diff --git a/ChangeLog.md b/ChangeLog.md --- a/ChangeLog.md +++ b/ChangeLog.md @@ -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. diff --git a/README.md b/README.md --- a/README.md +++ b/README.md @@ -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) diff --git a/benchmarks/BinaryBenchmarks.hs b/benchmarks/BinaryBenchmarks.hs new file mode 100644 --- /dev/null +++ b/benchmarks/BinaryBenchmarks.hs @@ -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 + ] diff --git a/benchmarks/EdwardsBenchmarks.hs b/benchmarks/EdwardsBenchmarks.hs new file mode 100644 --- /dev/null +++ b/benchmarks/EdwardsBenchmarks.hs @@ -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 + ] diff --git a/benchmarks/FieldBenchmarks.hs b/benchmarks/FieldBenchmarks.hs new file mode 100644 --- /dev/null +++ b/benchmarks/FieldBenchmarks.hs @@ -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 + ] diff --git a/benchmarks/GroupBenchmarks.hs b/benchmarks/GroupBenchmarks.hs new file mode 100644 --- /dev/null +++ b/benchmarks/GroupBenchmarks.hs @@ -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 diff --git a/benchmarks/Main.hs b/benchmarks/Main.hs --- a/benchmarks/Main.hs +++ b/benchmarks/Main.hs @@ -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] diff --git a/benchmarks/MontgomeryBenchmarks.hs b/benchmarks/MontgomeryBenchmarks.hs new file mode 100644 --- /dev/null +++ b/benchmarks/MontgomeryBenchmarks.hs @@ -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 + ] diff --git a/benchmarks/WeierstrassBenchmarks.hs b/benchmarks/WeierstrassBenchmarks.hs new file mode 100644 --- /dev/null +++ b/benchmarks/WeierstrassBenchmarks.hs @@ -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 + ] diff --git a/elliptic-curve.cabal b/elliptic-curve.cabal --- a/elliptic-curve.cabal +++ b/elliptic-curve.cabal @@ -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 diff --git a/generate/Generate/Binary/Curve.hs b/generate/Generate/Binary/Curve.hs new file mode 100644 --- /dev/null +++ b/generate/Generate/Binary/Curve.hs @@ -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 diff --git a/generate/Generate/Binary/Generate.hs b/generate/Generate/Binary/Generate.hs new file mode 100644 --- /dev/null +++ b/generate/Generate/Binary/Generate.hs @@ -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 diff --git a/generate/Generate/Binary/Parameters.hs b/generate/Generate/Binary/Parameters.hs new file mode 100644 --- /dev/null +++ b/generate/Generate/Binary/Parameters.hs @@ -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 + } + } diff --git a/generate/Generate/Binary/Types.hs b/generate/Generate/Binary/Types.hs new file mode 100644 --- /dev/null +++ b/generate/Generate/Binary/Types.hs @@ -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 + } diff --git a/generate/Generate/Curve.hs b/generate/Generate/Curve.hs new file mode 100644 --- /dev/null +++ b/generate/Generate/Curve.hs @@ -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 + <$$> "type" <+> pretty fq' <+> "= ExtensionField" <+> pretty fq <+> pretty q + where + prettyType' :: Maybe Field -> Doc + prettyType' (Just f) = prettyType f + prettyType' _ = mempty +prettyType (PrimeField fq q) + = "type" <+> pretty fq <+> "= PrimeField" <+> prettyInteger q diff --git a/generate/Generate/Edwards/Curve.hs b/generate/Generate/Edwards/Curve.hs new file mode 100644 --- /dev/null +++ b/generate/Generate/Edwards/Curve.hs @@ -0,0 +1,144 @@ +module Generate.Edwards.Curve + ( prettyCurve + ) where + +import Protolude + +import Text.PrettyPrint.Leijen.Text + +import Generate.Curve +import Generate.Edwards.Types +import Generate.Pretty + +------------------------------------------------------------------------------- +-- Curve +------------------------------------------------------------------------------- + +prettyImports :: Types -> Doc +prettyImports Types{..} + = "module Curve.Edwards." <> pretty curve + <$$> 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 + <$$> prettyParameters types parameters + <> prettyBreak diff --git a/generate/Generate/Edwards/Generate.hs b/generate/Generate/Edwards/Generate.hs new file mode 100644 --- /dev/null +++ b/generate/Generate/Edwards/Generate.hs @@ -0,0 +1,84 @@ +module Generate.Edwards.Generate + ( prettyGenerