type P = WPoint BrainpoolP224R1 Fp+-- | Affine BrainpoolP224R1 curve point.+type PA = WAPoint BrainpoolP224R1 Fq Fr +-- | Affine BrainpoolP224R1 curve is a Weierstrass affine curve.+instance WACurve BrainpoolP224R1 Fq Fr where+  gA_ = gA+  {-# INLINABLE gA_ #-}++-- | Jacobian BrainpoolP224R1 point.+type PJ = WJPoint BrainpoolP224R1 Fq Fr++-- | Jacobian BrainpoolP224R1 curve is a Weierstrass Jacobian curve.+instance WJCurve BrainpoolP224R1 Fq Fr where+  gJ_ = gJ+  {-# INLINABLE gJ_ #-}++-- | Projective BrainpoolP224R1 point.+type PP = WPPoint BrainpoolP224R1 Fq Fr++-- | Projective BrainpoolP224R1 curve is a Weierstrass projective curve.+instance WPCurve BrainpoolP224R1 Fq Fr where+  gP_ = gP+  {-# INLINABLE gP_ #-}+ ------------------------------------------------------------------------------- -- Parameters ------------------------------------------------------------------------------- --- | Coefficient @A@ of Brainpool-P224R1 curve-_a :: Fp+-- | Coefficient @A@ of BrainpoolP224R1 curve.+_a :: Fq _a = 0x68a5e62ca9ce6c1c299803a6c1530b514e182ad8b0042a59cad29f43-{-# INLINE _a #-}+{-# INLINABLE _a #-} --- | Coefficient @B@ of Brainpool-P224R1 curve-_b :: Fp+-- | Coefficient @B@ of BrainpoolP224R1 curve.+_b :: Fq _b = 0x2580f63ccfe44138870713b1a92369e33e2135d266dbb372386c400b-{-# INLINE _b #-}---- | Generator of Brainpool-P224R1 curve-_g :: P-_g = A-     0xd9029ad2c7e5cf4340823b2a87dc68c9e4ce3174c1e6efdee12c07d-     0x58aa56f772c0726f24c6b89e4ecdac24354b9e99caa3f6d3761402cd-{-# INLINE _g #-}+{-# INLINABLE _b #-} --- | Cofactor of Brainpool-P224R1 curve+-- | Cofactor of BrainpoolP224R1 curve. _h :: Integer-_h = 1-{-# INLINE _h #-}+_h = 0x1+{-# INLINABLE _h #-} --- | Order of Brainpool-P224R1 curve-_n :: Integer-_n = 0xd7c134aa264366862a18302575d0fb98d116bc4b6ddebca3a5a7939f-{-# INLINE _n #-}+-- | Characteristic of BrainpoolP224R1 curve.+_q :: Integer+_q = 0xd7c134aa264366862a18302575d1d787b09f075797da89f57ec8c0ff+{-# INLINABLE _q #-} --- | Characteristic of Brainpool-P224R1 curve-_p :: Integer-_p = 0xd7c134aa264366862a18302575d1d787b09f075797da89f57ec8c0ff-{-# INLINE _p #-}+-- | Order of BrainpoolP224R1 curve.+_r :: Integer+_r = 0xd7c134aa264366862a18302575d0fb98d116bc4b6ddebca3a5a7939f+{-# INLINABLE _r #-}++-- | Coordinate @X@ of BrainpoolP224R1 curve.+_x :: Fq+_x = 0xd9029ad2c7e5cf4340823b2a87dc68c9e4ce3174c1e6efdee12c07d+{-# INLINABLE _x #-}++-- | Coordinate @Y@ of BrainpoolP224R1 curve.+_y :: Fq+_y = 0x58aa56f772c0726f24c6b89e4ecdac24354b9e99caa3f6d3761402cd+{-# INLINABLE _y #-}++-- | Generator of affine BrainpoolP224R1 curve.+gA :: PA+gA = A _x _y+{-# INLINABLE gA #-}++-- | Generator of Jacobian BrainpoolP224R1 curve.+gJ :: PJ+gJ = J _x _y 1+{-# INLINABLE gJ #-}++-- | Generator of projective BrainpoolP224R1 curve.+gP :: PP+gP = P _x _y 1+{-# INLINABLE gP #-}

src/Curve/Weierstrass/BrainpoolP224T1.hs view

@@ -1,74 +1,118 @@ module Curve.Weierstrass.BrainpoolP224T1-  ( Fp-  , P-  , _a-  , _b-  , _g-  , _h-  , _n-  , _p+  ( module Curve.Weierstrass+  , module Curve.Weierstrass.BrainpoolP224T1   ) where  import Protolude -import PrimeField (PrimeField)+import PrimeField -import Curve.Weierstrass (Point(..), WCurve(..), WPoint)+import Curve.Weierstrass  ------------------------------------------------------------------------------- -- Types ------------------------------------------------------------------------------- --- | Brainpool-P224T1 curve+-- | BrainpoolP224T1 curve. data BrainpoolP224T1 --- | Field of Brainpool-P224T1 curve-type Fp = PrimeField 0xd7c134aa264366862a18302575d1d787b09f075797da89f57ec8c0ff+-- | Field of points of BrainpoolP224T1 curve.+type Fq = PrimeField 0xd7c134aa264366862a18302575d1d787b09f075797da89f57ec8c0ff --- | Brainpool-P224T1 curve is a Weierstrass curve-instance WCurve BrainpoolP224T1 Fp where+-- | Field of coefficients of BrainpoolP224T1 curve.+type Fr = PrimeField 0xd7c134aa264366862a18302575d0fb98d116bc4b6ddebca3a5a7939f++-- | BrainpoolP224T1 curve is a Weierstrass curve.+instance Curve 'Weierstrass c BrainpoolP224T1 Fq Fr => WCurve c BrainpoolP224T1 Fq Fr where   a_ = const _a-  {-# INLINE a_ #-}+  {-# INLINABLE a_ #-}   b_ = const _b-  {-# INLINE b_ #-}-  g_ = _g-  {-# INLINE g_ #-}+  {-# INLINABLE b_ #-}+  h_ = const _h+  {-# INLINABLE h_ #-}+  q_ = const _q+  {-# INLINABLE q_ #-}+  r_ = const _r+  {-# INLINABLE r_ #-}+  x_ = const _x+  {-# INLINABLE x_ #-}+  y_ = const _y+  {-# INLINABLE y_ #-} --- | Point of Brainpool-P224T1 curve-type P = WPoint BrainpoolP224T1 Fp+-- | Affine BrainpoolP224T1 curve point.+type PA = WAPoint BrainpoolP224T1 Fq Fr +-- | Affine BrainpoolP224T1 curve is a Weierstrass affine curve.+instance WACurve BrainpoolP224T1 Fq Fr where+  gA_ = gA+  {-# INLINABLE gA_ #-}++-- | Jacobian BrainpoolP224T1 point.+type PJ = WJPoint BrainpoolP224T1 Fq Fr++-- | Jacobian BrainpoolP224T1 curve is a Weierstrass Jacobian curve.+instance WJCurve BrainpoolP224T1 Fq Fr where+  gJ_ = gJ+  {-# INLINABLE gJ_ #-}++-- | Projective BrainpoolP224T1 point.+type PP = WPPoint BrainpoolP224T1 Fq Fr++-- | Projective BrainpoolP224T1 curve is a Weierstrass projective curve.+instance WPCurve BrainpoolP224T1 Fq Fr where+  gP_ = gP+  {-# INLINABLE gP_ #-}+ ------------------------------------------------------------------------------- -- Parameters ------------------------------------------------------------------------------- --- | Coefficient @A@ of Brainpool-P224T1 curve-_a :: Fp+-- | Coefficient @A@ of BrainpoolP224T1 curve.+_a :: Fq _a = 0xd7c134aa264366862a18302575d1d787b09f075797da89f57ec8c0fc-{-# INLINE _a #-}+{-# INLINABLE _a #-} --- | Coefficient @B@ of Brainpool-P224T1 curve-_b :: Fp+-- | Coefficient @B@ of BrainpoolP224T1 curve.+_b :: Fq _b = 0x4b337d934104cd7bef271bf60ced1ed20da14c08b3bb64f18a60888d-{-# INLINE _b #-}---- | Generator of Brainpool-P224T1 curve-_g :: P-_g = A-     0x6ab1e344ce25ff3896424e7ffe14762ecb49f8928ac0c76029b4d580-     0x374e9f5143e568cd23f3f4d7c0d4b1e41c8cc0d1c6abd5f1a46db4c-{-# INLINE _g #-}+{-# INLINABLE _b #-} --- | Cofactor of Brainpool-P224T1 curve+-- | Cofactor of BrainpoolP224T1 curve. _h :: Integer-_h = 1-{-# INLINE _h #-}+_h = 0x1+{-# INLINABLE _h #-} --- | Order of Brainpool-P224T1 curve-_n :: Integer-_n = 0xd7c134aa264366862a18302575d0fb98d116bc4b6ddebca3a5a7939f-{-# INLINE _n #-}+-- | Characteristic of BrainpoolP224T1 curve.+_q :: Integer+_q = 0xd7c134aa264366862a18302575d1d787b09f075797da89f57ec8c0ff+{-# INLINABLE _q #-} --- | Characteristic of Brainpool-P224T1 curve-_p :: Integer-_p = 0xd7c134aa264366862a18302575d1d787b09f075797da89f57ec8c0ff-{-# INLINE _p #-}+-- | Order of BrainpoolP224T1 curve.+_r :: Integer+_r = 0xd7c134aa264366862a18302575d0fb98d116bc4b6ddebca3a5a7939f+{-# INLINABLE _r #-}++-- | Coordinate @X@ of BrainpoolP224T1 curve.+_x :: Fq+_x = 0x6ab1e344ce25ff3896424e7ffe14762ecb49f8928ac0c76029b4d580+{-# INLINABLE _x #-}++-- | Coordinate @Y@ of BrainpoolP224T1 curve.+_y :: Fq+_y = 0x374e9f5143e568cd23f3f4d7c0d4b1e41c8cc0d1c6abd5f1a46db4c+{-# INLINABLE _y #-}++-- | Generator of affine BrainpoolP224T1 curve.+gA :: PA+gA = A _x _y+{-# INLINABLE gA #-}++-- | Generator of Jacobian BrainpoolP224T1 curve.+gJ :: PJ+gJ = J _x _y 1+{-# INLINABLE gJ #-}++-- | Generator of projective BrainpoolP224T1 curve.+gP :: PP+gP = P _x _y 1+{-# INLINABLE gP #-}

src/Curve/Weierstrass/BrainpoolP256R1.hs view

@@ -1,74 +1,118 @@ module Curve.Weierstrass.BrainpoolP256R1-  ( Fp-  , P-  , _a-  , _b-  , _g-  , _h-  , _n-  , _p+  ( module Curve.Weierstrass+  , module Curve.Weierstrass.BrainpoolP256R1   ) where  import Protolude -import PrimeField (PrimeField)+import PrimeField -import Curve.Weierstrass (Point(..), WCurve(..), WPoint)+import Curve.Weierstrass  ------------------------------------------------------------------------------- -- Types ------------------------------------------------------------------------------- --- | Brainpool-P256R1 curve+-- | BrainpoolP256R1 curve. data BrainpoolP256R1 --- | Field of Brainpool-P256R1 curve-type Fp = PrimeField 0xa9fb57dba1eea9bc3e660a909d838d726e3bf623d52620282013481d1f6e5377+-- | Field of points of BrainpoolP256R1 curve.+type Fq = PrimeField 0xa9fb57dba1eea9bc3e660a909d838d726e3bf623d52620282013481d1f6e5377 --- | Brainpool-P256R1 curve is a Weierstrass curve-instance WCurve BrainpoolP256R1 Fp where+-- | Field of coefficients of BrainpoolP256R1 curve.+type Fr = PrimeField 0xa9fb57dba1eea9bc3e660a909d838d718c397aa3b561a6f7901e0e82974856a7++-- | BrainpoolP256R1 curve is a Weierstrass curve.+instance Curve 'Weierstrass c BrainpoolP256R1 Fq Fr => WCurve c BrainpoolP256R1 Fq Fr where   a_ = const _a-  {-# INLINE a_ #-}+  {-# INLINABLE a_ #-}   b_ = const _b-  {-# INLINE b_ #-}-  g_ = _g-  {-# INLINE g_ #-}+  {-# INLINABLE b_ #-}+  h_ = const _h+  {-# INLINABLE h_ #-}+  q_ = const _q+  {-# INLINABLE q_ #-}+  r_ = const _r+  {-# INLINABLE r_ #-}+  x_ = const _x+  {-# INLINABLE x_ #-}+  y_ = const _y+  {-# INLINABLE y_ #-} --- | Point of Brainpool-P256R1 curve-type P = WPoint BrainpoolP256R1 Fp+-- | Affine BrainpoolP256R1 curve point.+type PA = WAPoint BrainpoolP256R1 Fq Fr +-- | Affine BrainpoolP256R1 curve is a Weierstrass affine curve.+instance WACurve BrainpoolP256R1 Fq Fr where+  gA_ = gA+  {-# INLINABLE gA_ #-}++-- | Jacobian BrainpoolP256R1 point.+type PJ = WJPoint BrainpoolP256R1 Fq Fr++-- | Jacobian BrainpoolP256R1 curve is a Weierstrass Jacobian curve.+instance WJCurve BrainpoolP256R1 Fq Fr where+  gJ_ = gJ+  {-# INLINABLE gJ_ #-}++-- | Projective BrainpoolP256R1 point.+type PP = WPPoint BrainpoolP256R1 Fq Fr++-- | Projective BrainpoolP256R1 curve is a Weierstrass projective curve.+instance WPCurve BrainpoolP256R1 Fq Fr where+  gP_ = gP+  {-# INLINABLE gP_ #-}+ ------------------------------------------------------------------------------- -- Parameters ------------------------------------------------------------------------------- --- | Coefficient @A@ of Brainpool-P256R1 curve-_a :: Fp+-- | Coefficient @A@ of BrainpoolP256R1 curve.+_a :: Fq _a = 0x7d5a0975fc2c3057eef67530417affe7fb8055c126dc5c6ce94a4b44f330b5d9-{-# INLINE _a #-}+{-# INLINABLE _a #-} --- | Coefficient @B@ of Brainpool-P256R1 curve-_b :: Fp+-- | Coefficient @B@ of BrainpoolP256R1 curve.+_b :: Fq _b = 0x26dc5c6ce94a4b44f330b5d9bbd77cbf958416295cf7e1ce6bccdc18ff8c07b6-{-# INLINE _b #-}---- | Generator of Brainpool-P256R1 curve-_g :: P-_g = A-     0x8bd2aeb9cb7e57cb2c4b482ffc81b7afb9de27e1e3bd23c23a4453bd9ace3262-     0x547ef835c3dac4fd97f8461a14611dc9c27745132ded8e545c1d54c72f046997-{-# INLINE _g #-}+{-# INLINABLE _b #-} --- | Cofactor of Brainpool-P256R1 curve+-- | Cofactor of BrainpoolP256R1 curve. _h :: Integer-_h = 1-{-# INLINE _h #-}+_h = 0x1+{-# INLINABLE _h #-} --- | Order of Brainpool-P256R1 curve-_n :: Integer-_n = 0xa9fb57dba1eea9bc3e660a909d838d718c397aa3b561a6f7901e0e82974856a7-{-# INLINE _n #-}+-- | Characteristic of BrainpoolP256R1 curve.+_q :: Integer+_q = 0xa9fb57dba1eea9bc3e660a909d838d726e3bf623d52620282013481d1f6e5377+{-# INLINABLE _q #-} --- | Characteristic of Brainpool-P256R1 curve-_p :: Integer-_p = 0xa9fb57dba1eea9bc3e660a909d838d726e3bf623d52620282013481d1f6e5377-{-# INLINE _p #-}+-- | Order of BrainpoolP256R1 curve.+_r :: Integer+_r = 0xa9fb57dba1eea9bc3e660a909d838d718c397aa3b561a6f7901e0e82974856a7+{-# INLINABLE _r #-}++-- | Coordinate @X@ of BrainpoolP256R1 curve.+_x :: Fq+_x = 0x8bd2aeb9cb7e57cb2c4b482ffc81b7afb9de27e1e3bd23c23a4453bd9ace3262+{-# INLINABLE _x #-}++-- | Coordinate @Y@ of BrainpoolP256R1 curve.+_y :: Fq+_y = 0x547ef835c3dac4fd97f8461a14611dc9c27745132ded8e545c1d54c72f046997+{-# INLINABLE _y #-}++-- | Generator of affine BrainpoolP256R1 curve.+gA :: PA+gA = A _x _y+{-# INLINABLE gA #-}++-- | Generator of Jacobian BrainpoolP256R1 curve.+gJ :: PJ+gJ = J _x _y 1+{-# INLINABLE gJ #-}++-- | Generator of projective BrainpoolP256R1 curve.+gP :: PP+gP = P _x _y 1+{-# INLINABLE gP #-}

src/Curve/Weierstrass/BrainpoolP256T1.hs view

@@ -1,74 +1,118 @@ module Curve.Weierstrass.BrainpoolP256T1-  ( Fp-  , P-  , _a-  , _b-  , _g-  , _h-  , _n-  , _p+  ( module Curve.Weierstrass+  , module Curve.Weierstrass.BrainpoolP256T1   ) where  import Protolude -import PrimeField (PrimeField)+import PrimeField -import Curve.Weierstrass (Point(..), WCurve(..), WPoint)+import Curve.Weierstrass  ------------------------------------------------------------------------------- -- Types ------------------------------------------------------------------------------- --- | Brainpool-P256T1 curve+-- | BrainpoolP256T1 curve. data BrainpoolP256T1 --- | Field of Brainpool-P256T1 curve-type Fp = PrimeField 0xa9fb57dba1eea9bc3e660a909d838d726e3bf623d52620282013481d1f6e5377+-- | Field of points of BrainpoolP256T1 curve.+type Fq = PrimeField 0xa9fb57dba1eea9bc3e660a909d838d726e3bf623d52620282013481d1f6e5377 --- | Brainpool-P256T1 curve is a Weierstrass curve-instance WCurve BrainpoolP256T1 Fp where+-- | Field of coefficients of BrainpoolP256T1 curve.+type Fr = PrimeField 0xa9fb57dba1eea9bc3e660a909d838d718c397aa3b561a6f7901e0e82974856a7++-- | BrainpoolP256T1 curve is a Weierstrass curve.+instance Curve 'Weierstrass c BrainpoolP256T1 Fq Fr => WCurve c BrainpoolP256T1 Fq Fr where   a_ = const _a-  {-# INLINE a_ #-}+  {-# INLINABLE a_ #-}   b_ = const _b-  {-# INLINE b_ #-}-  g_ = _g-  {-# INLINE g_ #-}+  {-# INLINABLE b_ #-}+  h_ = const _h+  {-# INLINABLE h_ #-}+  q_ = const _q+  {-# INLINABLE q_ #-}+  r_ = const _r+  {-# INLINABLE r_ #-}+  x_ = const _x+  {-# INLINABLE x_ #-}+  y_ = const _y+  {-# INLINABLE y_ #-} --- | Point of Brainpool-P256T1 curve-type P = WPoint BrainpoolP256T1 Fp+-- | Affine BrainpoolP256T1 curve point.+type PA = WAPoint BrainpoolP256T1 Fq Fr +-- | Affine BrainpoolP256T1 curve is a Weierstrass affine curve.+instance WACurve BrainpoolP256T1 Fq Fr where+  gA_ = gA+  {-# INLINABLE gA_ #-}++-- | Jacobian BrainpoolP256T1 point.+type PJ = WJPoint BrainpoolP256T1 Fq Fr++-- | Jacobian BrainpoolP256T1 curve is a Weierstrass Jacobian curve.+instance WJCurve BrainpoolP256T1 Fq Fr where+  gJ_ = gJ+  {-# INLINABLE gJ_ #-}++-- | Projective BrainpoolP256T1 point.+type PP = WPPoint BrainpoolP256T1 Fq Fr++-- | Projective BrainpoolP256T1 curve is a Weierstrass projective curve.+instance WPCurve BrainpoolP256T1 Fq Fr where+  gP_ = gP+  {-# INLINABLE gP_ #-}+ ------------------------------------------------------------------------------- -- Parameters ------------------------------------------------------------------------------- --- | Coefficient @A@ of Brainpool-P256T1 curve-_a :: Fp+-- | Coefficient @A@ of BrainpoolP256T1 curve.+_a :: Fq _a = 0xa9fb57dba1eea9bc3e660a909d838d726e3bf623d52620282013481d1f6e5374-{-# INLINE _a #-}+{-# INLINABLE _a #-} --- | Coefficient @B@ of Brainpool-P256T1 curve-_b :: Fp+-- | Coefficient @B@ of BrainpoolP256T1 curve.+_b :: Fq _b = 0x662c61c430d84ea4fe66a7733d0b76b7bf93ebc4af2f49256ae58101fee92b04-{-# INLINE _b #-}---- | Generator of Brainpool-P256T1 curve-_g :: P-_g = A-     0xa3e8eb3cc1cfe7b7732213b23a656149afa142c47aafbc2b79a191562e1305f4-     0x2d996c823439c56d7f7b22e14644417e69bcb6de39d027001dabe8f35b25c9be-{-# INLINE _g #-}+{-# INLINABLE _b #-} --- | Cofactor of Brainpool-P256T1 curve+-- | Cofactor of BrainpoolP256T1 curve. _h :: Integer-_h = 1-{-# INLINE _h #-}+_h = 0x1+{-# INLINABLE _h #-} --- | Order of Brainpool-P256T1 curve-_n :: Integer-_n = 0xa9fb57dba1eea9bc3e660a909d838d718c397aa3b561a6f7901e0e82974856a7-{-# INLINE _n #-}+-- | Characteristic of BrainpoolP256T1 curve.+_q :: Integer+_q = 0xa9fb57dba1eea9bc3e660a909d838d726e3bf623d52620282013481d1f6e5377+{-# INLINABLE _q #-} --- | Characteristic of Brainpool-P256T1 curve-_p :: Integer-_p = 0xa9fb57dba1eea9bc3e660a909d838d726e3bf623d52620282013481d1f6e5377-{-# INLINE _p #-}+-- | Order of BrainpoolP256T1 curve.+_r :: Integer+_r = 0xa9fb57dba1eea9bc3e660a909d838d718c397aa3b561a6f7901e0e82974856a7+{-# INLINABLE _r #-}++-- | Coordinate @X@ of BrainpoolP256T1 curve.+_x :: Fq+_x = 0xa3e8eb3cc1cfe7b7732213b23a656149afa142c47aafbc2b79a191562e1305f4+{-# INLINABLE _x #-}++-- | Coordinate @Y@ of BrainpoolP256T1 curve.+_y :: Fq+_y = 0x2d996c823439c56d7f7b22e14644417e69bcb6de39d027001dabe8f35b25c9be+{-# INLINABLE _y #-}++-- | Generator of affine BrainpoolP256T1 curve.+gA :: PA+gA = A _x _y+{-# INLINABLE gA #-}++-- | Generator of Jacobian BrainpoolP256T1 curve.+gJ :: PJ+gJ = J _x _y 1+{-# INLINABLE gJ #-}++-- | Generator of projective BrainpoolP256T1 curve.+gP :: PP+gP = P _x _y 1+{-# INLINABLE gP #-}

src/Curve/Weierstrass/BrainpoolP320R1.hs view

@@ -1,74 +1,118 @@ module Curve.Weierstrass.BrainpoolP320R1-  ( Fp-  , P-  , _a-  , _b-  , _g-  , _h-  , _n-  , _p+  ( module Curve.Weierstrass+  , module Curve.Weierstrass.BrainpoolP320R1   ) where  import Protolude -import PrimeField (PrimeField)+import PrimeField -import Curve.Weierstrass (Point(..), WCurve(..), WPoint)+import Curve.Weierstrass  ------------------------------------------------------------------------------- -- Types ------------------------------------------------------------------------------- --- | Brainpool-P320R1 curve+-- | BrainpoolP320R1 curve. data BrainpoolP320R1 --- | Field of Brainpool-P320R1 curve-type Fp = PrimeField 0xd35e472036bc4fb7e13c785ed201e065f98fcfa6f6f40def4f92b9ec7893ec28fcd412b1f1b32e27+-- | Field of points of BrainpoolP320R1 curve.+type Fq = PrimeField 0xd35e472036bc4fb7e13c785ed201e065f98fcfa6f6f40def4f92b9ec7893ec28fcd412b1f1b32e27 --- | Brainpool-P320R1 curve is a Weierstrass curve-instance WCurve BrainpoolP320R1 Fp where+-- | Field of coefficients of BrainpoolP320R1 curve.+type Fr = PrimeField 0xd35e472036bc4fb7e13c785ed201e065f98fcfa5b68f12a32d482ec7ee8658e98691555b44c59311++-- | BrainpoolP320R1 curve is a Weierstrass curve.+instance Curve 'Weierstrass c BrainpoolP320R1 Fq Fr => WCurve c BrainpoolP320R1 Fq Fr where   a_ = const _a-  {-# INLINE a_ #-}+  {-# INLINABLE a_ #-}   b_ = const _b-  {-# INLINE b_ #-}-  g_ = _g-  {-# INLINE g_ #-}+  {-# INLINABLE b_ #-}+  h_ = const _h+  {-# INLINABLE h_ #-}+  q_ = const _q+  {-# INLINABLE q_ #-}+  r_ = const _r+  {-# INLINABLE r_ #-}+  x_ = const _x+  {-# INLINABLE x_ #-}+  y_ = const _y+  {-# INLINABLE y_ #-} --- | Point of Brainpool-P320R1 curve-type P = WPoint BrainpoolP320R1 Fp+-- | Affine BrainpoolP320R1 curve point.+type PA = WAPoint BrainpoolP320R1 Fq Fr +-- | Affine BrainpoolP320R1 curve is a Weierstrass affine curve.+instance WACurve BrainpoolP320R1 Fq Fr where+  gA_ = gA+  {-# INLINABLE gA_ #-}++-- | Jacobian BrainpoolP320R1 point.+type PJ = WJPoint BrainpoolP320R1 Fq Fr++-- | Jacobian BrainpoolP320R1 curve is a Weierstrass Jacobian curve.+instance WJCurve BrainpoolP320R1 Fq Fr where+  gJ_ = gJ+  {-# INLINABLE gJ_ #-}++-- | Projective BrainpoolP320R1 point.+type PP = WPPoint BrainpoolP320R1 Fq Fr++-- | Projective BrainpoolP320R1 curve is a Weierstrass projective curve.+instance WPCurve BrainpoolP320R1 Fq Fr where+  gP_ = gP+  {-# INLINABLE gP_ #-}+ ------------------------------------------------------------------------------- -- Parameters ------------------------------------------------------------------------------- --- | Coefficient @A@ of Brainpool-P320R1 curve-_a :: Fp+-- | Coefficient @A@ of BrainpoolP320R1 curve.+_a :: Fq _a = 0x3ee30b568fbab0f883ccebd46d3f3bb8a2a73513f5eb79da66190eb085ffa9f492f375a97d860eb4-{-# INLINE _a #-}+{-# INLINABLE _a #-} --- | Coefficient @B@ of Brainpool-P320R1 curve-_b :: Fp+-- | Coefficient @B@ of BrainpoolP320R1 curve.+_b :: Fq _b = 0x520883949dfdbc42d3ad198640688a6fe13f41349554b49acc31dccd884539816f5eb4ac8fb1f1a6-{-# INLINE _b #-}---- | Generator of Brainpool-P320R1 curve-_g :: P-_g = A-     0x43bd7e9afb53d8b85289bcc48ee5bfe6f20137d10a087eb6e7871e2a10a599c710af8d0d39e20611-     0x14fdd05545ec1cc8ab4093247f77275e0743ffed117182eaa9c77877aaac6ac7d35245d1692e8ee1-{-# INLINE _g #-}+{-# INLINABLE _b #-} --- | Cofactor of Brainpool-P320R1 curve+-- | Cofactor of BrainpoolP320R1 curve. _h :: Integer-_h = 1-{-# INLINE _h #-}+_h = 0x1+{-# INLINABLE _h #-} --- | Order of Brainpool-P320R1 curve-_n :: Integer-_n = 0xd35e472036bc4fb7e13c785ed201e065f98fcfa5b68f12a32d482ec7ee8658e98691555b44c59311-{-# INLINE _n #-}+-- | Characteristic of BrainpoolP320R1 curve.+_q :: Integer+_q = 0xd35e472036bc4fb7e13c785ed201e065f98fcfa6f6f40def4f92b9ec7893ec28fcd412b1f1b32e27+{-# INLINABLE _q #-} --- | Characteristic of Brainpool-P320R1 curve-_p :: Integer-_p = 0xd35e472036bc4fb7e13c785ed201e065f98fcfa6f6f40def4f92b9ec7893ec28fcd412b1f1b32e27-{-# INLINE _p #-}+-- | Order of BrainpoolP320R1 curve.+_r :: Integer+_r = 0xd35e472036bc4fb7e13c785ed201e065f98fcfa5b68f12a32d482ec7ee8658e98691555b44c59311+{-# INLINABLE _r #-}++-- | Coordinate @X@ of BrainpoolP320R1 curve.+_x :: Fq+_x = 0x43bd7e9afb53d8b85289bcc48ee5bfe6f20137d10a087eb6e7871e2a10a599c710af8d0d39e20611+{-# INLINABLE _x #-}++-- | Coordinate @Y@ of BrainpoolP320R1 curve.+_y :: Fq+_y = 0x14fdd05545ec1cc8ab4093247f77275e0743ffed117182eaa9c77877aaac6ac7d35245d1692e8ee1+{-# INLINABLE _y #-}++-- | Generator of affine BrainpoolP320R1 curve.+gA :: PA+gA = A _x _y+{-# INLINABLE gA #-}++-- | Generator of Jacobian BrainpoolP320R1 curve.+gJ :: PJ+gJ = J _x _y 1+{-# INLINABLE gJ #-}++-- | Generator of projective BrainpoolP320R1 curve.+gP :: PP+gP = P _x _y 1+{-# INLINABLE gP #-}

src/Curve/Weierstrass/BrainpoolP320T1.hs view

@@ -1,74 +1,118 @@ module Curve.Weierstrass.BrainpoolP320T1-  ( Fp-  , P-  , _a-  , _b-  , _g-  , _h-  , _n-  , _p+  ( module Curve.Weierstrass+  , module Curve.Weierstrass.BrainpoolP320T1   ) where  import Protolude -import PrimeField (PrimeField)+import PrimeField -import Curve.Weierstrass (Point(..), WCurve(..), WPoint)+import Curve.Weierstrass  ------------------------------------------------------------------------------- -- Types ------------------------------------------------------------------------------- --- | Brainpool-P320T1 curve+-- | BrainpoolP320T1 curve. data BrainpoolP320T1 --- | Field of Brainpool-P320T1 curve-type Fp = PrimeField 0xd35e472036bc4fb7e13c785ed201e065f98fcfa6f6f40def4f92b9ec7893ec28fcd412b1f1b32e27+-- | Field of points of BrainpoolP320T1 curve.+type Fq = PrimeField 0xd35e472036bc4fb7e13c785ed201e065f98fcfa6f6f40def4f92b9ec7893ec28fcd412b1f1b32e27 --- | Brainpool-P320T1 curve is a Weierstrass curve-instance WCurve BrainpoolP320T1 Fp where+-- | Field of coefficients of BrainpoolP320T1 curve.+type Fr = PrimeField 0xd35e472036bc4fb7e13c785ed201e065f98fcfa5b68f12a32d482ec7ee8658e98691555b44c59311++-- | BrainpoolP320T1 curve is a Weierstrass curve.+instance Curve 'Weierstrass c BrainpoolP320T1 Fq Fr => WCurve c BrainpoolP320T1 Fq Fr where   a_ = const _a-  {-# INLINE a_ #-}+  {-# INLINABLE a_ #-}   b_ = const _b-  {-# INLINE b_ #-}-  g_ = _g-  {-# INLINE g_ #-}+  {-# INLINABLE b_ #-}+  h_ = const _h+  {-# INLINABLE h_ #-}+  q_ = const _q+  {-# INLINABLE q_ #-}+  r_ = const _r+  {-# INLINABLE r_ #-}+  x_ = const _x+  {-# INLINABLE x_ #-}+  y_ = const _y+  {-# INLINABLE y_ #-} --- | Point of Brainpool-P320T1 curve-type P = WPoint BrainpoolP320T1 Fp+-- | Affine BrainpoolP320T1 curve point.+type PA = WAPoint BrainpoolP320T1 Fq Fr +-- | Affine BrainpoolP320T1 curve is a Weierstrass affine curve.+instance WACurve BrainpoolP320T1 Fq Fr where+  gA_ = gA+  {-# INLINABLE gA_ #-}++-- | Jacobian BrainpoolP320T1 point.+type PJ = WJPoint BrainpoolP320T1 Fq Fr++-- | Jacobian BrainpoolP320T1 curve is a Weierstrass Jacobian curve.+instance WJCurve BrainpoolP320T1 Fq Fr where+  gJ_ = gJ+  {-# INLINABLE gJ_ #-}++-- | Projective BrainpoolP320T1 point.+type PP = WPPoint BrainpoolP320T1 Fq Fr++-- | Projective BrainpoolP320T1 curve is a Weierstrass projective curve.+instance WPCurve BrainpoolP320T1 Fq Fr where+  gP_ = gP+  {-# INLINABLE gP_ #-}+ ------------------------------------------------------------------------------- -- Parameters ------------------------------------------------------------------------------- --- | Coefficient @A@ of Brainpool-P320T1 curve-_a :: Fp+-- | Coefficient @A@ of BrainpoolP320T1 curve.+_a :: Fq _a = 0xd35e472036bc4fb7e13c785ed201e065f98fcfa6f6f40def4f92b9ec7893ec28fcd412b1f1b32e24-{-# INLINE _a #-}+{-# INLINABLE _a #-} --- | Coefficient @B@ of Brainpool-P320T1 curve-_b :: Fp+-- | Coefficient @B@ of BrainpoolP320T1 curve.+_b :: Fq _b = 0xa7f561e038eb1ed560b3d147db782013064c19f27ed27c6780aaf77fb8a547ceb5b4fef422340353-{-# INLINE _b #-}---- | Generator of Brainpool-P320T1 curve-_g :: P-_g = A-     0x925be9fb01afc6fb4d3e7d4990010f813408ab106c4f09cb7ee07868cc136fff3357f624a21bed52-     0x63ba3a7a27483ebf6671dbef7abb30ebee084e58a0b077ad42a5a0989d1ee71b1b9bc0455fb0d2c3-{-# INLINE _g #-}+{-# INLINABLE _b #-} --- | Cofactor of Brainpool-P320T1 curve+-- | Cofactor of BrainpoolP320T1 curve. _h :: Integer-_h = 1-{-# INLINE _h #-}+_h = 0x1+{-# INLINABLE _h #-} --- | Order of Brainpool-P320T1 curve-_n :: Integer-_n = 0xd35e472036bc4fb7e13c785ed201e065f98fcfa5b68f12a32d482ec7ee8658e98691555b44c59311-{-# INLINE _n #-}+-- | Characteristic of BrainpoolP320T1 curve.+_q :: Integer+_q = 0xd35e472036bc4fb7e13c785ed201e065f98fcfa6f6f40def4f92b9ec7893ec28fcd412b1f1b32e27+{-# INLINABLE _q #-} --- | Characteristic of Brainpool-P320T1 curve-_p :: Integer-_p = 0xd35e472036bc4fb7e13c785ed201e065f98fcfa6f6f40def4f92b9ec7893ec28fcd412b1f1b32e27-{-# INLINE _p #-}+-- | Order of BrainpoolP320T1 curve.+_r :: Integer+_r = 0xd35e472036bc4fb7e13c785ed201e065f98fcfa5b68f12a32d482ec7ee8658e98691555b44c59311+{-# INLINABLE _r #-}++-- | Coordinate @X@ of BrainpoolP320T1 curve.+_x :: Fq+_x = 0x925be9fb01afc6fb4d3e7d4990010f813408ab106c4f09cb7ee07868cc136fff3357f624a21bed52+{-# INLINABLE _x #-}++-- | Coordinate @Y@ of BrainpoolP320T1 curve.+_y :: Fq+_y = 0x63ba3a7a27483ebf6671dbef7abb30ebee084e58a0b077ad42a5a0989d1ee71b1b9bc0455fb0d2c3+{-# INLINABLE _y #-}++-- | Generator of affine BrainpoolP320T1 curve.+gA :: PA+gA = A _x _y+{-# INLINABLE gA #-}++-- | Generator of Jacobian BrainpoolP320T1 curve.+gJ :: PJ+gJ = J _x _y 1+{-# INLINABLE gJ #-}++-- | Generator of projective BrainpoolP320T1 curve.+gP :: PP+gP = P _x _y 1+{-# INLINABLE gP #-}

src/Curve/Weierstrass/BrainpoolP384R1.hs view

@@ -1,74 +1,118 @@ module Curve.Weierstrass.BrainpoolP384R1-  ( Fp-  , P-  , _a-  , _b-  , _g-  , _h-  , _n-  , _p+  ( module Curve.Weierstrass+  , module Curve.Weierstrass.BrainpoolP384R1   ) where  import Protolude -import PrimeField (PrimeField)+import PrimeField -import Curve.Weierstrass (Point(..), WCurve(..), WPoint)+import Curve.Weierstrass  ------------------------------------------------------------------------------- -- Types ------------------------------------------------------------------------------- --- | Brainpool-P384R1 curve+-- | BrainpoolP384R1 curve. data BrainpoolP384R1 --- | Field of Brainpool-P384R1 curve-type Fp = PrimeField 0x8cb91e82a3386d280f5d6f7e50e641df152f7109ed5456b412b1da197fb71123acd3a729901d1a71874700133107ec53+-- | Field of points of BrainpoolP384R1 curve.+type Fq = PrimeField 0x8cb91e82a3386d280f5d6f7e50e641df152f7109ed5456b412b1da197fb71123acd3a729901d1a71874700133107ec53 --- | Brainpool-P384R1 curve is a Weierstrass curve-instance WCurve BrainpoolP384R1 Fp where+-- | Field of coefficients of BrainpoolP384R1 curve.+type Fr = PrimeField 0x8cb91e82a3386d280f5d6f7e50e641df152f7109ed5456b31f166e6cac0425a7cf3ab6af6b7fc3103b883202e9046565++-- | BrainpoolP384R1 curve is a Weierstrass curve.+instance Curve 'Weierstrass c BrainpoolP384R1 Fq Fr => WCurve c BrainpoolP384R1 Fq Fr where   a_ = const _a-  {-# INLINE a_ #-}+  {-# INLINABLE a_ #-}   b_ = const _b-  {-# INLINE b_ #-}-  g_ = _g-  {-# INLINE g_ #-}+  {-# INLINABLE b_ #-}+  h_ = const _h+  {-# INLINABLE h_ #-}+  q_ = const _q+  {-# INLINABLE q_ #-}+  r_ = const _r+  {-# INLINABLE r_ #-}+  x_ = const _x+  {-# INLINABLE x_ #-}+  y_ = const _y+  {-# INLINABLE y_ #-} --- | Point of Brainpool-P384R1 curve-type P = WPoint BrainpoolP384R1 Fp+-- | Affine BrainpoolP384R1 curve point.+type PA = WAPoint BrainpoolP384R1 Fq Fr +-- | Affine BrainpoolP384R1 curve is a Weierstrass affine curve.+instance WACurve BrainpoolP384R1 Fq Fr where+  gA_ = gA+  {-# INLINABLE gA_ #-}++-- | Jacobian BrainpoolP384R1 point.+type PJ = WJPoint BrainpoolP384R1 Fq Fr++-- | Jacobian BrainpoolP384R1 curve is a Weierstrass Jacobian curve.+instance WJCurve BrainpoolP384R1 Fq Fr where+  gJ_ = gJ+  {-# INLINABLE gJ_ #-}++-- | Projective BrainpoolP384R1 point.+type PP = WPPoint BrainpoolP384R1 Fq Fr++-- | Projective BrainpoolP384R1 curve is a Weierstrass projective curve.+instance WPCurve BrainpoolP384R1 Fq Fr where+  gP_ = gP+  {-# INLINABLE gP_ #-}+ ------------------------------------------------------------------------------- -- Parameters ------------------------------------------------------------------------------- --- | Coefficient @A@ of Brainpool-P384R1 curve-_a :: Fp+-- | Coefficient @A@ of BrainpoolP384R1 curve.+_a :: Fq _a = 0x7bc382c63d8c150c3c72080ace05afa0c2bea28e4fb22787139165efba91f90f8aa5814a503ad4eb04a8c7dd22ce2826-{-# INLINE _a #-}+{-# INLINABLE _a #-} --- | Coefficient @B@ of Brainpool-P384R1 curve-_b :: Fp+-- | Coefficient @B@ of BrainpoolP384R1 curve.+_b :: Fq _b = 0x4a8c7dd22ce28268b39b55416f0447c2fb77de107dcd2a62e880ea53eeb62d57cb4390295dbc9943ab78696fa504c11-{-# INLINE _b #-}---- | Generator of Brainpool-P384R1 curve-_g :: P-_g = A-     0x1d1c64f068cf45ffa2a63a81b7c13f6b8847a3e77ef14fe3db7fcafe0cbd10e8e826e03436d646aaef87b2e247d4af1e-     0x8abe1d7520f9c2a45cb1eb8e95cfd55262b70b29feec5864e19c054ff99129280e4646217791811142820341263c5315-{-# INLINE _g #-}+{-# INLINABLE _b #-} --- | Cofactor of Brainpool-P384R1 curve+-- | Cofactor of BrainpoolP384R1 curve. _h :: Integer-_h = 1-{-# INLINE _h #-}+_h = 0x1+{-# INLINABLE _h #-} --- | Order of Brainpool-P384R1 curve-_n :: Integer-_n = 0x8cb91e82a3386d280f5d6f7e50e641df152f7109ed5456b31f166e6cac0425a7cf3ab6af6b7fc3103b883202e9046565-{-# INLINE _n #-}+-- | Characteristic of BrainpoolP384R1 curve.+_q :: Integer+_q = 0x8cb91e82a3386d280f5d6f7e50e641df152f7109ed5456b412b1da197fb71123acd3a729901d1a71874700133107ec53+{-# INLINABLE _q #-} --- | Characteristic of Brainpool-P384R1 curve-_p :: Integer-_p = 0x8cb91e82a3386d280f5d6f7e50e641df152f7109ed5456b412b1da197fb71123acd3a729901d1a71874700133107ec53-{-# INLINE _p #-}+-- | Order of BrainpoolP384R1 curve.+_r :: Integer+_r = 0x8cb91e82a3386d280f5d6f7e50e641df152f7109ed5456b31f166e6cac0425a7cf3ab6af6b7fc3103b883202e9046565+{-# INLINABLE _r #-}++-- | Coordinate @X@ of BrainpoolP384R1 curve.+_x :: Fq+_x = 0x1d1c64f068cf45ffa2a63a81b7c13f6b8847a3e77ef14fe3db7fcafe0cbd10e8e826e03436d646aaef87b2e247d4af1e+{-# INLINABLE _x #-}++-- | Coordinate @Y@ of BrainpoolP384R1 curve.+_y :: Fq+_y = 0x8abe1d7520f9c2a45cb1eb8e95cfd55262b70b29feec5864e19c054ff99129280e4646217791811142820341263c5315+{-# INLINABLE _y #-}++-- | Generator of affine BrainpoolP384R1 curve.+gA :: PA+gA = A _x _y+{-# INLINABLE gA #-}++-- | Generator of Jacobian BrainpoolP384R1 curve.+gJ :: PJ+gJ = J _x _y 1+{-# INLINABLE gJ #-}++-- | Generator of projective BrainpoolP384R1 curve.+gP :: PP+gP = P _x _y 1+{-# INLINABLE gP #-}

src/Curve/Weierstrass/BrainpoolP384T1.hs view

@@ -1,74 +1,118 @@ module Curve.Weierstrass.BrainpoolP384T1-  ( Fp-  , P-  , _a-  , _b-  , _g-  , _h-  , _n-  , _p+  ( module Curve.Weierstrass+  , module Curve.Weierstrass.BrainpoolP384T1   ) where  import Protolude -import PrimeField (PrimeField)+import PrimeField -import Curve.Weierstrass (Point(..), WCurve(..), WPoint)+import Curve.Weierstrass  ---------------------------------------------------------------------------------- Type+-- Types ------------------------------------------------------------------------------- --- | Brainpool-P384T1 curve+-- | BrainpoolP384T1 curve. data BrainpoolP384T1 --- | Field of Brainpool-P384T1 curve-type Fp = PrimeField 0x8cb91e82a3386d280f5d6f7e50e641df152f7109ed5456b412b1da197fb71123acd3a729901d1a71874700133107ec53+-- | Field of points of BrainpoolP384T1 curve.+type Fq = PrimeField 0x8cb91e82a3386d280f5d6f7e50e641df152f7109ed5456b412b1da197fb71123acd3a729901d1a71874700133107ec53 --- | Brainpool-P384T1 curve is a Weierstrass curve-instance WCurve BrainpoolP384T1 Fp where+-- | Field of coefficients of BrainpoolP384T1 curve.+type Fr = PrimeField 0x8cb91e82a3386d280f5d6f7e50e641df152f7109ed5456b31f166e6cac0425a7cf3ab6af6b7fc3103b883202e9046565++-- | BrainpoolP384T1 curve is a Weierstrass curve.+instance Curve 'Weierstrass c BrainpoolP384T1 Fq Fr => WCurve c BrainpoolP384T1 Fq Fr where   a_ = const _a-  {-# INLINE a_ #-}+  {-# INLINABLE a_ #-}   b_ = const _b-  {-# INLINE b_ #-}-  g_ = _g-  {-# INLINE g_ #-}+  {-# INLINABLE b_ #-}+  h_ = const _h+  {-# INLINABLE h_ #-}+  q_ = const _q+  {-# INLINABLE q_ #-}+  r_ = const _r+  {-# INLINABLE r_ #-}+  x_ = const _x+  {-# INLINABLE x_ #-}+  y_ = const _y+  {-# INLINABLE y_ #-} --- | Point of Brainpool-P384T1 curve-type P = WPoint BrainpoolP384T1 Fp+-- | Affine BrainpoolP384T1 curve point.+type PA = WAPoint BrainpoolP384T1 Fq Fr +-- | Affine BrainpoolP384T1 curve is a Weierstrass affine curve.+instance WACurve BrainpoolP384T1 Fq Fr where+  gA_ = gA+  {-# INLINABLE gA_ #-}++-- | Jacobian BrainpoolP384T1 point.+type PJ = WJPoint BrainpoolP384T1 Fq Fr++-- | Jacobian BrainpoolP384T1 curve is a Weierstrass Jacobian curve.+instance WJCurve BrainpoolP384T1 Fq Fr where+  gJ_ = gJ+  {-# INLINABLE gJ_ #-}++-- | Projective BrainpoolP384T1 point.+type PP = WPPoint BrainpoolP384T1 Fq Fr++-- | Projective BrainpoolP384T1 curve is a Weierstrass projective curve.+instance WPCurve BrainpoolP384T1 Fq Fr where+  gP_ = gP+  {-# INLINABLE gP_ #-}+ ------------------------------------------------------------------------------- -- Parameters ------------------------------------------------------------------------------- --- | Coefficient @A@ of Brainpool-P384T1 curve-_a :: Fp+-- | Coefficient @A@ of BrainpoolP384T1 curve.+_a :: Fq _a = 0x8cb91e82a3386d280f5d6f7e50e641df152f7109ed5456b412b1da197fb71123acd3a729901d1a71874700133107ec50-{-# INLINE _a #-}+{-# INLINABLE _a #-} --- | Coefficient @B@ of Brainpool-P384T1 curve-_b :: Fp+-- | Coefficient @B@ of BrainpoolP384T1 curve.+_b :: Fq _b = 0x7f519eada7bda81bd826dba647910f8c4b9346ed8ccdc64e4b1abd11756dce1d2074aa263b88805ced70355a33b471ee-{-# INLINE _b #-}---- | Generator of Brainpool-P384T1 curve-_g :: P-_g = A-     0x18de98b02db9a306f2afcd7235f72a819b80ab12ebd653172476fecd462aabffc4ff191b946a5f54d8d0aa2f418808cc-     0x25ab056962d30651a114afd2755ad336747f93475b7a1fca3b88f2b6a208ccfe469408584dc2b2912675bf5b9e582928-{-# INLINE _g #-}+{-# INLINABLE _b #-} --- | Cofactor of Brainpool-P384T1 curve+-- | Cofactor of BrainpoolP384T1 curve. _h :: Integer-_h = 1-{-# INLINE _h #-}+_h = 0x1+{-# INLINABLE _h #-} --- | Order of Brainpool-P384T1 curve-_n :: Integer-_n = 0x8cb91e82a3386d280f5d6f7e50e641df152f7109ed5456b31f166e6cac0425a7cf3ab6af6b7fc3103b883202e9046565-{-# INLINE _n #-}+-- | Characteristic of BrainpoolP384T1 curve.+_q :: Integer+_q = 0x8cb91e82a3386d280f5d6f7e50e641df152f7109ed5456b412b1da197fb71123acd3a729901d1a71874700133107ec53+{-# INLINABLE _q #-} --- | Characteristic of Brainpool-P384T1 curve-_p :: Integer-_p = 0x8cb91e82a3386d280f5d6f7e50e641df152f7109ed5456b412b1da197fb71123acd3a729901d1a71874700133107ec53-{-# INLINE _p #-}+-- | Order of BrainpoolP384T1 curve.+_r :: Integer+_r = 0x8cb91e82a3386d280f5d6f7e50e641df152f7109ed5456b31f166e6cac0425a7cf3ab6af6b7fc3103b883202e9046565+{-# INLINABLE _r #-}++-- | Coordinate @X@ of BrainpoolP384T1 curve.+_x :: Fq+_x = 0x18de98b02db9a306f2afcd7235f72a819b80ab12ebd653172476fecd462aabffc4ff191b946a5f54d8d0aa2f418808cc+{-# INLINABLE _x #-}++-- | Coordinate @Y@ of BrainpoolP384T1 curve.+_y :: Fq+_y = 0x25ab056962d30651a114afd2755ad336747f93475b7a1fca3b88f2b6a208ccfe469408584dc2b2912675bf5b9e582928+{-# INLINABLE _y #-}++-- | Generator of affine BrainpoolP384T1 curve.+gA :: PA+gA = A _x _y+{-# INLINABLE gA #-}++-- | Generator of Jacobian BrainpoolP384T1 curve.+gJ :: PJ+gJ = J _x _y 1+{-# INLINABLE gJ #-}++-- | Generator of projective BrainpoolP384T1 curve.+gP :: PP+gP = P _x _y 1+{-# INLINABLE gP #-}

src/Curve/Weierstrass/BrainpoolP512R1.hs view

@@ -1,74 +1,118 @@ module Curve.Weierstrass.BrainpoolP512R1-  ( Fp-  , P-  , _a-  , _b-  , _g-  , _h-  , _n-  , _p+  ( module Curve.Weierstrass+  , module Curve.Weierstrass.BrainpoolP512R1   ) where  import Protolude -import PrimeField (PrimeField)+import PrimeField -import Curve.Weierstrass (Point(..), WCurve(..), WPoint)+import Curve.Weierstrass  ------------------------------------------------------------------------------- -- Types ------------------------------------------------------------------------------- --- | Brainpool-P512R1 curve+-- | BrainpoolP512R1 curve. data BrainpoolP512R1 --- | Field of Brainpool-P512R1 curve-type Fp = PrimeField 0xaadd9db8dbe9c48b3fd4e6ae33c9fc07cb308db3b3c9d20ed6639cca703308717d4d9b009bc66842aecda12ae6a380e62881ff2f2d82c68528aa6056583a48f3+-- | Field of points of BrainpoolP512R1 curve.+type Fq = PrimeField 0xaadd9db8dbe9c48b3fd4e6ae33c9fc07cb308db3b3c9d20ed6639cca703308717d4d9b009bc66842aecda12ae6a380e62881ff2f2d82c68528aa6056583a48f3 --- | Brainpool-P512R1 curve is a Weierstrass curve-instance WCurve BrainpoolP512R1 Fp where+-- | Field of coefficients of BrainpoolP512R1 curve.+type Fr = PrimeField 0xaadd9db8dbe9c48b3fd4e6ae33c9fc07cb308db3b3c9d20ed6639cca70330870553e5c414ca92619418661197fac10471db1d381085ddaddb58796829ca90069++-- | BrainpoolP512R1 curve is a Weierstrass curve.+instance Curve 'Weierstrass c BrainpoolP512R1 Fq Fr => WCurve c BrainpoolP512R1 Fq Fr where   a_ = const _a-  {-# INLINE a_ #-}+  {-# INLINABLE a_ #-}   b_ = const _b-  {-# INLINE b_ #-}-  g_ = _g-  {-# INLINE g_ #-}+  {-# INLINABLE b_ #-}+  h_ = const _h+  {-# INLINABLE h_ #-}+  q_ = const _q+  {-# INLINABLE q_ #-}+  r_ = const _r+  {-# INLINABLE r_ #-}+  x_ = const _x+  {-# INLINABLE x_ #-}+  y_ = const _y+  {-# INLINABLE y_ #-} --- | Point of Brainpool-P512R1 curve-type P = WPoint BrainpoolP512R1 Fp+-- | Affine BrainpoolP512R1 curve point.+type PA = WAPoint BrainpoolP512R1 Fq Fr +-- | Affine BrainpoolP512R1 curve is a Weierstrass affine curve.+instance WACurve BrainpoolP512R1 Fq Fr where+  gA_ = gA+  {-# INLINABLE gA_ #-}++-- | Jacobian BrainpoolP512R1 point.+type PJ = WJPoint BrainpoolP512R1 Fq Fr++-- | Jacobian BrainpoolP512R1 curve is a Weierstrass Jacobian curve.+instance WJCurve BrainpoolP512R1 Fq Fr where+  gJ_ = gJ+  {-# INLINABLE gJ_ #-}++-- | Projective BrainpoolP512R1 point.+type PP = WPPoint BrainpoolP512R1 Fq Fr++-- | Projective BrainpoolP512R1 curve is a Weierstrass projective curve.+instance WPCurve BrainpoolP512R1 Fq Fr where+  gP_ = gP+  {-# INLINABLE gP_ #-}+ ------------------------------------------------------------------------------- -- Parameters ------------------------------------------------------------------------------- --- | Coefficient @A@ of Brainpool-P512R1 curve-_a :: Fp+-- | Coefficient @A@ of BrainpoolP512R1 curve.+_a :: Fq _a = 0x7830a3318b603b89e2327145ac234cc594cbdd8d3df91610a83441caea9863bc2ded5d5aa8253aa10a2ef1c98b9ac8b57f1117a72bf2c7b9e7c1ac4d77fc94ca-{-# INLINE _a #-}+{-# INLINABLE _a #-} --- | Coefficient @B@ of Brainpool-P512R1 curve-_b :: Fp+-- | Coefficient @B@ of BrainpoolP512R1 curve.+_b :: Fq _b = 0x3df91610a83441caea9863bc2ded5d5aa8253aa10a2ef1c98b9ac8b57f1117a72bf2c7b9e7c1ac4d77fc94cadc083e67984050b75ebae5dd2809bd638016f723-{-# INLINE _b #-}---- | Generator of Brainpool-P512R1 curve-_g :: P-_g = A-     0x81aee4bdd82ed9645a21322e9c4c6a9385ed9f70b5d916c1b43b62eef4d0098eff3b1f78e2d0d48d50d1687b93b97d5f7c6d5047406a5e688b352209bcb9f822-     0x7dde385d566332ecc0eabfa9cf7822fdf209f70024a57b1aa000c55b881f8111b2dcde494a5f485e5bca4bd88a2763aed1ca2b2fa8f0540678cd1e0f3ad80892-{-# INLINE _g #-}+{-# INLINABLE _b #-} --- | Cofactor of Brainpool-P512R1 curve+-- | Cofactor of BrainpoolP512R1 curve. _h :: Integer-_h = 1-{-# INLINE _h #-}+_h = 0x1+{-# INLINABLE _h #-} --- | Order of Brainpool-P512R1 curve-_n :: Integer-_n = 0xaadd9db8dbe9c48b3fd4e6ae33c9fc07cb308db3b3c9d20ed6639cca70330870553e5c414ca92619418661197fac10471db1d381085ddaddb58796829ca90069-{-# INLINE _n #-}+-- | Characteristic of BrainpoolP512R1 curve.+_q :: Integer+_q = 0xaadd9db8dbe9c48b3fd4e6ae33c9fc07cb308db3b3c9d20ed6639cca703308717d4d9b009bc66842aecda12ae6a380e62881ff2f2d82c68528aa6056583a48f3+{-# INLINABLE _q #-} --- | Characteristic of Brainpool-P512R1 curve-_p :: Integer-_p = 0xaadd9db8dbe9c48b3fd4e6ae33c9fc07cb308db3b3c9d20ed6639cca703308717d4d9b009bc66842aecda12ae6a380e62881ff2f2d82c68528aa6056583a48f3-{-# INLINE _p #-}+-- | Order of BrainpoolP512R1 curve.+_r :: Integer+_r = 0xaadd9db8dbe9c48b3fd4e6ae33c9fc07cb308db3b3c9d20ed6639cca70330870553e5c414ca92619418661197fac10471db1d381085ddaddb58796829ca90069+{-# INLINABLE _r #-}++-- | Coordinate @X@ of BrainpoolP512R1 curve.+_x :: Fq+_x = 0x81aee4bdd82ed9645a21322e9c4c6a9385ed9f70b5d916c1b43b62eef4d0098eff3b1f78e2d0d48d50d1687b93b97d5f7c6d5047406a5e688b352209bcb9f822+{-# INLINABLE _x #-}++-- | Coordinate @Y@ of BrainpoolP512R1 curve.+_y :: Fq+_y = 0x7dde385d566332ecc0eabfa9cf7822fdf209f70024a57b1aa000c55b881f8111b2dcde494a5f485e5bca4bd88a2763aed1ca2b2fa8f0540678cd1e0f3ad80892+{-# INLINABLE _y #-}++-- | Generator of affine BrainpoolP512R1 curve.+gA :: PA+gA = A _x _y+{-# INLINABLE gA #-}++-- | Generator of Jacobian BrainpoolP512R1 curve.+gJ :: PJ+gJ = J _x _y 1+{-# INLINABLE gJ #-}++-- | Generator of projective BrainpoolP512R1 curve.+gP :: PP+gP = P _x _y 1+{-# INLINABLE gP #-}

src/Curve/Weierstrass/BrainpoolP512T1.hs view

@@ -1,74 +1,118 @@ module Curve.Weierstrass.BrainpoolP512T1-  ( Fp-  , P-  , _a-  , _b-  , _g-  , _h-  , _n-  , _p+  ( module Curve.Weierstrass+  , module Curve.Weierstrass.BrainpoolP512T1   ) where  import Protolude -import PrimeField (PrimeField)+import PrimeField -import Curve.Weierstrass (Point(..), WCurve(..), WPoint)+import Curve.Weierstrass  ------------------------------------------------------------------------------- -- Types ------------------------------------------------------------------------------- --- | Brainpool-P512T1 curve+-- | BrainpoolP512T1 curve. data BrainpoolP512T1 --- | Field of Brainpool-P512T1 curve-type Fp = PrimeField 0xaadd9db8dbe9c48b3fd4e6ae33c9fc07cb308db3b3c9d20ed6639cca703308717d4d9b009bc66842aecda12ae6a380e62881ff2f2d82c68528aa6056583a48f3+-- | Field of points of BrainpoolP512T1 curve.+type Fq = PrimeField 0xaadd9db8dbe9c48b3fd4e6ae33c9fc07cb308db3b3c9d20ed6639cca703308717d4d9b009bc66842aecda12ae6a380e62881ff2f2d82c68528aa6056583a48f3 --- | Brainpool-P512T1 curve is a Weierstrass curve-instance WCurve BrainpoolP512T1 Fp where+-- | Field of coefficients of BrainpoolP512T1 curve.+type Fr = PrimeField 0xaadd9db8dbe9c48b3fd4e6ae33c9fc07cb308db3b3c9d20ed6639cca70330870553e5c414ca92619418661197fac10471db1d381085ddaddb58796829ca90069++-- | BrainpoolP512T1 curve is a Weierstrass curve.+instance Curve 'Weierstrass c BrainpoolP512T1 Fq Fr => WCurve c BrainpoolP512T1 Fq Fr where   a_ = const _a-  {-# INLINE a_ #-}+  {-# INLINABLE a_ #-}   b_ = const _b-  {-# INLINE b_ #-}-  g_ = _g-  {-# INLINE g_ #-}+  {-# INLINABLE b_ #-}+  h_ = const _h+  {-# INLINABLE h_ #-}+  q_ = const _q+  {-# INLINABLE q_ #-}+  r_ = const _r+  {-# INLINABLE r_ #-}+  x_ = const _x+  {-# INLINABLE x_ #-}+  y_ = const _y+  {-# INLINABLE y_ #-} --- | Point of Brainpool-P512T1 curve-type P = WPoint BrainpoolP512T1 Fp+-- | Affine BrainpoolP512T1 curve point.+type PA = WAPoint BrainpoolP512T1 Fq Fr +-- | Affine BrainpoolP512T1 curve is a Weierstrass affine curve.+instance WACurve BrainpoolP512T1 Fq Fr where+  gA_ = gA+  {-# INLINABLE gA_ #-}++-- | Jacobian BrainpoolP512T1 point.+type PJ = WJPoint BrainpoolP512T1 Fq Fr++-- | Jacobian BrainpoolP512T1 curve is a Weierstrass Jacobian curve.+instance WJCurve BrainpoolP512T1 Fq Fr where+  gJ_ = gJ+  {-# INLINABLE gJ_ #-}++-- | Projective BrainpoolP512T1 point.+type PP = WPPoint BrainpoolP512T1 Fq Fr++-- | Projective BrainpoolP512T1 curve is a Weierstrass projective curve.+instance WPCurve BrainpoolP512T1 Fq Fr where+  gP_ = gP+  {-# INLINABLE gP_ #-}+ ------------------------------------------------------------------------------- -- Parameters ------------------------------------------------------------------------------- --- | Coefficient @A@ of Brainpool-P512T1 curve-_a :: Fp+-- | Coefficient @A@ of BrainpoolP512T1 curve.+_a :: Fq _a = 0xaadd9db8dbe9c48b3fd4e6ae33c9fc07cb308db3b3c9d20ed6639cca703308717d4d9b009bc66842aecda12ae6a380e62881ff2f2d82c68528aa6056583a48f0-{-# INLINE _a #-}+{-# INLINABLE _a #-} --- | Coefficient @B@ of Brainpool-P512T1 curve-_b :: Fp+-- | Coefficient @B@ of BrainpoolP512T1 curve.+_b :: Fq _b = 0x7cbbbcf9441cfab76e1890e46884eae321f70c0bcb4981527897504bec3e36a62bcdfa2304976540f6450085f2dae145c22553b465763689180ea2571867423e-{-# INLINE _b #-}---- | Generator of Brainpool-P512T1 curve-_g :: P-_g = A-     0x640ece5c12788717b9c1ba06cbc2a6feba85842458c56dde9db1758d39c0313d82ba51735cdb3ea499aa77a7d6943a64f7a3f25fe26f06b51baa2696fa9035da-     0x5b534bd595f5af0fa2c892376c84ace1bb4e3019b71634c01131159cae03cee9d9932184beef216bd71df2dadf86a627306ecff96dbb8bace198b61e00f8b332-{-# INLINE _g #-}+{-# INLINABLE _b #-} --- | Cofactor of Brainpool-P512T1 curve+-- | Cofactor of BrainpoolP512T1 curve. _h :: Integer-_h = 1-{-# INLINE _h #-}+_h = 0x1+{-# INLINABLE _h #-} --- | Order of Brainpool-P512T1 curve-_n :: Integer-_n = 0xaadd9db8dbe9c48b3fd4e6ae33c9fc07cb308db3b3c9d20ed6639cca70330870553e5c414ca92619418661197fac10471db1d381085ddaddb58796829ca90069-{-# INLINE _n #-}+-- | Characteristic of BrainpoolP512T1 curve.+_q :: Integer+_q = 0xaadd9db8dbe9c48b3fd4e6ae33c9fc07cb308db3b3c9d20ed6639cca703308717d4d9b009bc66842aecda12ae6a380e62881ff2f2d82c68528aa6056583a48f3+{-# INLINABLE _q #-} --- | Characteristic of Brainpool-P512T1 curve-_p :: Integer-_p = 0xaadd9db8dbe9c48b3fd4e6ae33c9fc07cb308db3b3c9d20ed6639cca703308717d4d9b009bc66842aecda12ae6a380e62881ff2f2d82c68528aa6056583a48f3-{-# INLINE _p #-}+-- | Order of BrainpoolP512T1 curve.+_r :: Integer+_r = 0xaadd9db8dbe9c48b3fd4e6ae33c9fc07cb308db3b3c9d20ed6639cca70330870553e5c414ca92619418661197fac10471db1d381085ddaddb58796829ca90069+{-# INLINABLE _r #-}++-- | Coordinate @X@ of BrainpoolP512T1 curve.+_x :: Fq+_x = 0x640ece5c12788717b9c1ba06cbc2a6feba85842458c56dde9db1758d39c0313d82ba51735cdb3ea499aa77a7d6943a64f7a3f25fe26f06b51baa2696fa9035da+{-# INLINABLE _x #-}++-- | Coordinate @Y@ of BrainpoolP512T1 curve.+_y :: Fq+_y = 0x5b534bd595f5af0fa2c892376c84ace1bb4e3019b71634c01131159cae03cee9d9932184beef216bd71df2dadf86a627306ecff96dbb8bace198b61e00f8b332+{-# INLINABLE _y #-}++-- | Generator of affine BrainpoolP512T1 curve.+gA :: PA+gA = A _x _y+{-# INLINABLE gA #-}++-- | Generator of Jacobian BrainpoolP512T1 curve.+gJ :: PJ+gJ = J _x _y 1+{-# INLINABLE gJ #-}++-- | Generator of projective BrainpoolP512T1 curve.+gP :: PP+gP = P _x _y 1+{-# INLINABLE gP #-}

src/Curve/Weierstrass/SECP112R1.hs view

@@ -1,74 +1,118 @@ module Curve.Weierstrass.SECP112R1-  ( Fp-  , P-  , _a-  , _b-  , _g-  , _h-  , _n-  , _p+  ( module Curve.Weierstrass+  , module Curve.Weierstrass.SECP112R1   ) where  import Protolude -import PrimeField (PrimeField)+import PrimeField -import Curve.Weierstrass (Point(..), WCurve(..), WPoint)+import Curve.Weierstrass  ------------------------------------------------------------------------------- -- Types ------------------------------------------------------------------------------- --- | SECP112R1 curve+-- | SECP112R1 curve. data SECP112R1 --- | Field of SECP112R1 curve-type Fp = PrimeField 0xdb7c2abf62e35e668076bead208b+-- | Field of points of SECP112R1 curve.+type Fq = PrimeField 0xdb7c2abf62e35e668076bead208b --- | SECP112R1 curve is a Weierstrass curve-instance WCurve SECP112R1 Fp where+-- | Field of coefficients of SECP112R1 curve.+type Fr = PrimeField 0xdb7c2abf62e35e7628dfac6561c5++-- | SECP112R1 curve is a Weierstrass curve.+instance Curve 'Weierstrass c SECP112R1 Fq Fr => WCurve c SECP112R1 Fq Fr where   a_ = const _a-  {-# INLINE a_ #-}+  {-# INLINABLE a_ #-}   b_ = const _b-  {-# INLINE b_ #-}-  g_ = _g-  {-# INLINE g_ #-}+  {-# INLINABLE b_ #-}+  h_ = const _h+  {-# INLINABLE h_ #-}+  q_ = const _q+  {-# INLINABLE q_ #-}+  r_ = const _r+  {-# INLINABLE r_ #-}+  x_ = const _x+  {-# INLINABLE x_ #-}+  y_ = const _y+  {-# INLINABLE y_ #-} --- | Point of SECP112R1 curve-type P = WPoint SECP112R1 Fp+-- | Affine SECP112R1 curve point.+type PA = WAPoint SECP112R1 Fq Fr +-- | Affine SECP112R1 curve is a Weierstrass affine curve.+instance WACurve SECP112R1 Fq Fr where+  gA_ = gA+  {-# INLINABLE gA_ #-}++-- | Jacobian SECP112R1 point.+type PJ = WJPoint SECP112R1 Fq Fr++-- | Jacobian SECP112R1 curve is a Weierstrass Jacobian curve.+instance WJCurve SECP112R1 Fq Fr where+  gJ_ = gJ+  {-# INLINABLE gJ_ #-}++-- | Projective SECP112R1 point.+type PP = WPPoint SECP112R1 Fq Fr++-- | Projective SECP112R1 curve is a Weierstrass projective curve.+instance WPCurve SECP112R1 Fq Fr where+  gP_ = gP+  {-# INLINABLE gP_ #-}+ ------------------------------------------------------------------------------- -- Parameters ------------------------------------------------------------------------------- --- | Coefficient @A@ of SECP112R1 curve-_a :: Fp+-- | Coefficient @A@ of SECP112R1 curve.+_a :: Fq _a = 0xdb7c2abf62e35e668076bead2088-{-# INLINE _a #-}+{-# INLINABLE _a #-} --- | Coefficient @B@ of SECP112R1 curve-_b :: Fp+-- | Coefficient @B@ of SECP112R1 curve.+_b :: Fq _b = 0x659ef8ba043916eede8911702b22-{-# INLINE _b #-}---- | Generator of SECP112R1 curve-_g :: P-_g = A-     0x9487239995a5ee76b55f9c2f098-     0xa89ce5af8724c0a23e0e0ff77500-{-# INLINE _g #-}+{-# INLINABLE _b #-} --- | Cofactor of SECP112R1 curve+-- | Cofactor of SECP112R1 curve. _h :: Integer-_h = 1-{-# INLINE _h #-}+_h = 0x1+{-# INLINABLE _h #-} --- | Order of SECP112R1 curve-_n :: Integer-_n = 0xdb7c2abf62e35e7628dfac6561c5-{-# INLINE _n #-}+-- | Characteristic of SECP112R1 curve.+_q :: Integer+_q = 0xdb7c2abf62e35e668076bead208b+{-# INLINABLE _q #-} --- | Characteristic of SECP112R1 curve-_p :: Integer-_p = 0xdb7c2abf62e35e668076bead208b-{-# INLINE _p #-}+-- | Order of SECP112R1 curve.+_r :: Integer+_r = 0xdb7c2abf62e35e7628dfac6561c5+{-# INLINABLE _r #-}++-- | Coordinate @X@ of SECP112R1 curve.+_x :: Fq+_x = 0x9487239995a5ee76b55f9c2f098+{-# INLINABLE _x #-}++-- | Coordinate @Y@ of SECP112R1 curve.+_y :: Fq+_y = 0xa89ce5af8724c0a23e0e0ff77500+{-# INLINABLE _y #-}++-- | Generator of affine SECP112R1 curve.+gA :: PA+gA = A _x _y+{-# INLINABLE gA #-}++-- | Generator of Jacobian SECP112R1 curve.+gJ :: PJ+gJ = J _x _y 1+{-# INLINABLE gJ #-}++-- | Generator of projective SECP112R1 curve.+gP :: PP+gP = P _x _y 1+{-# INLINABLE gP #-}

src/Curve/Weierstrass/SECP112R2.hs view

@@ -1,74 +1,118 @@ module Curve.Weierstrass.SECP112R2-  ( Fp-  , P-  , _a-  , _b-  , _g-  , _h-  , _n-  , _p+  ( module Curve.Weierstrass+  , module Curve.Weierstrass.SECP112R2   ) where  import Protolude -import PrimeField (PrimeField)+import PrimeField -import Curve.Weierstrass (Point(..), WCurve(..), WPoint)+import Curve.Weierstrass  ------------------------------------------------------------------------------- -- Types ------------------------------------------------------------------------------- --- | SECP112R2 curve+-- | SECP112R2 curve. data SECP112R2 --- | Field of SECP112R2 curve-type Fp = PrimeField 0xdb7c2abf62e35e668076bead208b+-- | Field of points of SECP112R2 curve.+type Fq = PrimeField 0xdb7c2abf62e35e668076bead208b --- | SECP112R2 curve is a Weierstrass curve-instance WCurve SECP112R2 Fp where+-- | Field of coefficients of SECP112R2 curve.+type Fr = PrimeField 0x36df0aafd8b8d7597ca10520d04b++-- | SECP112R2 curve is a Weierstrass curve.+instance Curve 'Weierstrass c SECP112R2 Fq Fr => WCurve c SECP112R2 Fq Fr where   a_ = const _a-  {-# INLINE a_ #-}+  {-# INLINABLE a_ #-}   b_ = const _b-  {-# INLINE b_ #-}-  g_ = _g-  {-# INLINE g_ #-}+  {-# INLINABLE b_ #-}+  h_ = const _h+  {-# INLINABLE h_ #-}+  q_ = const _q+  {-# INLINABLE q_ #-}+  r_ = const _r+  {-# INLINABLE r_ #-}+  x_ = const _x+  {-# INLINABLE x_ #-}+  y_ = const _y+  {-# INLINABLE y_ #-} --- | Point of SECP112R2 curve-type P = WPoint SECP112R2 Fp+-- | Affine SECP112R2 curve point.+type PA = WAPoint SECP112R2 Fq Fr +-- | Affine SECP112R2 curve is a Weierstrass affine curve.+instance WACurve SECP112R2 Fq Fr where+  gA_ = gA+  {-# INLINABLE gA_ #-}++-- | Jacobian SECP112R2 point.+type PJ = WJPoint SECP112R2 Fq Fr++-- | Jacobian SECP112R2 curve is a Weierstrass Jacobian curve.+instance WJCurve SECP112R2 Fq Fr where+  gJ_ = gJ+  {-# INLINABLE gJ_ #-}++-- | Projective SECP112R2 point.+type PP = WPPoint SECP112R2 Fq Fr++-- | Projective SECP112R2 curve is a Weierstrass projective curve.+instance WPCurve SECP112R2 Fq Fr where+  gP_ = gP+  {-# INLINABLE gP_ #-}+ ------------------------------------------------------------------------------- -- Parameters ------------------------------------------------------------------------------- --- | Coefficient @A@ of SECP112R2 curve-_a :: Fp+-- | Coefficient @A@ of SECP112R2 curve.+_a :: Fq _a = 0x6127c24c05f38a0aaaf65c0ef02c-{-# INLINE _a #-}+{-# INLINABLE _a #-} --- | Coefficient @B@ of SECP112R2 curve-_b :: Fp+-- | Coefficient @B@ of SECP112R2 curve.+_b :: Fq _b = 0x51def1815db5ed74fcc34c85d709-{-# INLINE _b #-}---- | Generator of SECP112R2 curve-_g :: P-_g = A-     0x4ba30ab5e892b4e1649dd0928643-     0xadcd46f5882e3747def36e956e97-{-# INLINE _g #-}+{-# INLINABLE _b #-} --- | Cofactor of SECP112R2 curve+-- | Cofactor of SECP112R2 curve. _h :: Integer-_h = 4-{-# INLINE _h #-}+_h = 0x4+{-# INLINABLE _h #-} --- | Order of SECP112R2 curve-_n :: Integer-_n = 0x36df0aafd8b8d7597ca10520d04b-{-# INLINE _n #-}+-- | Characteristic of SECP112R2 curve.+_q :: Integer+_q = 0xdb7c2abf62e35e668076bead208b+{-# INLINABLE _q #-} --- | Characteristic of SECP112R2 curve-_p :: Integer-_p = 0xdb7c2abf62e35e668076bead208b-{-# INLINE _p #-}+-- | Order of SECP112R2 curve.+_r :: Integer+_r = 0x36df0aafd8b8d7597ca10520d04b+{-# INLINABLE _r #-}++-- | Coordinate @X@ of SECP112R2 curve.+_x :: Fq+_x = 0x4ba30ab5e892b4e1649dd0928643+{-# INLINABLE _x #-}++-- | Coordinate @Y@ of SECP112R2 curve.+_y :: Fq+_y = 0xadcd46f5882e3747def36e956e97+{-# INLINABLE _y #-}++-- | Generator of affine SECP112R2 curve.+gA :: PA+gA = A _x _y+{-# INLINABLE gA #-}++-- | Generator of Jacobian SECP112R2 curve.+gJ :: PJ+gJ = J _x _y 1+{-# INLINABLE gJ #-}++-- | Generator of projective SECP112R2 curve.+gP :: PP+gP = P _x _y 1+{-# INLINABLE gP #-}

src/Curve/Weierstrass/SECP128R1.hs view

@@ -1,74 +1,118 @@ module Curve.Weierstrass.SECP128R1-  ( Fp-  , P-  , _a-  , _b-  , _g-  , _h-  , _n-  , _p+  ( module Curve.Weierstrass+  , module Curve.Weierstrass.SECP128R1   ) where  import Protolude -import PrimeField (PrimeField)+import PrimeField -import Curve.Weierstrass (Point(..), WCurve(..), WPoint)+import Curve.Weierstrass  ------------------------------------------------------------------------------- -- Types ------------------------------------------------------------------------------- --- | SECP128R1 curve+-- | SECP128R1 curve. data SECP128R1 --- | Field of SECP128R1 curve-type Fp = PrimeField 0xfffffffdffffffffffffffffffffffff+-- | Field of points of SECP128R1 curve.+type Fq = PrimeField 0xfffffffdffffffffffffffffffffffff --- | SECP128R1 curve is a Weierstrass curve-instance WCurve SECP128R1 Fp where+-- | Field of coefficients of SECP128R1 curve.+type Fr = PrimeField 0xfffffffe0000000075a30d1b9038a115++-- | SECP128R1 curve is a Weierstrass curve.+instance Curve 'Weierstrass c SECP128R1 Fq Fr => WCurve c SECP128R1 Fq Fr where   a_ = const _a-  {-# INLINE a_ #-}+  {-# INLINABLE a_ #-}   b_ = const _b-  {-# INLINE b_ #-}-  g_ = _g-  {-# INLINE g_ #-}+  {-# INLINABLE b_ #-}+  h_ = const _h+  {-# INLINABLE h_ #-}+  q_ = const _q+  {-# INLINABLE q_ #-}+  r_ = const _r+  {-# INLINABLE r_ #-}+  x_ = const _x+  {-# INLINABLE x_ #-}+  y_ = const _y+  {-# INLINABLE y_ #-} --- | Point of SECP128R1 curve-type P = WPoint SECP128R1 Fp+-- | Affine SECP128R1 curve point.+type PA = WAPoint SECP128R1 Fq Fr +-- | Affine SECP128R1 curve is a Weierstrass affine curve.+instance WACurve SECP128R1 Fq Fr where+  gA_ = gA+  {-# INLINABLE gA_ #-}++-- | Jacobian SECP128R1 point.+type PJ = WJPoint SECP128R1 Fq Fr++-- | Jacobian SECP128R1 curve is a Weierstrass Jacobian curve.+instance WJCurve SECP128R1 Fq Fr where+  gJ_ = gJ+  {-# INLINABLE gJ_ #-}++-- | Projective SECP128R1 point.+type PP = WPPoint SECP128R1 Fq Fr++-- | Projective SECP128R1 curve is a Weierstrass projective curve.+instance WPCurve SECP128R1 Fq Fr where+  gP_ = gP+  {-# INLINABLE gP_ #-}+ ------------------------------------------------------------------------------- -- Parameters ------------------------------------------------------------------------------- --- | Coefficient @A@ of SECP128R1 curve-_a :: Fp+-- | Coefficient @A@ of SECP128R1 curve.+_a :: Fq _a = 0xfffffffdfffffffffffffffffffffffc-{-# INLINE _a #-}+{-# INLINABLE _a #-} --- | Coefficient @B@ of SECP128R1 curve-_b :: Fp+-- | Coefficient @B@ of SECP128R1 curve.+_b :: Fq _b = 0xe87579c11079f43dd824993c2cee5ed3-{-# INLINE _b #-}---- | Generator of SECP128R1 curve-_g :: P-_g = A-     0x161ff7528b899b2d0c28607ca52c5b86-     0xcf5ac8395bafeb13c02da292dded7a83-{-# INLINE _g #-}+{-# INLINABLE _b #-} --- | Cofactor of SECP128R1 curve+-- | Cofactor of SECP128R1 curve. _h :: Integer-_h = 1-{-# INLINE _h #-}+_h = 0x1+{-# INLINABLE _h #-} --- | Order of SECP128R1 curve-_n :: Integer-_n = 0xfffffffe0000000075a30d1b9038a115-{-# INLINE _n #-}+-- | Characteristic of SECP128R1 curve.+_q :: Integer+_q = 0xfffffffdffffffffffffffffffffffff+{-# INLINABLE _q #-} --- | Characteristic of SECP128R1 curve-_p :: Integer-_p = 0xfffffffdffffffffffffffffffffffff-{-# INLINE _p #-}+-- | Order of SECP128R1 curve.+_r :: Integer+_r = 0xfffffffe0000000075a30d1b9038a115+{-# INLINABLE _r #-}++-- | Coordinate @X@ of SECP128R1 curve.+_x :: Fq+_x = 0x161ff7528b899b2d0c28607ca52c5b86+{-# INLINABLE _x #-}++-- | Coordinate @Y@ of SECP128R1 curve.+_y :: Fq+_y = 0xcf5ac8395bafeb13c02da292dded7a83+{-# INLINABLE _y #-}++-- | Generator of affine SECP128R1 curve.+gA :: PA+gA = A _x _y+{-# INLINABLE gA #-}++-- | Generator of Jacobian SECP128R1 curve.+gJ :: PJ+gJ = J _x _y 1+{-# INLINABLE gJ #-}++-- | Generator of projective SECP128R1 curve.+gP :: PP+gP = P _x _y 1+{-# INLINABLE gP #-}

src/Curve/Weierstrass/SECP128R2.hs view

@@ -1,74 +1,118 @@ module Curve.Weierstrass.SECP128R2-  ( Fp-  , P-  , _a-  , _b-  , _g-  , _h-  , _n-  , _p+  ( module Curve.Weierstrass+  , module Curve.Weierstrass.SECP128R2   ) where  import Protolude -import PrimeField (PrimeField)+import PrimeField -import Curve.Weierstrass (Point(..), WCurve(..), WPoint)+import Curve.Weierstrass  ------------------------------------------------------------------------------- -- Types ------------------------------------------------------------------------------- --- | SECP128R2 curve+-- | SECP128R2 curve. data SECP128R2 --- | Field of SECP128R2 curve-type Fp = PrimeField 0xfffffffdffffffffffffffffffffffff+-- | Field of points of SECP128R2 curve.+type Fq = PrimeField 0xfffffffdffffffffffffffffffffffff --- | SECP128R2 curve is a Weierstrass curve-instance WCurve SECP128R2 Fp where+-- | Field of coefficients of SECP128R2 curve.+type Fr = PrimeField 0x3fffffff7fffffffbe0024720613b5a3++-- | SECP128R2 curve is a Weierstrass curve.+instance Curve 'Weierstrass c SECP128R2 Fq Fr => WCurve c SECP128R2 Fq Fr where   a_ = const _a-  {-# INLINE a_ #-}+  {-# INLINABLE a_ #-}   b_ = const _b-  {-# INLINE b_ #-}-  g_ = _g-  {-# INLINE g_ #-}+  {-# INLINABLE b_ #-}+  h_ = const _h+  {-# INLINABLE h_ #-}+  q_ = const _q+  {-# INLINABLE q_ #-}+  r_ = const _r+  {-# INLINABLE r_ #-}+  x_ = const _x+  {-# INLINABLE x_ #-}+  y_ = const _y+  {-# INLINABLE y_ #-} --- | Point of SECP128R2 curve-type P = WPoint SECP128R2 Fp+-- | Affine SECP128R2 curve point.+type PA = WAPoint SECP128R2 Fq Fr +-- | Affine SECP128R2 curve is a Weierstrass affine curve.+instance WACurve SECP128R2 Fq Fr where+  gA_ = gA+  {-# INLINABLE gA_ #-}++-- | Jacobian SECP128R2 point.+type PJ = WJPoint SECP128R2 Fq Fr++-- | Jacobian SECP128R2 curve is a Weierstrass Jacobian curve.+instance WJCurve SECP128R2 Fq Fr where+  gJ_ = gJ+  {-# INLINABLE gJ_ #-}++-- | Projective SECP128R2 point.+type PP = WPPoint SECP128R2 Fq Fr++-- | Projective SECP128R2 curve is a Weierstrass projective curve.+instance WPCurve SECP128R2 Fq Fr where+  gP_ = gP+  {-# INLINABLE gP_ #-}+ ------------------------------------------------------------------------------- -- Parameters ------------------------------------------------------------------------------- --- | Coefficient @A@ of SECP128R2 curve-_a :: Fp+-- | Coefficient @A@ of SECP128R2 curve.+_a :: Fq _a = 0xd6031998d1b3bbfebf59cc9bbff9aee1-{-# INLINE _a #-}+{-# INLINABLE _a #-} --- | Coefficient @B@ of SECP128R2 curve-_b :: Fp+-- | Coefficient @B@ of SECP128R2 curve.+_b :: Fq _b = 0x5eeefca380d02919dc2c6558bb6d8a5d-{-# INLINE _b #-}---- | Generator of SECP128R2 curve-_g :: P-_g = A-     0x7b6aa5d85e572983e6fb32a7cdebc140-     0x27b6916a894d3aee7106fe805fc34b44-{-# INLINE _g #-}+{-# INLINABLE _b #-} --- | Cofactor of SECP128R2 curve+-- | Cofactor of SECP128R2 curve. _h :: Integer-_h = 4-{-# INLINE _h #-}+_h = 0x4+{-# INLINABLE _h #-} --- | Order of SECP128R2 curve-_n :: Integer-_n = 0x3fffffff7fffffffbe0024720613b5a3-{-# INLINE _n #-}+-- | Characteristic of SECP128R2 curve.+_q :: Integer+_q = 0xfffffffdffffffffffffffffffffffff+{-# INLINABLE _q #-} --- | Characteristic of SECP128R2 curve-_p :: Integer-_p = 0xfffffffdffffffffffffffffffffffff-{-# INLINE _p #-}+-- | Order of SECP128R2 curve.+_r :: Integer+_r = 0x3fffffff7fffffffbe0024720613b5a3+{-# INLINABLE _r #-}++-- | Coordinate @X@ of SECP128R2 curve.+_x :: Fq+_x = 0x7b6aa5d85e572983e6fb32a7cdebc140+{-# INLINABLE _x #-}++-- | Coordinate @Y@ of SECP128R2 curve.+_y :: Fq+_y = 0x27b6916a894d3aee7106fe805fc34b44+{-# INLINABLE _y #-}++-- | Generator of affine SECP128R2 curve.+gA :: PA+gA = A _x _y+{-# INLINABLE gA #-}++-- | Generator of Jacobian SECP128R2 curve.+gJ :: PJ+gJ = J _x _y 1+{-# INLINABLE gJ #-}++-- | Generator of projective SECP128R2 curve.+gP :: PP+gP = P _x _y 1+{-# INLINABLE gP #-}

src/Curve/Weierstrass/SECP160K1.hs view

@@ -1,74 +1,118 @@ module Curve.Weierstrass.SECP160K1-  ( Fp-  , P-  , _a-  , _b-  , _g-  , _h-  , _n-  , _p+  ( module Curve.Weierstrass+  , module Curve.Weierstrass.SECP160K1   ) where  import Protolude -import PrimeField (PrimeField)+import PrimeField -import Curve.Weierstrass (Point(..), WCurve(..), WPoint)+import Curve.Weierstrass  ------------------------------------------------------------------------------- -- Types ------------------------------------------------------------------------------- --- | SECP160K1 curve+-- | SECP160K1 curve. data SECP160K1 --- | Field of SECP160K1 curve-type Fp = PrimeField 0xfffffffffffffffffffffffffffffffeffffac73+-- | Field of points of SECP160K1 curve.+type Fq = PrimeField 0xfffffffffffffffffffffffffffffffeffffac73 --- | SECP160K1 curve is a Weierstrass curve-instance WCurve SECP160K1 Fp where+-- | Field of coefficients of SECP160K1 curve.+type Fr = PrimeField 0x100000000000000000001b8fa16dfab9aca16b6b3++-- | SECP160K1 curve is a Weierstrass curve.+instance Curve 'Weierstrass c SECP160K1 Fq Fr => WCurve c SECP160K1 Fq Fr where   a_ = const _a-  {-# INLINE a_ #-}+  {-# INLINABLE a_ #-}   b_ = const _b-  {-# INLINE b_ #-}-  g_ = _g-  {-# INLINE g_ #-}+  {-# INLINABLE b_ #-}+  h_ = const _h+  {-# INLINABLE h_ #-}+  q_ = const _q+  {-# INLINABLE q_ #-}+  r_ = const _r+  {-# INLINABLE r_ #-}+  x_ = const _x+  {-# INLINABLE x_ #-}+  y_ = const _y+  {-# INLINABLE y_ #-} --- | Point of SECP160K1 curve-type P = WPoint SECP160K1 Fp+-- | Affine SECP160K1 curve point.+type PA = WAPoint SECP160K1 Fq Fr +-- | Affine SECP160K1 curve is a Weierstrass affine curve.+instance WACurve SECP160K1 Fq Fr where+  gA_ = gA+  {-# INLINABLE gA_ #-}++-- | Jacobian SECP160K1 point.+type PJ = WJPoint SECP160K1 Fq Fr++-- | Jacobian SECP160K1 curve is a Weierstrass Jacobian curve.+instance WJCurve SECP160K1 Fq Fr where+  gJ_ = gJ+  {-# INLINABLE gJ_ #-}++-- | Projective SECP160K1 point.+type PP = WPPoint SECP160K1 Fq Fr++-- | Projective SECP160K1 curve is a Weierstrass projective curve.+instance WPCurve SECP160K1 Fq Fr where+  gP_ = gP+  {-# INLINABLE gP_ #-}+ ------------------------------------------------------------------------------- -- Parameters ------------------------------------------------------------------------------- --- | Coefficient @A@ of SECP160K1 curve-_a :: Fp-_a = 0-{-# INLINE _a #-}---- | Coefficient @B@ of SECP160K1 curve-_b :: Fp-_b = 7-{-# INLINE _b #-}+-- | Coefficient @A@ of SECP160K1 curve.+_a :: Fq+_a = 0x0+{-# INLINABLE _a #-} --- | Generator of SECP160K1 curve-_g :: P-_g = A-     0x3b4c382ce37aa192a4019e763036f4f5dd4d7ebb-     0x938cf935318fdced6bc28286531733c3f03c4fee-{-# INLINE _g #-}+-- | Coefficient @B@ of SECP160K1 curve.+_b :: Fq+_b = 0x7+{-# INLINABLE _b #-} --- | Cofactor of SECP160K1 curve+-- | Cofactor of SECP160K1 curve. _h :: Integer-_h = 1-{-# INLINE _h #-}+_h = 0x1+{-# INLINABLE _h #-} --- | Order of SECP160K1 curve-_n :: Integer-_n = 0x100000000000000000001b8fa16dfab9aca16b6b3-{-# INLINE _n #-}+-- | Characteristic of SECP160K1 curve.+_q :: Integer+_q = 0xfffffffffffffffffffffffffffffffeffffac73+{-# INLINABLE _q #-} --- | Characteristic of SECP160K1 curve-_p :: Integer-_p = 0xfffffffffffffffffffffffffffffffeffffac73-{-# INLINE _p #-}+-- | Order of SECP160K1 curve.+_r :: Integer+_r = 0x100000000000000000001b8fa16dfab9aca16b6b3+{-# INLINABLE _r #-}++-- | Coordinate @X@ of SECP160K1 curve.+_x :: Fq+_x = 0x3b4c382ce37aa192a4019e763036f4f5dd4d7ebb+{-# INLINABLE _x #-}++-- | Coordinate @Y@ of SECP160K1 curve.+_y :: Fq+_y = 0x938cf935318fdced6bc28286531733c3f03c4fee+{-# INLINABLE _y #-}++-- | Generator of affine SECP160K1 curve.+gA :: PA+gA = A _x _y+{-# INLINABLE gA #-}++-- | Generator of Jacobian SECP160K1 curve.+gJ :: PJ+gJ = J _x _y 1+{-# INLINABLE gJ #-}++-- | Generator of projective SECP160K1 curve.+gP :: PP+gP = P _x _y 1+{-# INLINABLE gP #-}

src/Curve/Weierstrass/SECP160R1.hs view

@@ -1,74 +1,118 @@ module Curve.Weierstrass.SECP160R1-  ( Fp-  , P-  , _a-  , _b-  , _g-  , _h-  , _n-  , _p+  ( module Curve.Weierstrass+  , module Curve.Weierstrass.SECP160R1   ) where  import Protolude -import PrimeField (PrimeField)+import PrimeField -import Curve.Weierstrass (Point(..), WCurve(..), WPoint)+import Curve.Weierstrass  ------------------------------------------------------------------------------- -- Types ------------------------------------------------------------------------------- --- | SECP160R1 curve+-- | SECP160R1 curve. data SECP160R1 --- | Field of SECP160R1 curve-type Fp = PrimeField 0xffffffffffffffffffffffffffffffff7fffffff+-- | Field of points of SECP160R1 curve.+type Fq = PrimeField 0xffffffffffffffffffffffffffffffff7fffffff --- | SECP160R1 curve is a Weierstrass curve-instance WCurve SECP160R1 Fp where+-- | Field of coefficients of SECP160R1 curve.+type Fr = PrimeField 0x100000000000000000001f4c8f927aed3ca752257++-- | SECP160R1 curve is a Weierstrass curve.+instance Curve 'Weierstrass c SECP160R1 Fq Fr => WCurve c SECP160R1 Fq Fr where   a_ = const _a-  {-# INLINE a_ #-}+  {-# INLINABLE a_ #-}   b_ = const _b-  {-# INLINE b_ #-}-  g_ = _g-  {-# INLINE g_ #-}+  {-# INLINABLE b_ #-}+  h_ = const _h+  {-# INLINABLE h_ #-}+  q_ = const _q+  {-# INLINABLE q_ #-}+  r_ = const _r+  {-# INLINABLE r_ #-}+  x_ = const _x+  {-# INLINABLE x_ #-}+  y_ = const _y+  {-# INLINABLE y_ #-} --- | Point of SECP160R1 curve-type P = WPoint SECP160R1 Fp+-- | Affine SECP160R1 curve point.+type PA = WAPoint SECP160R1 Fq Fr +-- | Affine SECP160R1 curve is a Weierstrass affine curve.+instance WACurve SECP160R1 Fq Fr where+  gA_ = gA+  {-# INLINABLE gA_ #-}++-- | Jacobian SECP160R1 point.+type PJ = WJPoint SECP160R1 Fq Fr++-- | Jacobian SECP160R1 curve is a Weierstrass Jacobian curve.+instance WJCurve SECP160R1 Fq Fr where+  gJ_ = gJ+  {-# INLINABLE gJ_ #-}++-- | Projective SECP160R1 point.+type PP = WPPoint SECP160R1 Fq Fr++-- | Projective SECP160R1 curve is a Weierstrass projective curve.+instance WPCurve SECP160R1 Fq Fr where+  gP_ = gP+  {-# INLINABLE gP_ #-}+ ------------------------------------------------------------------------------- -- Parameters ------------------------------------------------------------------------------- --- | Coefficient @A@ of SECP160R1 curve-_a :: Fp+-- | Coefficient @A@ of SECP160R1 curve.+_a :: Fq _a = 0xffffffffffffffffffffffffffffffff7ffffffc-{-# INLINE _a #-}+{-# INLINABLE _a #-} --- | Coefficient @B@ of SECP160R1 curve-_b :: Fp+-- | Coefficient @B@ of SECP160R1 curve.+_b :: Fq _b = 0x1c97befc54bd7a8b65acf89f81d4d4adc565fa45-{-# INLINE _b #-}---- | Generator of SECP160R1 curve-_g :: P-_g = A-     0x4a96b5688ef573284664698968c38bb913cbfc82-     0x23a628553168947d59dcc912042351377ac5fb32-{-# INLINE _g #-}+{-# INLINABLE _b #-} --- | Cofactor of SECP160R1 curve+-- | Cofactor of SECP160R1 curve. _h :: Integer-_h = 1-{-# INLINE _h #-}+_h = 0x1+{-# INLINABLE _h #-} --- | Order of SECP160R1 curve-_n :: Integer-_n = 0x100000000000000000001f4c8f927aed3ca752257-{-# INLINE _n #-}+-- | Characteristic of SECP160R1 curve.+_q :: Integer+_q = 0xffffffffffffffffffffffffffffffff7fffffff+{-# INLINABLE _q #-} --- | Characteristic of SECP160R1 curve-_p :: Integer-_p = 0xffffffffffffffffffffffffffffffff7fffffff-{-# INLINE _p #-}+-- | Order of SECP160R1 curve.+_r :: Integer+_r = 0x100000000000000000001f4c8f927aed3ca752257+{-# INLINABLE _r #-}++-- | Coordinate @X@ of SECP160R1 curve.+_x :: Fq+_x = 0x4a96b5688ef573284664698968c38bb913cbfc82+{-# INLINABLE _x #-}++-- | Coordinate @Y@ of SECP160R1 curve.+_y :: Fq+_y = 0x23a628553168947d59dcc912042351377ac5fb32+{-# INLINABLE _y #-}++-- | Generator of affine SECP160R1 curve.+gA :: PA+gA = A _x _y+{-# INLINABLE gA #-}++-- | Generator of Jacobian SECP160R1 curve.+gJ :: PJ+gJ = J _x _y 1+{-# INLINABLE gJ #-}++-- | Generator of projective SECP160R1 curve.+gP :: PP+gP = P _x _y 1+{-# INLINABLE gP #-}

src/Curve/Weierstrass/SECP160R2.hs view

@@ -1,74 +1,118 @@ module Curve.Weierstrass.SECP160R2-  ( Fp-  , P-  , _a-  , _b-  , _g-  , _h-  , _n-  , _p+  ( module Curve.Weierstrass+  , module Curve.Weierstrass.SECP160R2   ) where  import Protolude -import PrimeField (PrimeField)+import PrimeField -import Curve.Weierstrass (Point(..), WCurve(..), WPoint)+import Curve.Weierstrass  ------------------------------------------------------------------------------- -- Types ------------------------------------------------------------------------------- --- | SECP160R2 curve+-- | SECP160R2 curve. data SECP160R2 --- | Field of SECP160R2 curve-type Fp = PrimeField 0xfffffffffffffffffffffffffffffffeffffac73+-- | Field of points of SECP160R2 curve.+type Fq = PrimeField 0xfffffffffffffffffffffffffffffffeffffac73 --- | SECP160R2 curve is a Weierstrass curve-instance WCurve SECP160R2 Fp where+-- | Field of coefficients of SECP160R2 curve.+type Fr = PrimeField 0x100000000000000000000351ee786a818f3a1a16b++-- | SECP160R2 curve is a Weierstrass curve.+instance Curve 'Weierstrass c SECP160R2 Fq Fr => WCurve c SECP160R2 Fq Fr where   a_ = const _a-  {-# INLINE a_ #-}+  {-# INLINABLE a_ #-}   b_ = const _b-  {-# INLINE b_ #-}-  g_ = _g-  {-# INLINE g_ #-}+  {-# INLINABLE b_ #-}+  h_ = const _h+  {-# INLINABLE h_ #-}+  q_ = const _q+  {-# INLINABLE q_ #-}+  r_ = const _r+  {-# INLINABLE r_ #-}+  x_ = const _x+  {-# INLINABLE x_ #-}+  y_ = const _y+  {-# INLINABLE y_ #-} --- | Point of SECP160R2 curve-type P = WPoint SECP160R2 Fp+-- | Affine SECP160R2 curve point.+type PA = WAPoint SECP160R2 Fq Fr +-- | Affine SECP160R2 curve is a Weierstrass affine curve.+instance WACurve SECP160R2 Fq Fr where+  gA_ = gA+  {-# INLINABLE gA_ #-}++-- | Jacobian SECP160R2 point.+type PJ = WJPoint SECP160R2 Fq Fr++-- | Jacobian SECP160R2 curve is a Weierstrass Jacobian curve.+instance WJCurve SECP160R2 Fq Fr where+  gJ_ = gJ+  {-# INLINABLE gJ_ #-}++-- | Projective SECP160R2 point.+type PP = WPPoint SECP160R2 Fq Fr++-- | Projective SECP160R2 curve is a Weierstrass projective curve.+instance WPCurve SECP160R2 Fq Fr where+  gP_ = gP+  {-# INLINABLE gP_ #-}+ ------------------------------------------------------------------------------- -- Parameters ------------------------------------------------------------------------------- --- | Coefficient @A@ of SECP160R2 curve-_a :: Fp+-- | Coefficient @A@ of SECP160R2 curve.+_a :: Fq _a = 0xfffffffffffffffffffffffffffffffeffffac70-{-# INLINE _a #-}+{-# INLINABLE _a #-} --- | Coefficient @B@ of SECP160R2 curve-_b :: Fp+-- | Coefficient @B@ of SECP160R2 curve.+_b :: Fq _b = 0xb4e134d3fb59eb8bab57274904664d5af50388ba-{-# INLINE _b #-}---- | Generator of SECP160R2 curve-_g :: P-_g = A-     0x52dcb034293a117e1f4ff11b30f7199d3144ce6d-     0xfeaffef2e331f296e071fa0df9982cfea7d43f2e-{-# INLINE _g #-}+{-# INLINABLE _b #-} --- | Cofactor of SECP160R2 curve+-- | Cofactor of SECP160R2 curve. _h :: Integer-_h = 1-{-# INLINE _h #-}+_h = 0x1+{-# INLINABLE _h #-} --- | Order of SECP160R2 curve-_n :: Integer-_n = 0x100000000000000000000351ee786a818f3a1a16b-{-# INLINE _n #-}+-- | Characteristic of SECP160R2 curve.+_q :: Integer+_q = 0xfffffffffffffffffffffffffffffffeffffac73+{-# INLINABLE _q #-} --- | Characteristic of SECP160R2 curve-_p :: Integer-_p = 0xfffffffffffffffffffffffffffffffeffffac73-{-# INLINE _p #-}+-- | Order of SECP160R2 curve.+_r :: Integer+_r = 0x100000000000000000000351ee786a818f3a1a16b+{-# INLINABLE _r #-}++-- | Coordinate @X@ of SECP160R2 curve.+_x :: Fq+_x = 0x52dcb034293a117e1f4ff11b30f7199d3144ce6d+{-# INLINABLE _x #-}++-- | Coordinate @Y@ of SECP160R2 curve.+_y :: Fq+_y = 0xfeaffef2e331f296e071fa0df9982cfea7d43f2e+{-# INLINABLE _y #-}++-- | Generator of affine SECP160R2 curve.+gA :: PA+gA = A _x _y+{-# INLINABLE gA #-}++-- | Generator of Jacobian SECP160R2 curve.+gJ :: PJ+gJ = J _x _y 1+{-# INLINABLE gJ #-}++-- | Generator of projective SECP160R2 curve.+gP :: PP+gP = P _x _y 1+{-# INLINABLE gP #-}

src/Curve/Weierstrass/SECP192K1.hs view

@@ -1,74 +1,118 @@ module Curve.Weierstrass.SECP192K1-  ( Fp-  , P-  , _a-  , _b-  , _g-  , _h-  , _n-  , _p+  ( module Curve.Weierstrass+  , module Curve.Weierstrass.SECP192K1   ) where  import Protolude -import PrimeField (PrimeField)+import PrimeField -import Curve.Weierstrass (Point(..), WCurve(..), WPoint)+import Curve.Weierstrass  ------------------------------------------------------------------------------- -- Types ------------------------------------------------------------------------------- --- | SECP192K1 curve+-- | SECP192K1 curve. data SECP192K1 --- | Field of SECP192K1 curve-type Fp = PrimeField 0xfffffffffffffffffffffffffffffffffffffffeffffee37+-- | Field of points of SECP192K1 curve.+type Fq = PrimeField 0xfffffffffffffffffffffffffffffffffffffffeffffee37 --- | SECP192K1 curve is a Weierstrass curve-instance WCurve SECP192K1 Fp where+-- | Field of coefficients of SECP192K1 curve.+type Fr = PrimeField 0xfffffffffffffffffffffffe26f2fc170f69466a74defd8d++-- | SECP192K1 curve is a Weierstrass curve.+instance Curve 'Weierstrass c SECP192K1 Fq Fr => WCurve c SECP192K1 Fq Fr where   a_ = const _a-  {-# INLINE a_ #-}+  {-# INLINABLE a_ #-}   b_ = const _b-  {-# INLINE b_ #-}-  g_ = _g-  {-# INLINE g_ #-}+  {-# INLINABLE b_ #-}+  h_ = const _h+  {-# INLINABLE h_ #-}+  q_ = const _q+  {-# INLINABLE q_ #-}+  r_ = const _r+  {-# INLINABLE r_ #-}+  x_ = const _x+  {-# INLINABLE x_ #-}+  y_ = const _y+  {-# INLINABLE y_ #-} --- | Point of SECP192K1 curve-type P = WPoint SECP192K1 Fp+-- | Affine SECP192K1 curve point.+type PA = WAPoint SECP192K1 Fq Fr +-- | Affine SECP192K1 curve is a Weierstrass affine curve.+instance WACurve SECP192K1 Fq Fr where+  gA_ = gA+  {-# INLINABLE gA_ #-}++-- | Jacobian SECP192K1 point.+type PJ = WJPoint SECP192K1 Fq Fr++-- | Jacobian SECP192K1 curve is a Weierstrass Jacobian curve.+instance WJCurve SECP192K1 Fq Fr where+  gJ_ = gJ+  {-# INLINABLE gJ_ #-}++-- | Projective SECP192K1 point.+type PP = WPPoint SECP192K1 Fq Fr++-- | Projective SECP192K1 curve is a Weierstrass projective curve.+instance WPCurve SECP192K1 Fq Fr where+  gP_ = gP+  {-# INLINABLE gP_ #-}+ ------------------------------------------------------------------------------- -- Parameters ------------------------------------------------------------------------------- --- | Coefficient @A@ of SECP192K1 curve-_a :: Fp-_a = 0-{-# INLINE _a #-}---- | Coefficient @B@ of SECP192K1 curve-_b :: Fp-_b = 3-{-# INLINE _b #-}+-- | Coefficient @A@ of SECP192K1 curve.+_a :: Fq+_a = 0x0+{-# INLINABLE _a #-} --- | Generator of SECP192K1 curve-_g :: P-_g = A-     0xdb4ff10ec057e9ae26b07d0280b7f4341da5d1b1eae06c7d-     0x9b2f2f6d9c5628a7844163d015be86344082aa88d95e2f9d-{-# INLINE _g #-}+-- | Coefficient @B@ of SECP192K1 curve.+_b :: Fq+_b = 0x3+{-# INLINABLE _b #-} --- | Cofactor of SECP192K1 curve+-- | Cofactor of SECP192K1 curve. _h :: Integer-_h = 1-{-# INLINE _h #-}+_h = 0x1+{-# INLINABLE _h #-} --- | Order of SECP192K1 curve-_n :: Integer-_n = 0xfffffffffffffffffffffffe26f2fc170f69466a74defd8d-{-# INLINE _n #-}+-- | Characteristic of SECP192K1 curve.+_q :: Integer+_q = 0xfffffffffffffffffffffffffffffffffffffffeffffee37+{-# INLINABLE _q #-} --- | Characteristic of SECP192K1 curve-_p :: Integer-_p = 0xfffffffffffffffffffffffffffffffffffffffeffffee37-{-# INLINE _p #-}+-- | Order of SECP192K1 curve.+_r :: Integer+_r = 0xfffffffffffffffffffffffe26f2fc170f69466a74defd8d+{-# INLINABLE _r #-}++-- | Coordinate @X@ of SECP192K1 curve.+_x :: Fq+_x = 0xdb4ff10ec057e9ae26b07d0280b7f4341da5d1b1eae06c7d+{-# INLINABLE _x #-}++-- | Coordinate @Y@ of SECP192K1 curve.+_y :: Fq+_y = 0x9b2f2f6d9c5628a7844163d015be86344082aa88d95e2f9d+{-# INLINABLE _y #-}++-- | Generator of affine SECP192K1 curve.+gA :: PA+gA = A _x _y+{-# INLINABLE gA #-}++-- | Generator of Jacobian SECP192K1 curve.+gJ :: PJ+gJ = J _x _y 1+{-# INLINABLE gJ #-}++-- | Generator of projective SECP192K1 curve.+gP :: PP+gP = P _x _y 1+{-# INLINABLE gP #-}

src/Curve/Weierstrass/SECP192R1.hs view

@@ -1,74 +1,118 @@ module Curve.Weierstrass.SECP192R1-  ( Fp-  , P-  , _a-  , _b-  , _g-  , _h-  , _n-  , _p+  ( module Curve.Weierstrass+  , module Curve.Weierstrass.SECP192R1   ) where  import Protolude -import PrimeField (PrimeField)+import PrimeField -import Curve.Weierstrass (Point(..), WCurve(..), WPoint)+import Curve.Weierstrass  ------------------------------------------------------------------------------- -- Types ------------------------------------------------------------------------------- --- | SECP192R1 curve+-- | SECP192R1 curve. data SECP192R1 --- | Field of SECP192R1 curve-type Fp = PrimeField 0xfffffffffffffffffffffffffffffffeffffffffffffffff+-- | Field of points of SECP192R1 curve.+type Fq = PrimeField 0xfffffffffffffffffffffffffffffffeffffffffffffffff --- | SECP192R1 curve is a Weierstrass curve-instance WCurve SECP192R1 Fp where+-- | Field of coefficients of SECP192R1 curve.+type Fr = PrimeField 0xffffffffffffffffffffffff99def836146bc9b1b4d22831++-- | SECP192R1 curve is a Weierstrass curve.+instance Curve 'Weierstrass c SECP192R1 Fq Fr => WCurve c SECP192R1 Fq Fr where   a_ = const _a-  {-# INLINE a_ #-}+  {-# INLINABLE a_ #-}   b_ = const _b-  {-# INLINE b_ #-}-  g_ = _g-  {-# INLINE g_ #-}+  {-# INLINABLE b_ #-}+  h_ = const _h+  {-# INLINABLE h_ #-}+  q_ = const _q+  {-# INLINABLE q_ #-}+  r_ = const _r+  {-# INLINABLE r_ #-}+  x_ = const _x+  {-# INLINABLE x_ #-}+  y_ = const _y+  {-# INLINABLE y_ #-} --- | Point of SECP192R1 curve-type P = WPoint SECP192R1 Fp+-- | Affine SECP192R1 curve point.+type PA = WAPoint SECP192R1 Fq Fr +-- | Affine SECP192R1 curve is a Weierstrass affine curve.+instance WACurve SECP192R1 Fq Fr where+  gA_ = gA+  {-# INLINABLE gA_ #-}++-- | Jacobian SECP192R1 point.+type PJ = WJPoint SECP192R1 Fq Fr++-- | Jacobian SECP192R1 curve is a Weierstrass Jacobian curve.+instance WJCurve SECP192R1 Fq Fr where+  gJ_ = gJ+  {-# INLINABLE gJ_ #-}++-- | Projective SECP192R1 point.+type PP = WPPoint SECP192R1 Fq Fr++-- | Projective SECP192R1 curve is a Weierstrass projective curve.+instance WPCurve SECP192R1 Fq Fr where+  gP_ = gP+  {-# INLINABLE gP_ #-}+ ------------------------------------------------------------------------------- -- Parameters ------------------------------------------------------------------------------- --- | Coefficient @A@ of SECP192R1 curve-_a :: Fp+-- | Coefficient @A@ of SECP192R1 curve.+_a :: Fq _a = 0xfffffffffffffffffffffffffffffffefffffffffffffffc-{-# INLINE _a #-}+{-# INLINABLE _a #-} --- | Coefficient @B@ of SECP192R1 curve-_b :: Fp+-- | Coefficient @B@ of SECP192R1 curve.+_b :: Fq _b = 0x64210519e59c80e70fa7e9ab72243049feb8deecc146b9b1-{-# INLINE _b #-}---- | Generator of SECP192R1 curve-_g :: P-_g = A-     0x188da80eb03090f67cbf20eb43a18800f4ff0afd82ff1012-     0x7192b95ffc8da78631011ed6b24cdd573f977a11e794811-{-# INLINE _g #-}+{-# INLINABLE _b #-} --- | Cofactor of SECP192R1 curve+-- | Cofactor of SECP192R1 curve. _h :: Integer-_h = 1-{-# INLINE _h #-}+_h = 0x1+{-# INLINABLE _h #-} --- | Order of SECP192R1 curve-_n :: Integer-_n = 0xffffffffffffffffffffffff99def836146bc9b1b4d22831-{-# INLINE _n #-}+-- | Characteristic of SECP192R1 curve.+_q :: Integer+_q = 0xfffffffffffffffffffffffffffffffeffffffffffffffff+{-# INLINABLE _q #-} --- | Characteristic of SECP192R1 curve-_p :: Integer-_p = 0xfffffffffffffffffffffffffffffffeffffffffffffffff-{-# INLINE _p #-}+-- | Order of SECP192R1 curve.+_r :: Integer+_r = 0xffffffffffffffffffffffff99def836146bc9b1b4d22831+{-# INLINABLE _r #-}++-- | Coordinate @X@ of SECP192R1 curve.+_x :: Fq+_x = 0x188da80eb03090f67cbf20eb43a18800f4ff0afd82ff1012+{-# INLINABLE _x #-}++-- | Coordinate @Y@ of SECP192R1 curve.+_y :: Fq+_y = 0x7192b95ffc8da78631011ed6b24cdd573f977a11e794811+{-# INLINABLE _y #-}++-- | Generator of affine SECP192R1 curve.+gA :: PA+gA = A _x _y+{-# INLINABLE gA #-}++-- | Generator of Jacobian SECP192R1 curve.+gJ :: PJ+gJ = J _x _y 1+{-# INLINABLE gJ #-}++-- | Generator of projective SECP192R1 curve.+gP :: PP+gP = P _x _y 1+{-# INLINABLE gP #-}

src/Curve/Weierstrass/SECP224K1.hs view

@@ -1,74 +1,118 @@ module Curve.Weierstrass.SECP224K1-  ( Fp-  , P-  , _a-  , _b-  , _g-  , _h-  , _n-  , _p+  ( module Curve.Weierstrass+  , module Curve.Weierstrass.SECP224K1   ) where  import Protolude -import PrimeField (PrimeField)+import PrimeField -import Curve.Weierstrass (Point(..), WCurve(..), WPoint)+import Curve.Weierstrass  ------------------------------------------------------------------------------- -- Types ------------------------------------------------------------------------------- --- | SECP224K1 curve+-- | SECP224K1 curve. data SECP224K1 --- | Field of SECP224K1 curve-type Fp = PrimeField 0xfffffffffffffffffffffffffffffffffffffffffffffffeffffe56d+-- | Field of points of SECP224K1 curve.+type Fq = PrimeField 0xfffffffffffffffffffffffffffffffffffffffffffffffeffffe56d --- | SECP224K1 curve is a Weierstrass curve-instance WCurve SECP224K1 Fp where+-- | Field of coefficients of SECP224K1 curve.+type Fr = PrimeField 0x10000000000000000000000000001dce8d2ec6184caf0a971769fb1f7++-- | SECP224K1 curve is a Weierstrass curve.+instance Curve 'Weierstrass c SECP224K1 Fq Fr => WCurve c SECP224K1 Fq Fr where   a_ = const _a-  {-# INLINE a_ #-}+  {-# INLINABLE a_ #-}   b_ = const _b-  {-# INLINE b_ #-}-  g_ = _g-  {-# INLINE g_ #-}+  {-# INLINABLE b_ #-}+  h_ = const _h+  {-# INLINABLE h_ #-}+  q_ = const _q+  {-# INLINABLE q_ #-}+  r_ = const _r+  {-# INLINABLE r_ #-}+  x_ = const _x+  {-# INLINABLE x_ #-}+  y_ = const _y+  {-# INLINABLE y_ #-} --- | Point of SECP224K1 curve-type P = WPoint SECP224K1 Fp+-- | Affine SECP224K1 curve point.+type PA = WAPoint SECP224K1 Fq Fr +-- | Affine SECP224K1 curve is a Weierstrass affine curve.+instance WACurve SECP224K1 Fq Fr where+  gA_ = gA+  {-# INLINABLE gA_ #-}++-- | Jacobian SECP224K1 point.+type PJ = WJPoint SECP224K1 Fq Fr++-- | Jacobian SECP224K1 curve is a Weierstrass Jacobian curve.+instance WJCurve SECP224K1 Fq Fr where+  gJ_ = gJ+  {-# INLINABLE gJ_ #-}++-- | Projective SECP224K1 point.+type PP = WPPoint SECP224K1 Fq Fr++-- | Projective SECP224K1 curve is a Weierstrass projective curve.+instance WPCurve SECP224K1 Fq Fr where+  gP_ = gP+  {-# INLINABLE gP_ #-}+ ------------------------------------------------------------------------------- -- Parameters ------------------------------------------------------------------------------- --- | Coefficient @A@ of SECP224K1 curve-_a :: Fp-_a = 0-{-# INLINE _a #-}---- | Coefficient @B@ of SECP224K1 curve-_b :: Fp-_b = 5-{-# INLINE _b #-}+-- | Coefficient @A@ of SECP224K1 curve.+_a :: Fq+_a = 0x0+{-# INLINABLE _a #-} --- | Generator of SECP224K1 curve-_g :: P-_g = A-     0xa1455b334df099df30fc28a169a467e9e47075a90f7e650eb6b7a45c-     0x7e089fed7fba344282cafbd6f7e319f7c0b0bd59e2ca4bdb556d61a5-{-# INLINE _g #-}+-- | Coefficient @B@ of SECP224K1 curve.+_b :: Fq+_b = 0x5+{-# INLINABLE _b #-} --- | Cofactor of SECP224K1 curve+-- | Cofactor of SECP224K1 curve. _h :: Integer-_h = 1-{-# INLINE _h #-}+_h = 0x1+{-# INLINABLE _h #-} --- | Order of SECP224K1 curve-_n :: Integer-_n = 0x10000000000000000000000000001dce8d2ec6184caf0a971769fb1f7-{-# INLINE _n #-}+-- | Characteristic of SECP224K1 curve.+_q :: Integer+_q = 0xfffffffffffffffffffffffffffffffffffffffffffffffeffffe56d+{-# INLINABLE _q #-} --- | Characteristic of SECP224K1 curve-_p :: Integer-_p = 0xfffffffffffffffffffffffffffffffffffffffffffffffeffffe56d-{-# INLINE _p #-}+-- | Order of SECP224K1 curve.+_r :: Integer+_r = 0x10000000000000000000000000001dce8d2ec6184caf0a971769fb1f7+{-# INLINABLE _r #-}++-- | Coordinate @X@ of SECP224K1 curve.+_x :: Fq+_x = 0xa1455b334df099df30fc28a169a467e9e47075a90f7e650eb6b7a45c+{-# INLINABLE _x #-}++-- | Coordinate @Y@ of SECP224K1 curve.+_y :: Fq+_y = 0x7e089fed7fba344282cafbd6f7e319f7c0b0bd59e2ca4bdb556d61a5+{-# INLINABLE _y #-}++-- | Generator of affine SECP224K1 curve.+gA :: PA+gA = A _x _y+{-# INLINABLE gA #-}++-- | Generator of Jacobian SECP224K1 curve.+gJ :: PJ+gJ = J _x _y 1+{-# INLINABLE gJ #-}++-- | Generator of projective SECP224K1 curve.+gP :: PP+gP = P _x _y 1+{-# INLINABLE gP #-}

src/Curve/Weierstrass/SECP224R1.hs view

@@ -1,74 +1,118 @@ module Curve.Weierstrass.SECP224R1-  ( Fp-  , P-  , _a-  , _b-  , _g-  , _h-  , _n-  , _p+  ( module Curve.Weierstrass+  , module Curve.Weierstrass.SECP224R1   ) where  import Protolude -import PrimeField (PrimeField)+import PrimeField -import Curve.Weierstrass (Point(..), WCurve(..), WPoint)+import Curve.Weierstrass  ------------------------------------------------------------------------------- -- Types ------------------------------------------------------------------------------- --- | SECP224R1 curve+-- | SECP224R1 curve. data SECP224R1 --- | Field of SECP224R1 curve-type Fp = PrimeField 0xffffffffffffffffffffffffffffffff000000000000000000000001+-- | Field of points of SECP224R1 curve.+type Fq = PrimeField 0xffffffffffffffffffffffffffffffff000000000000000000000001 --- | SECP224R1 curve is a Weierstrass curve-instance WCurve SECP224R1 Fp where+-- | Field of coefficients of SECP224R1 curve.+type Fr = PrimeField 0xffffffffffffffffffffffffffff16a2e0b8f03e13dd29455c5c2a3d++-- | SECP224R1 curve is a Weierstrass curve.+instance Curve 'Weierstrass c SECP224R1 Fq Fr => WCurve c SECP224R1 Fq Fr where   a_ = const _a-  {-# INLINE a_ #-}+  {-# INLINABLE a_ #-}   b_ = const _b-  {-# INLINE b_ #-}-  g_ = _g-  {-# INLINE g_ #-}+  {-# INLINABLE b_ #-}+  h_ = const _h+  {-# INLINABLE h_ #-}+  q_ = const _q+  {-# INLINABLE q_ #-}+  r_ = const _r+  {-# INLINABLE r_ #-}+  x_ = const _x+  {-# INLINABLE x_ #-}+  y_ = const _y+  {-# INLINABLE y_ #-} --- | Point of SECP224R1 curve-type P = WPoint SECP224R1 Fp+-- | Affine SECP224R1 curve point.+type PA = WAPoint SECP224R1 Fq Fr +-- | Affine SECP224R1 curve is a Weierstrass affine curve.+instance WACurve SECP224R1 Fq Fr where+  gA_ = gA+  {-# INLINABLE gA_ #-}++-- | Jacobian SECP224R1 point.+type PJ = WJPoint SECP224R1 Fq Fr++-- | Jacobian SECP224R1 curve is a Weierstrass Jacobian curve.+instance WJCurve SECP224R1 Fq Fr where+  gJ_ = gJ+  {-# INLINABLE gJ_ #-}++-- | Projective SECP224R1 point.+type PP = WPPoint SECP224R1 Fq Fr++-- | Projective SECP224R1 curve is a Weierstrass projective curve.+instance WPCurve SECP224R1 Fq Fr where+  gP_ = gP+  {-# INLINABLE gP_ #-}+ ------------------------------------------------------------------------------- -- Parameters ------------------------------------------------------------------------------- --- | Coefficient @A@ of SECP224R1 curve-_a :: Fp+-- | Coefficient @A@ of SECP224R1 curve.+_a :: Fq _a = 0xfffffffffffffffffffffffffffffffefffffffffffffffffffffffe-{-# INLINE _a #-}+{-# INLINABLE _a #-} --- | Coefficient @B@ of SECP224R1 curve-_b :: Fp+-- | Coefficient @B@ of SECP224R1 curve.+_b :: Fq _b = 0xb4050a850c04b3abf54132565044b0b7d7bfd8ba270b39432355ffb4-{-# INLINE _b #-}---- | Generator of SECP224R1 curve-_g :: P-_g = A-     0xb70e0cbd6bb4bf7f321390b94a03c1d356c21122343280d6115c1d21-     0xbd376388b5f723fb4c22dfe6cd4375a05a07476444d5819985007e34-{-# INLINE _g #-}+{-# INLINABLE _b #-} --- | Cofactor of SECP224R1 curve+-- | Cofactor of SECP224R1 curve. _h :: Integer-_h = 1-{-# INLINE _h #-}+_h = 0x1+{-# INLINABLE _h #-} --- | Order of SECP224R1 curve-_n :: Integer-_n = 0xffffffffffffffffffffffffffff16a2e0b8f03e13dd29455c5c2a3d-{-# INLINE _n #-}+-- | Characteristic of SECP224R1 curve.+_q :: Integer+_q = 0xffffffffffffffffffffffffffffffff000000000000000000000001+{-# INLINABLE _q #-} --- | Characteristic of SECP224R1 curve-_p :: Integer-_p = 0xffffffffffffffffffffffffffffffff000000000000000000000001-{-# INLINE _p #-}+-- | Order of SECP224R1 curve.+_r :: Integer+_r = 0xffffffffffffffffffffffffffff16a2e0b8f03e13dd29455c5c2a3d+{-# INLINABLE _r #-}++-- | Coordinate @X@ of SECP224R1 curve.+_x :: Fq+_x = 0xb70e0cbd6bb4bf7f321390b94a03c1d356c21122343280d6115c1d21+{-# INLINABLE _x #-}++-- | Coordinate @Y@ of SECP224R1 curve.+_y :: Fq+_y = 0xbd376388b5f723fb4c22dfe6cd4375a05a07476444d5819985007e34+{-# INLINABLE _y #-}++-- | Generator of affine SECP224R1 curve.+gA :: PA+gA = A _x _y+{-# INLINABLE gA #-}++-- | Generator of Jacobian SECP224R1 curve.+gJ :: PJ+gJ = J _x _y 1+{-# INLINABLE gJ #-}++-- | Generator of projective SECP224R1 curve.+gP :: PP+gP = P _x _y 1+{-# INLINABLE gP #-}

src/Curve/Weierstrass/SECP256K1.hs view

@@ -1,74 +1,118 @@ module Curve.Weierstrass.SECP256K1-  ( Fp-  , P-  , _a-  , _b-  , _g-  , _h-  , _n-  , _p+  ( module Curve.Weierstrass+  , module Curve.Weierstrass.SECP256K1   ) where  import Protolude -import PrimeField (PrimeField)+import PrimeField -import Curve.Weierstrass (Point(..), WCurve(..), WPoint)+import Curve.Weierstrass  ------------------------------------------------------------------------------- -- Types ------------------------------------------------------------------------------- --- | SECP256K1 curve+-- | SECP256K1 curve. data SECP256K1 --- | Field of SECP256K1 curve-type Fp = PrimeField 0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f+-- | Field of points of SECP256K1 curve.+type Fq = PrimeField 0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f --- | SECP256K1 curve is a Weierstrass curve-instance WCurve SECP256K1 Fp where+-- | Field of coefficients of SECP256K1 curve.+type Fr = PrimeField 0xfffffffffffffffffffffffffffffffebaaedce6af48a03bbfd25e8cd0364141++-- | SECP256K1 curve is a Weierstrass curve.+instance Curve 'Weierstrass c SECP256K1 Fq Fr => WCurve c SECP256K1 Fq Fr where   a_ = const _a-  {-# INLINE a_ #-}+  {-# INLINABLE a_ #-}   b_ = const _b-  {-# INLINE b_ #-}-  g_ = _g-  {-# INLINE g_ #-}+  {-# INLINABLE b_ #-}+  h_ = const _h+  {-# INLINABLE h_ #-}+  q_ = const _q+  {-# INLINABLE q_ #-}+  r_ = const _r+  {-# INLINABLE r_ #-}+  x_ = const _x+  {-# INLINABLE x_ #-}+  y_ = const _y+  {-# INLINABLE y_ #-} --- | Point of SECP256K1 curve-type P = WPoint SECP256K1 Fp+-- | Affine SECP256K1 curve point.+type PA = WAPoint SECP256K1 Fq Fr +-- | Affine SECP256K1 curve is a Weierstrass affine curve.+instance WACurve SECP256K1 Fq Fr where+  gA_ = gA+  {-# INLINABLE gA_ #-}++-- | Jacobian SECP256K1 point.+type PJ = WJPoint SECP256K1 Fq Fr++-- | Jacobian SECP256K1 curve is a Weierstrass Jacobian curve.+instance WJCurve SECP256K1 Fq Fr where+  gJ_ = gJ+  {-# INLINABLE gJ_ #-}++-- | Projective SECP256K1 point.+type PP = WPPoint SECP256K1 Fq Fr++-- | Projective SECP256K1 curve is a Weierstrass projective curve.+instance WPCurve SECP256K1 Fq Fr where+  gP_ = gP+  {-# INLINABLE gP_ #-}+ ------------------------------------------------------------------------------- -- Parameters ------------------------------------------------------------------------------- --- | Coefficient @A@ of SECP256K1 curve-_a :: Fp-_a = 0-{-# INLINE _a #-}---- | Coefficient @B@ of SECP256K1 curve-_b :: Fp-_b = 7-{-# INLINE _b #-}+-- | Coefficient @A@ of SECP256K1 curve.+_a :: Fq+_a = 0x0+{-# INLINABLE _a #-} --- | Generator of SECP256K1 curve-_g :: P-_g = A-     0x79be667ef9dcbbac55a06295ce870b07029bfcdb2dce28d959f2815b16f81798-     0x483ada7726a3c4655da4fbfc0e1108a8fd17b448a68554199c47d08ffb10d4b8-{-# INLINE _g #-}+-- | Coefficient @B@ of SECP256K1 curve.+_b :: Fq+_b = 0x7+{-# INLINABLE _b #-} --- | Cofactor of SECP256K1 curve+-- | Cofactor of SECP256K1 curve. _h :: Integer-_h = 1-{-# INLINE _h #-}+_h = 0x1+{-# INLINABLE _h #-} --- | Order of SECP256K1 curve-_n :: Integer-_n = 0xfffffffffffffffffffffffffffffffebaaedce6af48a03bbfd25e8cd0364141-{-# INLINE _n #-}+-- | Characteristic of SECP256K1 curve.+_q :: Integer+_q = 0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f+{-# INLINABLE _q #-} --- | Characteristic of SECP256K1 curve-_p :: Integer-_p = 0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f-{-# INLINE _p #-}+-- | Order of SECP256K1 curve.+_r :: Integer+_r = 0xfffffffffffffffffffffffffffffffebaaedce6af48a03bbfd25e8cd0364141+{-# INLINABLE _r #-}++-- | Coordinate @X@ of SECP256K1 curve.+_x :: Fq+_x = 0x79be667ef9dcbbac55a06295ce870b07029bfcdb2dce28d959f2815b16f81798+{-# INLINABLE _x #-}++-- | Coordinate @Y@ of SECP256K1 curve.+_y :: Fq+_y = 0x483ada7726a3c4655da4fbfc0e1108a8fd17b448a68554199c47d08ffb10d4b8+{-# INLINABLE _y #-}++-- | Generator of affine SECP256K1 curve.+gA :: PA+gA = A _x _y+{-# INLINABLE gA #-}++-- | Generator of Jacobian SECP256K1 curve.+gJ :: PJ+gJ = J _x _y 1+{-# INLINABLE gJ #-}++-- | Generator of projective SECP256K1 curve.+gP :: PP+gP = P _x _y 1+{-# INLINABLE gP #-}

src/Curve/Weierstrass/SECP256R1.hs view

@@ -1,74 +1,118 @@ module Curve.Weierstrass.SECP256R1-  ( Fp-  , P-  , _a-  , _b-  , _g-  , _h-  , _n-  , _p+  ( module Curve.Weierstrass+  , module Curve.Weierstrass.SECP256R1   ) where  import Protolude -import PrimeField (PrimeField)+import PrimeField -import Curve.Weierstrass (Point(..), WCurve(..), WPoint)+import Curve.Weierstrass  ------------------------------------------------------------------------------- -- Types ------------------------------------------------------------------------------- --- | SECP256R1 curve+-- | SECP256R1 curve. data SECP256R1 --- | Field of SECP256R1 curve-type Fp = PrimeField 0xffffffff00000001000000000000000000000000ffffffffffffffffffffffff+-- | Field of points of SECP256R1 curve.+type Fq = PrimeField 0xffffffff00000001000000000000000000000000ffffffffffffffffffffffff --- | SECP256R1 curve is a Weierstrass curve-instance WCurve SECP256R1 Fp where+-- | Field of coefficients of SECP256R1 curve.+type Fr = PrimeField 0xffffffff00000000ffffffffffffffffbce6faada7179e84f3b9cac2fc632551++-- | SECP256R1 curve is a Weierstrass curve.+instance Curve 'Weierstrass c SECP256R1 Fq Fr => WCurve c SECP256R1 Fq Fr where   a_ = const _a-  {-# INLINE a_ #-}+  {-# INLINABLE a_ #-}   b_ = const _b-  {-# INLINE b_ #-}-  g_ = _g-  {-# INLINE g_ #-}+  {-# INLINABLE b_ #-}+  h_ = const _h+  {-# INLINABLE h_ #-}+  q_ = const _q+  {-# INLINABLE q_ #-}+  r_ = const _r+  {-# INLINABLE r_ #-}+  x_ = const _x+  {-# INLINABLE x_ #-}+  y_ = const _y+  {-# INLINABLE y_ #-} --- | Point of SECP256R1 curve-type P = WPoint SECP256R1 Fp+-- | Affine SECP256R1 curve point.+type PA = WAPoint SECP256R1 Fq Fr +-- | Affine SECP256R1 curve is a Weierstrass affine curve.+instance WACurve SECP256R1 Fq Fr where+  gA_ = gA+  {-# INLINABLE gA_ #-}++-- | Jacobian SECP256R1 point.+type PJ = WJPoint SECP256R1 Fq Fr++-- | Jacobian SECP256R1 curve is a Weierstrass Jacobian curve.+instance WJCurve SECP256R1 Fq Fr where+  gJ_ = gJ+  {-# INLINABLE gJ_ #-}++-- | Projective SECP256R1 point.+type PP = WPPoint SECP256R1 Fq Fr++-- | Projective SECP256R1 curve is a Weierstrass projective curve.+instance WPCurve SECP256R1 Fq Fr where+  gP_ = gP+  {-# INLINABLE gP_ #-}+ ------------------------------------------------------------------------------- -- Parameters ------------------------------------------------------------------------------- --- | Coefficient @A@ of SECP256R1 curve-_a :: Fp+-- | Coefficient @A@ of SECP256R1 curve.+_a :: Fq _a = 0xffffffff00000001000000000000000000000000fffffffffffffffffffffffc-{-# INLINE _a #-}+{-# INLINABLE _a #-} --- | Coefficient @B@ of SECP256R1 curve-_b :: Fp+-- | Coefficient @B@ of SECP256R1 curve.+_b :: Fq _b = 0x5ac635d8aa3a93e7b3ebbd55769886bc651d06b0cc53b0f63bce3c3e27d2604b-{-# INLINE _b #-}---- | Generator of SECP256R1 curve-_g :: P-_g = A-     0x6b17d1f2e12c4247f8bce6e563a440f277037d812deb33a0f4a13945d898c296-     0x4fe342e2fe1a7f9b8ee7eb4a7c0f9e162bce33576b315ececbb6406837bf51f5-{-# INLINE _g #-}+{-# INLINABLE _b #-} --- | Cofactor of SECP256R1 curve+-- | Cofactor of SECP256R1 curve. _h :: Integer-_h = 1-{-# INLINE _h #-}+_h = 0x1+{-# INLINABLE _h #-} --- | Order of SECP256R1 curve-_n :: Integer-_n = 0xffffffff00000000ffffffffffffffffbce6faada7179e84f3b9cac2fc632551-{-# INLINE _n #-}+-- | Characteristic of SECP256R1 curve.+_q :: Integer+_q = 0xffffffff00000001000000000000000000000000ffffffffffffffffffffffff+{-# INLINABLE _q #-} --- | Characteristic of SECP256R1 curve-_p :: Integer-_p = 0xffffffff00000001000000000000000000000000ffffffffffffffffffffffff-{-# INLINE _p #-}+-- | Order of SECP256R1 curve.+_r :: Integer+_r = 0xffffffff00000000ffffffffffffffffbce6faada7179e84f3b9cac2fc632551+{-# INLINABLE _r #-}++-- | Coordinate @X@ of SECP256R1 curve.+_x :: Fq+_x = 0x6b17d1f2e12c4247f8bce6e563a440f277037d812deb33a0f4a13945d898c296+{-# INLINABLE _x #-}++-- | Coordinate @Y@ of SECP256R1 curve.+_y :: Fq+_y = 0x4fe342e2fe1a7f9b8ee7eb4a7c0f9e162bce33576b315ececbb6406837bf51f5+{-# INLINABLE _y #-}++-- | Generator of affine SECP256R1 curve.+gA :: PA+gA = A _x _y+{-# INLINABLE gA #-}++-- | Generator of Jacobian SECP256R1 curve.+gJ :: PJ+gJ = J _x _y 1+{-# INLINABLE gJ #-}++-- | Generator of projective SECP256R1 curve.+gP :: PP+gP = P _x _y 1+{-# INLINABLE gP #-}

src/Curve/Weierstrass/SECP384R1.hs view

@@ -1,74 +1,118 @@ module Curve.Weierstrass.SECP384R1-  ( Fp-  , P-  , _a-  , _b-  , _g-  , _h-  , _n-  , _p+  ( module Curve.Weierstrass+  , module Curve.Weierstrass.SECP384R1   ) where  import Protolude -import PrimeField (PrimeField)+import PrimeField -import Curve.Weierstrass (Point(..), WCurve(..), WPoint)+import Curve.Weierstrass  ------------------------------------------------------------------------------- -- Types ------------------------------------------------------------------------------- --- | SECP384R1 curve+-- | SECP384R1 curve. data SECP384R1 --- | Field of SECP384R1 curve-type Fp = PrimeField 0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffeffffffff0000000000000000ffffffff+-- | Field of points of SECP384R1 curve.+type Fq = PrimeField 0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffeffffffff0000000000000000ffffffff --- | SECP384R1 curve is a Weierstrass curve-instance WCurve SECP384R1 Fp where+-- | Field of coefficients of SECP384R1 curve.+type Fr = PrimeField 0xffffffffffffffffffffffffffffffffffffffffffffffffc7634d81f4372ddf581a0db248b0a77aecec196accc52973++-- | SECP384R1 curve is a Weierstrass curve.+instance Curve 'Weierstrass c SECP384R1 Fq Fr => WCurve c SECP384R1 Fq Fr where   a_ = const _a-  {-# INLINE a_ #-}+  {-# INLINABLE a_ #-}   b_ = const _b-  {-# INLINE b_ #-}-  g_ = _g-  {-# INLINE g_ #-}+  {-# INLINABLE b_ #-}+  h_ = const _h+  {-# INLINABLE h_ #-}+  q_ = const _q+  {-# INLINABLE q_ #-}+  r_ = const _r+  {-# INLINABLE r_ #-}+  x_ = const _x+  {-# INLINABLE x_ #-}+  y_ = const _y+  {-# INLINABLE y_ #-} --- | Point of SECP384R1 curve-type P = WPoint SECP384R1 Fp+-- | Affine SECP384R1 curve point.+type PA = WAPoint SECP384R1 Fq Fr +-- | Affine SECP384R1 curve is a Weierstrass affine curve.+instance WACurve SECP384R1 Fq Fr where+  gA_ = gA+  {-# INLINABLE gA_ #-}++-- | Jacobian SECP384R1 point.+type PJ = WJPoint SECP384R1 Fq Fr++-- | Jacobian SECP384R1 curve is a Weierstrass Jacobian curve.+instance WJCurve SECP384R1 Fq Fr where+  gJ_ = gJ+  {-# INLINABLE gJ_ #-}++-- | Projective SECP384R1 point.+type PP = WPPoint SECP384R1 Fq Fr++-- | Projective SECP384R1 curve is a Weierstrass projective curve.+instance WPCurve SECP384R1 Fq Fr where+  gP_ = gP+  {-# INLINABLE gP_ #-}+ ------------------------------------------------------------------------------- -- Parameters ------------------------------------------------------------------------------- --- | Coefficient @A@ of SECP384R1 curve-_a :: Fp+-- | Coefficient @A@ of SECP384R1 curve.+_a :: Fq _a = 0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffeffffffff0000000000000000fffffffc-{-# INLINE _a #-}+{-# INLINABLE _a #-} --- | Coefficient @B@ of SECP384R1 curve-_b :: Fp+-- | Coefficient @B@ of SECP384R1 curve.+_b :: Fq _b = 0xb3312fa7e23ee7e4988e056be3f82d19181d9c6efe8141120314088f5013875ac656398d8a2ed19d2a85c8edd3ec2aef-{-# INLINE _b #-}---- | Generator of SECP384R1 curve-_g :: P-_g = A-     0xaa87ca22be8b05378eb1c71ef320ad746e1d3b628ba79b9859f741e082542a385502f25dbf55296c3a545e3872760ab7-     0x3617de4a96262c6f5d9e98bf9292dc29f8f41dbd289a147ce9da3113b5f0b8c00a60b1ce1d7e819d7a431d7c90ea0e5f-{-# INLINE _g #-}+{-# INLINABLE _b #-} --- | Cofactor of SECP384R1 curve+-- | Cofactor of SECP384R1 curve. _h :: Integer-_h = 1-{-# INLINE _h #-}+_h = 0x1+{-# INLINABLE _h #-} --- | Order of SECP384R1 curve-_n :: Integer-_n = 0xffffffffffffffffffffffffffffffffffffffffffffffffc7634d81f4372ddf581a0db248b0a77aecec196accc52973-{-# INLINE _n #-}+-- | Characteristic of SECP384R1 curve.+_q :: Integer+_q = 0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffeffffffff0000000000000000ffffffff+{-# INLINABLE _q #-} --- | Characteristic of SECP384R1 curve-_p :: Integer-_p = 0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffeffffffff0000000000000000ffffffff-{-# INLINE _p #-}+-- | Order of SECP384R1 curve.+_r :: Integer+_r = 0xffffffffffffffffffffffffffffffffffffffffffffffffc7634d81f4372ddf581a0db248b0a77aecec196accc52973+{-# INLINABLE _r #-}++-- | Coordinate @X@ of SECP384R1 curve.+_x :: Fq+_x = 0xaa87ca22be8b05378eb1c71ef320ad746e1d3b628ba79b9859f741e082542a385502f25dbf55296c3a545e3872760ab7+{-# INLINABLE _x #-}++-- | Coordinate @Y@ of SECP384R1 curve.+_y :: Fq+_y = 0x3617de4a96262c6f5d9e98bf9292dc29f8f41dbd289a147ce9da3113b5f0b8c00a60b1ce1d7e819d7a431d7c90ea0e5f+{-# INLINABLE _y #-}++-- | Generator of affine SECP384R1 curve.+gA :: PA+gA = A _x _y+{-# INLINABLE gA #-}++-- | Generator of Jacobian SECP384R1 curve.+gJ :: PJ+gJ = J _x _y 1+{-# INLINABLE gJ #-}++-- | Generator of projective SECP384R1 curve.+gP :: PP+gP = P _x _y 1+{-# INLINABLE gP #-}

src/Curve/Weierstrass/SECP521R1.hs view

@@ -1,74 +1,118 @@ module Curve.Weierstrass.SECP521R1-  ( Fp-  , P-  , _a-  , _b-  , _g-  , _h-  , _n-  , _p+  ( module Curve.Weierstrass+  , module Curve.Weierstrass.SECP521R1   ) where  import Protolude -import PrimeField (PrimeField)+import PrimeField -import Curve.Weierstrass (Point(..), WCurve(..), WPoint)+import Curve.Weierstrass  ------------------------------------------------------------------------------- -- Types ------------------------------------------------------------------------------- --- | SECP521R1 curve+-- | SECP521R1 curve. data SECP521R1 --- | Field of SECP521R1 curve-type Fp = PrimeField 0x1ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff+-- | Field of points of SECP521R1 curve.+type Fq = PrimeField 0x1ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff --- | SECP521R1 curve is a Weierstrass curve-instance WCurve SECP521R1 Fp where+-- | Field of coefficients of SECP521R1 curve.+type Fr = PrimeField 0x1fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffa51868783bf2f966b7fcc0148f709a5d03bb5c9b8899c47aebb6fb71e91386409++-- | SECP521R1 curve is a Weierstrass curve.+instance Curve 'Weierstrass c SECP521R1 Fq Fr => WCurve c SECP521R1 Fq Fr where   a_ = const _a-  {-# INLINE a_ #-}+  {-# INLINABLE a_ #-}   b_ = const _b-  {-# INLINE b_ #-}-  g_ = _g-  {-# INLINE g_ #-}+  {-# INLINABLE b_ #-}+  h_ = const _h+  {-# INLINABLE h_ #-}+  q_ = const _q+  {-# INLINABLE q_ #-}+  r_ = const _r+  {-# INLINABLE r_ #-}+  x_ = const _x+  {-# INLINABLE x_ #-}+  y_ = const _y+  {-# INLINABLE y_ #-} --- | Point of SECP521R1 curve-type P = WPoint SECP521R1 Fp+-- | Affine SECP521R1 curve point.+type PA = WAPoint SECP521R1 Fq Fr +-- | Affine SECP521R1 curve is a Weierstrass affine curve.+instance WACurve SECP521R1 Fq Fr where+  gA_ = gA+  {-# INLINABLE gA_ #-}++-- | Jacobian SECP521R1 point.+type PJ = WJPoint SECP521R1 Fq Fr++-- | Jacobian SECP521R1 curve is a Weierstrass Jacobian curve.+instance WJCurve SECP521R1 Fq Fr where+  gJ_ = gJ+  {-# INLINABLE gJ_ #-}++-- | Projective SECP521R1 point.+type PP = WPPoint SECP521R1 Fq Fr++-- | Projective SECP521R1 curve is a Weierstrass projective curve.+instance WPCurve SECP521R1 Fq Fr where+  gP_ = gP+  {-# INLINABLE gP_ #-}+ ------------------------------------------------------------------------------- -- Parameters ------------------------------------------------------------------------------- --- | Coefficient @A@ of SECP521R1 curve-_a :: Fp+-- | Coefficient @A@ of SECP521R1 curve.+_a :: Fq _a = 0x1fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffc-{-# INLINE _a #-}+{-# INLINABLE _a #-} --- | Coefficient @B@ of SECP521R1 curve-_b :: Fp+-- | Coefficient @B@ of SECP521R1 curve.+_b :: Fq _b = 0x51953eb9618e1c9a1f929a21a0b68540eea2da725b99b315f3b8b489918ef109e156193951ec7e937b1652c0bd3bb1bf073573df883d2c34f1ef451fd46b503f00-{-# INLINE _b #-}---- | Generator of SECP521R1 curve-_g :: P-_g = A-     0xc6858e06b70404e9cd9e3ecb662395b4429c648139053fb521f828af606b4d3dbaa14b5e77efe75928fe1dc127a2ffa8de3348b3c1856a429bf97e7e31c2e5bd66-     0x11839296a789a3bc0045c8a5fb42c7d1bd998f54449579b446817afbd17273e662c97ee72995ef42640c550b9013fad0761353c7086a272c24088be94769fd16650-{-# INLINE _g #-}+{-# INLINABLE _b #-} --- | Cofactor of SECP521R1 curve+-- | Cofactor of SECP521R1 curve. _h :: Integer-_h = 1-{-# INLINE _h #-}+_h = 0x1+{-# INLINABLE _h #-} --- | Order of SECP521R1 curve-_n :: Integer-_n = 0x1fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffa51868783bf2f966b7fcc0148f709a5d03bb5c9b8899c47aebb6fb71e91386409-{-# INLINE _n #-}+-- | Characteristic of SECP521R1 curve.+_q :: Integer+_q = 0x1ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff+{-# INLINABLE _q #-} --- | Characteristic of SECP521R1 curve-_p :: Integer-_p = 0x1ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff-{-# INLINE _p #-}+-- | Order of SECP521R1 curve.+_r :: Integer+_r = 0x1fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffa51868783bf2f966b7fcc0148f709a5d03bb5c9b8899c47aebb6fb71e91386409+{-# INLINABLE _r #-}++-- | Coordinate @X@ of SECP521R1 curve.+_x :: Fq+_x = 0xc6858e06b70404e9cd9e3ecb662395b4429c648139053fb521f828af606b4d3dbaa14b5e77efe75928fe1dc127a2ffa8de3348b3c1856a429bf97e7e31c2e5bd66+{-# INLINABLE _x #-}++-- | Coordinate @Y@ of SECP521R1 curve.+_y :: Fq+_y = 0x11839296a789a3bc0045c8a5fb42c7d1bd998f54449579b446817afbd17273e662c97ee72995ef42640c550b9013fad0761353c7086a272c24088be94769fd16650+{-# INLINABLE _y #-}++-- | Generator of affine SECP521R1 curve.+gA :: PA+gA = A _x _y+{-# INLINABLE gA #-}++-- | Generator of Jacobian SECP521R1 curve.+gJ :: PJ+gJ = J _x _y 1+{-# INLINABLE gJ #-}++-- | Generator of projective SECP521R1 curve.+gP :: PP+gP = P _x _y 1+{-# INLINABLE gP #-}

+ src/Group.hs view

@@ -0,0 +1,56 @@+module Group+  ( Group(..)+  ) where++import Protolude++import Control.Monad.Random (MonadRandom, Random, getRandom)+import Test.Tasty.QuickCheck (Arbitrary)+import Text.PrettyPrint.Leijen.Text (Pretty)++-------------------------------------------------------------------------------+-- Types+-------------------------------------------------------------------------------++-- | Groups.+class (Arbitrary g, Eq g, Generic g,+       Monoid g, Pretty g, Random g, Show g) => Group g where+  {-# MINIMAL add, dbl, def, gen, id, inv, order #-}++  -- | Element addition.+  add :: g -> g -> g++  -- | Element doubling.+  dbl :: g -> g++  -- | Check well-defined.+  def :: g -> Bool++  -- | Group generator.+  gen :: g++  -- | Identity element.+  id :: g++  -- | Element inversion.+  inv :: g -> g++  -- | Element multiplication.+  mul' :: g -> Integer -> g+  mul' p n+    | n < 0     = inv (mul' p (-n))+    | n == 0    = id+    | n == 1    = p+    | even n    = p'+    | otherwise = add p p'+    where+      p' = mul' (dbl p) (div n 2)+  {-# INLINABLE mul' #-}++  -- | Curve order.+  order :: g -> Integer++  -- | Random element.+  rnd :: MonadRandom m => m g+  rnd = getRandom+  {-# INLINABLE rnd #-}

+ src/Group/Field.hs view

@@ -0,0 +1,100 @@+module Group.Field+  ( module Group+  , module Group.Field+  ) where++import Protolude++import Control.Monad.Random (Random(..))+import GaloisField (GaloisField(..))+import Test.Tasty.QuickCheck (Arbitrary(..), suchThatMap)+import Text.PrettyPrint.Leijen.Text (Pretty(..))++import Group (Group(..))++-------------------------------------------------------------------------------+-- Types+-------------------------------------------------------------------------------++-- | Field groups.+class GaloisField k => FGroup k where+  {-# MINIMAL g_, q_, r_, x_ #-}+  g_ :: Element k            -- ^ Group generator.+  q_ :: Element k -> Integer -- ^ Group characteristic.+  r_ :: Element k -> Integer -- ^ Group order.+  x_ :: k                    -- ^ Group element.++-- | Field elements.+newtype Element k = F k+  deriving (Eq, Functor, Generic, NFData, Read, Show)++-------------------------------------------------------------------------------+-- Operations+-------------------------------------------------------------------------------++-- Field elements are groups.+instance FGroup k => Group (Element k) where++  add = (<>)+  {-# INLINABLE add #-}++  dbl = join (<>)+  {-# INLINABLE dbl #-}++  def (F x) = x /= 0+  {-# INLINABLE def #-}++  gen = g_+  {-# INLINABLE gen #-}++  id = mempty+  {-# INLINABLE id #-}++  inv (F x) = F (recip x)+  {-# INLINABLE inv #-}++  mul' (F x) n = F (pow x n)+  {-# INLINABLE mul' #-}++  order = r_+  {-# INLINABLE order #-}++-- Field elements are monoids.+instance FGroup k => Monoid (Element k) where++  mempty = F 1+  {-# INLINABLE mempty #-}++-- Field elements are semigroups.+instance FGroup k => Semigroup (Element k) where++  F x <> F y = F (x * y)+  {-# INLINABLE (<>) #-}++-------------------------------------------------------------------------------+-- Instances+-------------------------------------------------------------------------------++-- Field elements are arbitrary.+instance FGroup k => Arbitrary (Element k) where++  arbitrary = suchThatMap arbitrary defX+    where+      defX 0 = Nothing+      defX x = Just (F x)+  {-# INLINABLE arbitrary #-}++-- Field elements are pretty.+instance FGroup k => Pretty (Element k) where++  pretty (F x) = pretty x++-- Field elements are random.+instance FGroup k => Random (Element k) where++  random g = case random g of+    (0, g') -> random g'+    (x, g') -> (F x, g')+  {-# INLINABLE random #-}++  randomR  = panic "not implemented."

+ src/Group/Field/BN254TF.hs view

@@ -0,0 +1,85 @@+module Group.Field.BN254TF+  ( module Group+  , module Group.Field+  , module Group.Field.BN254TF+  ) where++import Protolude++import ExtensionField++import Curve.Weierstrass.BN254T (Fq2)+import Group+import Group.Field++-------------------------------------------------------------------------------+-- Types+-------------------------------------------------------------------------------++-- | Field of BN254TF group.+data PolynomialV+instance IrreducibleMonic Fq2 PolynomialV where+  split _ = X3 - Y X - 9+type Fq6 = ExtensionField Fq2 PolynomialV+data PolynomialW+instance IrreducibleMonic Fq6 PolynomialW where+  split _ = X2 - Y X+type Fq12 = ExtensionField Fq6 PolynomialW++-- | BN254TF group is a field group.+instance FGroup Fq12 where+  g_ = _g+  {-# INLINABLE g_ #-}+  q_ = const _q+  {-# INLINABLE q_ #-}+  r_ = const _r+  {-# INLINABLE r_ #-}+  x_ = _x+  {-# INLINABLE x_ #-}++-- | Element of BN254TF group.+type P = Element Fq12++-------------------------------------------------------------------------------+-- Parameters+-------------------------------------------------------------------------------++-- | Generator of BN254TF group.+_g :: P+_g = F _x+{-# INLINABLE _g #-}++-- | Characteristic of BN254TF group.+_q :: Integer+_q = 0x30644e72e131a029b85045b68181585d97816a916871ca8d3c208c16d87cfd47+{-# INLINABLE _q #-}++-- | Order of BN254TF group.+_r :: Integer+_r = 0x30644e72e131a029b85045b68181585d2833e84879b9709143e1f593f0000001+{-# INLINABLE _r #-}++-- | Element @X@ of BN254TF group.+_x :: Fq12+_x = toField [ toField [ toField [ 0x12c70e90e12b7874510cd1707e8856f71bf7f61d72631e268fca81000db9a1f5+                                 , 0x84f330485b09e866bc2f2ea2b897394deaf3f12aa31f28cb0552990967d4704+                                 ]+                       , toField [ 0xe841c2ac18a4003ac9326b9558380e0bc27fdd375e3605f96b819a358d34bde+                                 , 0x2067586885c3318eeffa1938c754fe3c60224ee5ae15e66af6b5104c47c8c5d8+                                 ]+                       , toField [ 0x1676555de427abc409c4a394bc5426886302996919d4bf4bdd02236e14b3636+                                 , 0x2b03614464f04dd772d86df88674c270ffc8747ea13e72da95e3594468f222c4+                                 ]+                       ]+             , toField [ toField [ 0x2c53748bcd21a7c038fb30ddc8ac3bf0af25d7859cfbc12c30c866276c565909+                                 , 0x27ed208e7a0b55ae6e710bbfbd2fd922669c026360e37cc5b2ab862411536104+                                 ]+                       , toField [ 0x1ad9db1937fd72f4ac462173d31d3d6117411fa48dba8d499d762b47edb3b54a+                                 , 0x279db296f9d479292532c7c493d8e0722b6efae42158387564889c79fc038ee3+                                 ]+                       , toField [ 0xdc26f240656bbe2029bd441d77c221f0ba4c70c94b29b5f17f0f6d08745a069+                                 , 0x108c19d15f9446f744d0f110405d3856d6cc3bda6c4d537663729f5257628417+                                 ]+                       ]+             ]+{-# INLINABLE _x #-}

tests/BinaryTests.hs view

@@ -1,8 +1,7 @@ module BinaryTests where -import Test.Tasty+import Protolude -import CurveTests import qualified Curve.Binary.SECT113R1 as SECT113R1 import qualified Curve.Binary.SECT113R2 as SECT113R2 import qualified Curve.Binary.SECT131R1 as SECT131R1@@ -21,25 +20,34 @@ import qualified Curve.Binary.SECT409R1 as SECT409R1 import qualified Curve.Binary.SECT571K1 as SECT571K1 import qualified Curve.Binary.SECT571R1 as SECT571R1+import Test.Tasty+import Test.Tasty.QuickCheck +import GroupTests+ testBinary :: TestTree testBinary = testGroup "Binary"-  [ test "SECT113R1" SECT113R1._g SECT113R1._h SECT113R1._n 2-  , test "SECT113R2" SECT113R2._g SECT113R2._h SECT113R2._n 2-  , test "SECT131R1" SECT131R1._g SECT131R1._h SECT131R1._n 2-  , test "SECT131R2" SECT131R2._g SECT131R2._h SECT131R2._n 2-  , test "SECT163K1" SECT163K1._g SECT163K1._h SECT163K1._n 2-  , test "SECT163R1" SECT163R1._g SECT163R1._h SECT163R1._n 2-  , test "SECT163R2" SECT163R2._g SECT163R2._h SECT163R2._n 2-  , test "SECT193R1" SECT193R1._g SECT193R1._h SECT193R1._n 2-  , test "SECT193R2" SECT193R2._g SECT193R2._h SECT193R2._n 2-  , test "SECT233K1" SECT233K1._g SECT233K1._h SECT233K1._n 2-  , test "SECT233R1" SECT233R1._g SECT233R1._h SECT233R1._n 2-  , test "SECT239K1" SECT239K1._g SECT239K1._h SECT239K1._n 2-  , test "SECT283K1" SECT283K1._g SECT283K1._h SECT283K1._n 2-  , test "SECT283R1" SECT283R1._g SECT283R1._h SECT283R1._n 2-  , test "SECT409K1" SECT409K1._g SECT409K1._h SECT409K1._n 2-  , test "SECT409R1" SECT409R1._g SECT409R1._h SECT409R1._n 2-  , test "SECT571K1" SECT571K1._g SECT571K1._h SECT571K1._n 2-  , test "SECT571R1" SECT571R1._g SECT571R1._h SECT571R1._n 2+  [ testBinary' 1 "SECT113R1" SECT113R1._h 2 SECT113R1._r SECT113R1.gA SECT113R1.gP+  , testBinary' 1 "SECT113R2" SECT113R2._h 2 SECT113R2._r SECT113R2.gA SECT113R2.gP+  , testBinary' 1 "SECT131R1" SECT131R1._h 2 SECT131R1._r SECT131R1.gA SECT131R1.gP+  , testBinary' 1 "SECT131R2" SECT131R2._h 2 SECT131R2._r SECT131R2.gA SECT131R2.gP+  , testBinary' 1 "SECT163K1" SECT163K1._h 2 SECT163K1._r SECT163K1.gA SECT163K1.gP+  , testBinary' 1 "SECT163R1" SECT163R1._h 2 SECT163R1._r SECT163R1.gA SECT163R1.gP+  , testBinary' 1 "SECT163R2" SECT163R2._h 2 SECT163R2._r SECT163R2.gA SECT163R2.gP+  , testBinary' 1 "SECT193R1" SECT193R1._h 2 SECT193R1._r SECT193R1.gA SECT193R1.gP+  , testBinary' 1 "SECT193R2" SECT193R2._h 2 SECT193R2._r SECT193R2.gA SECT193R2.gP+  , testBinary' 1 "SECT233K1" SECT233K1._h 2 SECT233K1._r SECT233K1.gA SECT233K1.gP+  , testBinary' 1 "SECT233R1" SECT233R1._h 2 SECT233R1._r SECT233R1.gA SECT233R1.gP+  , testBinary' 1 "SECT239K1" SECT239K1._h 2 SECT239K1._r SECT239K1.gA SECT239K1.gP+  , testBinary' 1 "SECT283K1" SECT283K1._h 2 SECT283K1._r SECT283K1.gA SECT283K1.gP+  , testBinary' 1 "SECT283R1" SECT283R1._h 2 SECT283R1._r SECT283R1.gA SECT283R1.gP+  , testBinary' 1 "SECT409K1" SECT409K1._h 2 SECT409K1._r SECT409K1.gA SECT409K1.gP+  , testBinary' 1 "SECT409R1" SECT409R1._h 2 SECT409R1._r SECT409R1.gA SECT409R1.gP+  , testBinary' 1 "SECT571K1" SECT571K1._h 2 SECT571K1._r SECT571K1.gA SECT571K1.gP+  , testBinary' 1 "SECT571R1" SECT571R1._h 2 SECT571R1._r SECT571R1.gA SECT571R1.gP   ]+  where+    testBinary' n c h q r a p = localOption (QuickCheckTests n) $ testGroup c+      [ test "Affine" a h q r+      , test "Projective" p h q r+      ]

− tests/CurveTests.hs

@@ -1,74 +0,0 @@-module CurveTests where--import Protolude--import Curve-import GaloisField-import Math.NumberTheory.Primes.Testing-import Test.Tasty-import Test.Tasty.HUnit-import Test.Tasty.QuickCheck--identities :: Eq a => (a -> a -> a) -> a -> a -> Bool-identities op e x = op x e == x && op e x == x--inverses :: Eq a => (a -> a -> a) -> (a -> a) -> a -> a -> Bool-inverses op neg e x = op x (neg x) == e && op (neg x) x == e--commutativity :: Eq a => (a -> a -> a) -> a -> a -> Bool-commutativity op x y = op x y == op y x--associativity :: Eq a => (a -> a -> a) -> a -> a -> a -> Bool-associativity op x y z = op x (op y z) == op (op x y) z--groupAxioms :: forall r c k .-  (Arbitrary (Point r c k), Curve r c k, Eq (Point r c k), GaloisField k, Show (Point r c k))-  => Point r c k -> TestTree-groupAxioms _ = testGroup "Group axioms"-  [ testCase "identity closure" $-    def (id :: Point r c k) @?= True-  , testProperty "point closure" $-    def . (identity :: Point r c k -> Point r c k)-  , testProperty "inversion closure" $-    def . (inv :: Point r c k -> Point r c k)-  , testProperty "addition closure" $-    (.) def . (add :: Point r c k -> Point r c k -> Point r c k)-  , testProperty "doubling closure" $-    def . (double :: Point r c k -> Point r c k)-  , testProperty "multiplication closure" $-    def . (mul (6 :: Int) :: Point r c k -> Point r c k)-  , testProperty "identity" $-    identities (add :: Point r c k -> Point r c k -> Point r c k) mempty-  , testProperty "inverses" $-    inverses (add :: Point r c k -> Point r c k -> Point r c k) inv mempty-  , testProperty "commutativity" $-    commutativity (add :: Point r c k -> Point r c k -> Point r c k)-  , testProperty "associativity" $-    associativity (add :: Point r c k -> Point r c k -> Point r c k)-  ]--hasse :: Integer -> Integer -> Integer -> Bool-hasse h n q = (h * n - q - 1) ^ (2 :: Int) <= 4 * q--curveParameters :: forall r c k .-  (Arbitrary (Point r c k), Curve r c k, Eq (Point r c k), GaloisField k, Show (Point r c k))-  => Point r c k -> Integer -> Integer -> Integer -> TestTree-curveParameters g h n p = testGroup "Curve parameters"-  [ testCase "characteristic is typed" $-    char (witness :: k) @?= p-  , testCase "characteristic is prime" $-    isPrime p @?= True-  , testCase "discriminant is nonzero" $-    disc (witness :: Point r c k) /= 0 @?= True-  , testCase "generator is in cyclic subgroup" $-    mul n g @?= id-  , testCase "cyclic subgroup has prime order" $-    isPrime n @?= True-  , testCase "hasse theorem holds" $-    hasse h n (order (witness :: k)) @?= True-  ]--test :: forall r c k .-  (Arbitrary (Point r c k), Curve r c k, Eq (Point r c k), GaloisField k, Show (Point r c k))-  => TestName -> Point r c k -> Integer -> Integer -> Integer -> TestTree-test s g h n p = testGroup s [groupAxioms g, curveParameters g h n p]

tests/EdwardsTests.hs view

@@ -1,8 +1,7 @@ module EdwardsTests where -import Test.Tasty+import Protolude -import CurveTests import qualified Curve.Edwards.Curve1174  as Curve1174 import qualified Curve.Edwards.Curve41417 as Curve41417 import qualified Curve.Edwards.E222       as E222@@ -12,16 +11,25 @@ import qualified Curve.Edwards.Ed3363     as Ed3363 import qualified Curve.Edwards.Ed25519    as Ed25519 import qualified Curve.Edwards.JubJub     as JubJub+import Test.Tasty+import Test.Tasty.QuickCheck +import GroupTests+ testEdwards :: TestTree testEdwards = testGroup "Edwards"-  [ test  "Curve1174"  Curve1174._g  Curve1174._h  Curve1174._n  Curve1174._p-  , test "Curve41417" Curve41417._g Curve41417._h Curve41417._n Curve41417._p-  , test      "E-222"       E222._g       E222._h       E222._n       E222._p-  , test      "E-382"       E382._g       E382._h       E382._n       E382._p-  , test      "E-521"       E521._g       E521._h       E521._n       E521._p-  , test      "Ed448"      Ed448._g      Ed448._h      Ed448._n      Ed448._p-  , test     "Ed3363"     Ed3363._g     Ed3363._h     Ed3363._n     Ed3363._p-  , test    "Ed25519"    Ed25519._g    Ed25519._h    Ed25519._n    Ed25519._p-  , test     "JubJub"     JubJub._g     JubJub._h     JubJub._n     JubJub._p+  [ testEdwards' 100  "Curve1174"  Curve1174._h  Curve1174._q  Curve1174._r  Curve1174.gA  Curve1174.gP+  , testEdwards' 100 "Curve41417" Curve41417._h Curve41417._q Curve41417._r Curve41417.gA Curve41417.gP+  , testEdwards' 100       "E222"       E222._h       E222._q       E222._r       E222.gA       E222.gP+  , testEdwards' 100       "E382"       E382._h       E382._q       E382._r       E382.gA       E382.gP+  , testEdwards' 100       "E521"       E521._h       E521._q       E521._r       E521.gA       E521.gP+  , testEdwards' 100      "Ed448"      Ed448._h      Ed448._q      Ed448._r      Ed448.gA      Ed448.gP+  , testEdwards' 100     "Ed3363"     Ed3363._h     Ed3363._q     Ed3363._r     Ed3363.gA     Ed3363.gP+  , testEdwards' 100    "Ed25519"    Ed25519._h    Ed25519._q    Ed25519._r    Ed25519.gA    Ed25519.gP+  , testEdwards' 100     "JubJub"     JubJub._h     JubJub._q     JubJub._r     JubJub.gA     JubJub.gP   ]+  where+    testEdwards' n c h q r a p = localOption (QuickCheckTests n) $ testGroup c+      [ test "Affine" a h q r+      , test "Projective" p h q r+      ]

+ tests/FieldTests.hs view

@@ -0,0 +1,11 @@+module FieldTests where++import qualified Group.Field.BN254TF as BN254TF+import Test.Tasty++import GroupTests++testField :: TestTree+testField = testGroup "Field"+  [ test' "BN254TF" BN254TF._g BN254TF._q BN254TF._r+  ]

+ tests/GroupTests.hs view

@@ -0,0 +1,122 @@+module GroupTests where++import Protolude++import Curve+import GaloisField+import Group+import Group.Field+import Math.NumberTheory.Primes.Testing+import PrimeField+import Test.Tasty+import Test.Tasty.HUnit+import Test.Tasty.QuickCheck++identities :: Eq a => (a -> a -> a) -> a -> a -> Bool+identities op e x = op x e == x && op e x == x++inverses :: Eq a => (a -> a -> a) -> (a -> a) -> a -> a -> Bool+inverses op neg e x = op x (neg x) == e && op (neg x) x == e++commutativity :: Eq a => (a -> a -> a) -> a -> a -> Bool+commutativity op x y = op x y == op y x++associativity :: Eq a => (a -> a -> a) -> a -> a -> a -> Bool+associativity op x y z = op x (op y z) == op (op x y) z++groupAxioms :: forall g . Group g => g -> TestTree+groupAxioms _ = testGroup "Group axioms"+  [ testCase "identity closure" $+    def (mempty :: g) @?= True+  , testProperty "point closure" $+    (def :: g -> Bool)+  , testProperty "inversion closure" $+    def . (inv :: g -> g)+  , testProperty "addition closure" $+    (.) def . ((<>) :: g -> g -> g)+  , testProperty "doubling closure" $+    def . (join (<>) :: g -> g)+  , testProperty "multiplication closure" $+    def . (flip mul' (-3) :: g -> g)+  , testProperty "identity" $+    identities ((<>) :: g -> g -> g) mempty+  , testProperty "inverses" $+    inverses ((<>) :: g -> g -> g) inv mempty+  , testProperty "commutativity" $+    commutativity ((<>) :: g -> g -> g)+  , testProperty "associativity" $+    associativity ((<>) :: g -> g -> g)+  ]++hasseTheorem :: Integer -> Integer -> Integer -> Bool+hasseTheorem h r q = join (*) (h * r - q - 1) <= 4 * q++doubleIdentities :: (Eq a, Eq b) => (a -> b) -> (b -> a) -> a -> b -> Bool+doubleIdentities f t e e' = f e == e' && t e' == e++doubleDefined :: (a -> Bool) -> (b -> Bool) -> (b -> a) -> b -> Bool+doubleDefined d d' t x = d' x && d (t x)++doubleInverses :: (Eq a, Eq b) => (a -> b) -> (b -> a) -> b -> Bool+doubleInverses f t x = f (t x) == x && t (f (t x)) == t x++doubleHomeomorphism :: (Eq a, Eq b) => (a -> a) -> (b -> b) -> (a -> b) -> (b -> a) -> b -> Bool+doubleHomeomorphism op op' f t x = t (op' x) == op (t x) && f (op (t x)) == op' x++curveParameters :: forall f c e q r p+  . (r ~ PrimeField p, Curve f 'Affine e q r, Curve f c e q r)+  => Point f c e q r -> Integer -> Integer -> Integer -> TestTree+curveParameters g h q r = testGroup "Curve parameters"+  [ testCase "generator is parametrised" $+    gen @?= g+  , testCase "cofactor is parametrised" $+    cof (witness :: Point f c e q r) @?= h+  , testCase "characteristic is parametrised" $+    Curve.char (witness :: Point f c e q r) @?= q+  , testCase "order is parametrised" $+    Group.order (witness :: Point f c e q r) @?= r+  , testCase "characteristic is prime" $+    isPrime q @?= True+  , testCase "discriminant is nonzero" $+    disc (witness :: Point f c e q r) /= 0 @?= True+  , testCase "generator is well-defined" $+    def (gen :: Point f c e q r) @?= True+  , testCase "generator is in cyclic subgroup" $+    mul' g r @?= mempty+  , testCase "cyclic subgroup has prime order" $+    isPrime r @?= True+  , testCase "hasse theorem holds" $+    hasseTheorem h r (GaloisField.order (witness :: q)) @?= True+  , testCase "affine transformation is doubly identity-preserving" $+    doubleIdentities fromA (toA :: Point f c e q r -> Point f 'Affine e q r) mempty mempty @?= True+  , testProperty "affine transformation is doubly well-defined" $+    doubleDefined def def (toA :: Point f c e q r -> Point f 'Affine e q r)+  , testProperty "affine transformation is doubly invertible" $+    doubleInverses fromA (toA :: Point f c e q r -> Point f 'Affine e q r)+  , testProperty "affine transformation is doubly homeomorphic" $+    doubleHomeomorphism (flip mul 3) (flip mul 3) fromA (toA :: Point f c e q r -> Point f 'Affine e q r)+  ]++test :: (r ~ PrimeField p, Curve f c e q r, Curve f 'Affine e q r)+  => TestName -> Point f c e q r -> Integer -> Integer -> Integer -> TestTree+test s g h q r = testGroup s [groupAxioms g, curveParameters g h q r]++fieldParameters :: forall k . FGroup k+  => Element k -> Integer -> Integer -> TestTree+fieldParameters g q r = testGroup "Group parameters"+  [ testCase "generator is parametrised" $+    gen @?= g+  , testCase "characteristic is parametrised" $+    GaloisField.char (witness :: k) @?= q+  , testCase "order is parametrised" $+    Group.order (witness :: Element k) @?= r+  , testCase "characteristic is prime" $+    isPrime q @?= True+  , testCase "generator is well-defined" $+    def (gen :: Element k) @?= True+  , testCase "generator is in cyclic subgroup" $+    mul' g r @?= mempty+  ]++test' :: FGroup k => TestName -> Element k -> Integer -> Integer -> TestTree+test' s g q r = testGroup s [groupAxioms g, fieldParameters g q r]

tests/Main.hs view

@@ -6,9 +6,10 @@  import BinaryTests import EdwardsTests+import FieldTests import MontgomeryTests import WeierstrassTests  main :: IO () main = defaultMain $-  testGroup "Tests" [testBinary, testEdwards, testMontgomery, testWeierstrass]+  testGroup "Tests" [testBinary, testEdwards, testMontgomery, testWeierstrass, testField]

tests/MontgomeryTests.hs view

@@ -1,21 +1,28 @@ module MontgomeryTests where +import Protolude++import qualified Curve.Montgomery.Curve448    as Curve448+import qualified Curve.Montgomery.Curve25519  as Curve25519+import qualified Curve.Montgomery.Curve383187 as Curve383187+import qualified Curve.Montgomery.M221        as M221+import qualified Curve.Montgomery.M383        as M383+import qualified Curve.Montgomery.M511        as M511 import Test.Tasty+import Test.Tasty.QuickCheck -import CurveTests-import qualified Curve.Montgomery.Curve448         as Curve448-import qualified Curve.Montgomery.Curve25519       as Curve25519-import qualified Curve.Montgomery.Curve383187      as Curve383187-import qualified Curve.Montgomery.M221             as M221-import qualified Curve.Montgomery.M383             as M383-import qualified Curve.Montgomery.M511             as M511+import GroupTests  testMontgomery :: TestTree testMontgomery = testGroup "Montgomery"-  [ test    "Curve448"    Curve448._g    Curve448._h    Curve448._n    Curve448._p-  , test  "Curve25519"  Curve25519._g  Curve25519._h  Curve25519._n  Curve25519._p-  , test "Curve383187" Curve383187._g Curve383187._h Curve383187._n Curve383187._p-  , test       "M-221"        M221._g        M221._h        M221._n        M221._p-  , test       "M-383"        M383._g        M383._h        M383._n        M383._p-  , test       "M-511"        M511._g        M511._h        M511._n        M511._p+  [ testMontgomery' 100    "Curve448"    Curve448._h    Curve448._q    Curve448._r    Curve448.gA+  , testMontgomery' 100  "Curve25519"  Curve25519._h  Curve25519._q  Curve25519._r  Curve25519.gA+  , testMontgomery' 100 "Curve383187" Curve383187._h Curve383187._q Curve383187._r Curve383187.gA+  , testMontgomery' 100        "M221"        M221._h        M221._q        M221._r        M221.gA+  , testMontgomery' 100        "M383"        M383._h        M383._q        M383._r        M383.gA+  , testMontgomery' 100        "M511"        M511._h        M511._q        M511._r        M511.gA   ]+  where+    testMontgomery' n c h q r a = localOption (QuickCheckTests n) $ testGroup c+      [ test "Affine" a h q r+      ]

tests/WeierstrassTests.hs view

@@ -1,14 +1,13 @@ module WeierstrassTests where -import Test.Tasty+import Protolude -import CurveTests import qualified Curve.Weierstrass.Anomalous       as Anomalous import qualified Curve.Weierstrass.ANSSIFRP256V1   as ANSSIFRP256V1-import qualified Curve.Weierstrass.BLS12_381       as BLS12_381-import qualified Curve.Weierstrass.BLS12_381T      as BLS12_381T-import qualified Curve.Weierstrass.BLS48_581       as BLS48_581-import qualified Curve.Weierstrass.BLS48_581T      as BLS48_581T+import qualified Curve.Weierstrass.BLS12381        as BLS12381+import qualified Curve.Weierstrass.BLS12381T       as BLS12381T+import qualified Curve.Weierstrass.BLS48581        as BLS48581+import qualified Curve.Weierstrass.BLS48581T       as BLS48581T import qualified Curve.Weierstrass.BN224           as BN224 import qualified Curve.Weierstrass.BN254           as BN254 import qualified Curve.Weierstrass.BN254T          as BN254T@@ -50,54 +49,64 @@ import qualified Curve.Weierstrass.SECP256R1       as SECP256R1 import qualified Curve.Weierstrass.SECP384R1       as SECP384R1 import qualified Curve.Weierstrass.SECP521R1       as SECP521R1+import Test.Tasty+import Test.Tasty.QuickCheck +import GroupTests+ testWeierstrass :: TestTree testWeierstrass = testGroup "Weierstrass"-  [ test        "Anomalous"       Anomalous._g       Anomalous._h       Anomalous._n       Anomalous._p-  , test   "ANSSI-FRP256V1"   ANSSIFRP256V1._g   ANSSIFRP256V1._h   ANSSIFRP256V1._n   ANSSIFRP256V1._p-  , test        "BLS12-381"       BLS12_381._g       BLS12_381._h       BLS12_381._n       BLS12_381._p-  , test       "BLS12-381T"      BLS12_381T._g      BLS12_381T._h      BLS12_381T._n      BLS12_381T._p-  , test        "BLS48-581"       BLS48_581._g       BLS48_581._h       BLS48_581._n       BLS48_581._p-  , test       "BLS48-581T"      BLS48_581T._g      BLS48_581T._h      BLS48_581T._n      BLS48_581T._p-  , test            "BN224"           BN224._g           BN224._h           BN224._n           BN224._p-  , test            "BN254"           BN254._g           BN254._h           BN254._n           BN254._p-  , test           "BN254T"          BN254T._g          BN254T._h          BN254T._n          BN254T._p-  , test           "BN254A"          BN254A._g          BN254A._h          BN254A._n          BN254A._p-  , test          "BN254AT"         BN254AT._g         BN254AT._h         BN254AT._n         BN254AT._p-  , test           "BN254B"          BN254B._g          BN254B._h          BN254B._n          BN254B._p-  , test          "BN254BT"         BN254BT._g         BN254BT._h         BN254BT._n         BN254BT._p-  , test            "BN256"           BN256._g           BN256._h           BN256._n           BN256._p-  , test            "BN384"           BN384._g           BN384._h           BN384._n           BN384._p-  , test            "BN462"           BN462._g           BN462._h           BN462._n           BN462._p-  , test           "BN462T"          BN462T._g          BN462T._h          BN462T._n          BN462T._p-  , test            "BN512"           BN512._g           BN512._h           BN512._n           BN512._p-  , test "Brainpool-P160R1" BrainpoolP160R1._g BrainpoolP160R1._h BrainpoolP160R1._n BrainpoolP160R1._p-  , test "Brainpool-P160T1" BrainpoolP160T1._g BrainpoolP160T1._h BrainpoolP160T1._n BrainpoolP160T1._p-  , test "Brainpool-P192R1" BrainpoolP192R1._g BrainpoolP192R1._h BrainpoolP192R1._n BrainpoolP192R1._p-  , test "Brainpool-P192T1" BrainpoolP192T1._g BrainpoolP192T1._h BrainpoolP192T1._n BrainpoolP192T1._p-  , test "Brainpool-P224R1" BrainpoolP224R1._g BrainpoolP224R1._h BrainpoolP224R1._n BrainpoolP224R1._p-  , test "Brainpool-P224T1" BrainpoolP224T1._g BrainpoolP224T1._h BrainpoolP224T1._n BrainpoolP224T1._p-  , test "Brainpool-P256R1" BrainpoolP256R1._g BrainpoolP256R1._h BrainpoolP256R1._n BrainpoolP256R1._p-  , test "Brainpool-P256T1" BrainpoolP256T1._g BrainpoolP256T1._h BrainpoolP256T1._n BrainpoolP256T1._p-  , test "Brainpool-P320R1" BrainpoolP320R1._g BrainpoolP320R1._h BrainpoolP320R1._n BrainpoolP320R1._p-  , test "Brainpool-P320T1" BrainpoolP320T1._g BrainpoolP320T1._h BrainpoolP320T1._n BrainpoolP320T1._p-  , test "Brainpool-P384R1" BrainpoolP384R1._g BrainpoolP384R1._h BrainpoolP384R1._n BrainpoolP384R1._p-  , test "Brainpool-P384T1" BrainpoolP384T1._g BrainpoolP384T1._h BrainpoolP384T1._n BrainpoolP384T1._p-  , test "Brainpool-P512R1" BrainpoolP512R1._g BrainpoolP512R1._h BrainpoolP512R1._n BrainpoolP512R1._p-  , test "Brainpool-P512T1" BrainpoolP512T1._g BrainpoolP512T1._h BrainpoolP512T1._n BrainpoolP512T1._p-  , test        "SECP112R1"       SECP112R1._g       SECP112R1._h       SECP112R1._n       SECP112R1._p-  , test        "SECP112R2"       SECP112R2._g       SECP112R2._h       SECP112R2._n       SECP112R2._p-  , test        "SECP128R1"       SECP128R1._g       SECP128R1._h       SECP128R1._n       SECP128R1._p-  , test        "SECP128R2"       SECP128R2._g       SECP128R2._h       SECP128R2._n       SECP128R2._p-  , test        "SECP160K1"       SECP160K1._g       SECP160K1._h       SECP160K1._n       SECP160K1._p-  , test        "SECP160R1"       SECP160R1._g       SECP160R1._h       SECP160R1._n       SECP160R1._p-  , test        "SECP160R2"       SECP160R2._g       SECP160R2._h       SECP160R2._n       SECP160R2._p-  , test        "SECP192K1"       SECP192K1._g       SECP192K1._h       SECP192K1._n       SECP192K1._p-  , test        "SECP192R1"       SECP192R1._g       SECP192R1._h       SECP192R1._n       SECP192R1._p-  , test        "SECP224K1"       SECP224K1._g       SECP224K1._h       SECP224K1._n       SECP224K1._p-  , test        "SECP224R1"       SECP224R1._g       SECP224R1._h       SECP224R1._n       SECP224R1._p-  , test        "SECP256K1"       SECP256K1._g       SECP256K1._h       SECP256K1._n       SECP256K1._p-  , test        "SECP256R1"       SECP256R1._g       SECP256R1._h       SECP256R1._n       SECP256R1._p-  , test        "SECP384R1"       SECP384R1._g       SECP384R1._h       SECP384R1._n       SECP384R1._p-  , test        "SECP521R1"       SECP521R1._g       SECP521R1._h       SECP521R1._n       SECP521R1._p+  [ testWeierstrass' 100       "Anomalous"       Anomalous._h       Anomalous._q       Anomalous._r       Anomalous.gA       Anomalous.gJ       Anomalous.gP+  , testWeierstrass' 100   "ANSSIFRP256V1"   ANSSIFRP256V1._h   ANSSIFRP256V1._q   ANSSIFRP256V1._r   ANSSIFRP256V1.gA   ANSSIFRP256V1.gJ   ANSSIFRP256V1.gP+  , testWeierstrass' 100        "BLS12381"        BLS12381._h        BLS12381._q        BLS12381._r        BLS12381.gA        BLS12381.gJ        BLS12381.gP+  , testWeierstrass'  10       "BLS12381T"       BLS12381T._h       BLS12381T._q       BLS12381T._r       BLS12381T.gA       BLS12381T.gJ       BLS12381T.gP+  , testWeierstrass' 100        "BLS48581"        BLS48581._h        BLS48581._q        BLS48581._r        BLS48581.gA        BLS48581.gJ        BLS48581.gP+  , testWeierstrass'   0       "BLS48581T"       BLS48581T._h       BLS48581T._q       BLS48581T._r       BLS48581T.gA       BLS48581T.gJ       BLS48581T.gP+  , testWeierstrass' 100           "BN224"           BN224._h           BN224._q           BN224._r           BN224.gA           BN224.gJ           BN224.gP+  , testWeierstrass' 100           "BN254"           BN254._h           BN254._q           BN254._r           BN254.gA           BN254.gJ           BN254.gP+  , testWeierstrass'  10          "BN254T"          BN254T._h          BN254T._q          BN254T._r          BN254T.gA          BN254T.gJ          BN254T.gP+  , testWeierstrass' 100          "BN254A"          BN254A._h          BN254A._q          BN254A._r          BN254A.gA          BN254A.gJ          BN254A.gP+  , testWeierstrass'  10         "BN254AT"         BN254AT._h         BN254AT._q         BN254AT._r         BN254AT.gA         BN254AT.gJ         BN254AT.gP+  , testWeierstrass' 100          "BN254B"          BN254B._h          BN254B._q          BN254B._r          BN254B.gA          BN254B.gJ          BN254B.gP+  , testWeierstrass'  10         "BN254BT"         BN254BT._h         BN254BT._q         BN254BT._r         BN254BT.gA         BN254BT.gJ         BN254BT.gP+  , testWeierstrass' 100           "BN256"           BN256._h           BN256._q           BN256._r           BN256.gA           BN256.gJ           BN256.gP+  , testWeierstrass' 100           "BN384"           BN384._h           BN384._q           BN384._r           BN384.gA           BN384.gJ           BN384.gP+  , testWeierstrass' 100           "BN462"           BN462._h           BN462._q           BN462._r           BN462.gA           BN462.gJ           BN462.gP+  , testWeierstrass'  10          "BN462T"          BN462T._h          BN462T._q          BN462T._r          BN462T.gA          BN462T.gJ          BN462T.gP+  , testWeierstrass' 100           "BN512"           BN512._h           BN512._q           BN512._r           BN512.gA           BN512.gJ           BN512.gP+  , testWeierstrass' 100 "BrainpoolP160R1" BrainpoolP160R1._h BrainpoolP160R1._q BrainpoolP160R1._r BrainpoolP160R1.gA BrainpoolP160R1.gJ BrainpoolP160R1.gP+  , testWeierstrass' 100 "BrainpoolP160T1" BrainpoolP160T1._h BrainpoolP160T1._q BrainpoolP160T1._r BrainpoolP160T1.gA BrainpoolP160T1.gJ BrainpoolP160T1.gP+  , testWeierstrass' 100 "BrainpoolP192R1" BrainpoolP192R1._h BrainpoolP192R1._q BrainpoolP192R1._r BrainpoolP192R1.gA BrainpoolP192R1.gJ BrainpoolP192R1.gP+  , testWeierstrass' 100 "BrainpoolP192T1" BrainpoolP192T1._h BrainpoolP192T1._q BrainpoolP192T1._r BrainpoolP192T1.gA BrainpoolP192T1.gJ BrainpoolP192T1.gP+  , testWeierstrass' 100 "BrainpoolP224R1" BrainpoolP224R1._h BrainpoolP224R1._q BrainpoolP224R1._r BrainpoolP224R1.gA BrainpoolP224R1.gJ BrainpoolP224R1.gP+  , testWeierstrass' 100 "BrainpoolP224T1" BrainpoolP224T1._h BrainpoolP224T1._q BrainpoolP224T1._r BrainpoolP224T1.gA BrainpoolP224T1.gJ BrainpoolP224T1.gP+  , testWeierstrass' 100 "BrainpoolP256R1" BrainpoolP256R1._h BrainpoolP256R1._q BrainpoolP256R1._r BrainpoolP256R1.gA BrainpoolP256R1.gJ BrainpoolP256R1.gP+  , testWeierstrass' 100 "BrainpoolP256T1" BrainpoolP256T1._h BrainpoolP256T1._q BrainpoolP256T1._r BrainpoolP256T1.gA BrainpoolP256T1.gJ BrainpoolP256T1.gP+  , testWeierstrass' 100 "BrainpoolP320R1" BrainpoolP320R1._h BrainpoolP320R1._q BrainpoolP320R1._r BrainpoolP320R1.gA BrainpoolP320R1.gJ BrainpoolP320R1.gP+  , testWeierstrass' 100 "BrainpoolP320T1" BrainpoolP320T1._h BrainpoolP320T1._q BrainpoolP320T1._r BrainpoolP320T1.gA BrainpoolP320T1.gJ BrainpoolP320T1.gP+  , testWeierstrass' 100 "BrainpoolP384R1" BrainpoolP384R1._h BrainpoolP384R1._q BrainpoolP384R1._r BrainpoolP384R1.gA BrainpoolP384R1.gJ BrainpoolP384R1.gP+  , testWeierstrass' 100 "BrainpoolP384T1" BrainpoolP384T1._h BrainpoolP384T1._q BrainpoolP384T1._r BrainpoolP384T1.gA BrainpoolP384T1.gJ BrainpoolP384T1.gP+  , testWeierstrass' 100 "BrainpoolP512R1" BrainpoolP512R1._h BrainpoolP512R1._q BrainpoolP512R1._r BrainpoolP512R1.gA BrainpoolP512R1.gJ BrainpoolP512R1.gP+  , testWeierstrass' 100 "BrainpoolP512T1" BrainpoolP512T1._h BrainpoolP512T1._q BrainpoolP512T1._r BrainpoolP512T1.gA BrainpoolP512T1.gJ BrainpoolP512T1.gP+  , testWeierstrass' 100       "SECP112R1"       SECP112R1._h       SECP112R1._q       SECP112R1._r       SECP112R1.gA       SECP112R1.gJ       SECP112R1.gP+  , testWeierstrass' 100       "SECP112R2"       SECP112R2._h       SECP112R2._q       SECP112R2._r       SECP112R2.gA       SECP112R2.gJ       SECP112R2.gP+  , testWeierstrass' 100       "SECP128R1"       SECP128R1._h       SECP128R1._q       SECP128R1._r       SECP128R1.gA       SECP128R1.gJ       SECP128R1.gP+  , testWeierstrass' 100       "SECP128R2"       SECP128R2._h       SECP128R2._q       SECP128R2._r       SECP128R2.gA       SECP128R2.gJ       SECP128R2.gP+  , testWeierstrass' 100       "SECP160K1"       SECP160K1._h       SECP160K1._q       SECP160K1._r       SECP160K1.gA       SECP160K1.gJ       SECP160K1.gP+  , testWeierstrass' 100       "SECP160R1"       SECP160R1._h       SECP160R1._q       SECP160R1._r       SECP160R1.gA       SECP160R1.gJ       SECP160R1.gP+  , testWeierstrass' 100       "SECP160R2"       SECP160R2._h       SECP160R2._q       SECP160R2._r       SECP160R2.gA       SECP160R2.gJ       SECP160R2.gP+  , testWeierstrass' 100       "SECP192K1"       SECP192K1._h       SECP192K1._q       SECP192K1._r       SECP192K1.gA       SECP192K1.gJ       SECP192K1.gP+  , testWeierstrass' 100       "SECP192R1"       SECP192R1._h       SECP192R1._q       SECP192R1._r       SECP192R1.gA       SECP192R1.gJ       SECP192R1.gP+  , testWeierstrass' 100       "SECP224K1"       SECP224K1._h       SECP224K1._q       SECP224K1._r       SECP224K1.gA       SECP224K1.gJ       SECP224K1.gP+  , testWeierstrass' 100       "SECP224R1"       SECP224R1._h       SECP224R1._q       SECP224R1._r       SECP224R1.gA       SECP224R1.gJ       SECP224R1.gP+  , testWeierstrass' 100       "SECP256K1"       SECP256K1._h       SECP256K1._q       SECP256K1._r       SECP256K1.gA       SECP256K1.gJ       SECP256K1.gP+  , testWeierstrass' 100       "SECP256R1"       SECP256R1._h       SECP256R1._q       SECP256R1._r       SECP256R1.gA       SECP256R1.gJ       SECP256R1.gP+  , testWeierstrass' 100       "SECP384R1"       SECP384R1._h       SECP384R1._q       SECP384R1._r       SECP384R1.gA       SECP384R1.gJ       SECP384R1.gP+  , testWeierstrass' 100       "SECP521R1"       SECP521R1._h       SECP521R1._q       SECP521R1._r       SECP521R1.gA       SECP521R1.gJ       SECP521R1.gP   ]+  where+    testWeierstrass' n c h q r a j p = localOption (QuickCheckTests n) $ testGroup c+      [ test "Affine" a h q r+      , test "Jacobian" j h q r+      , test "Projective" p h q r+      ]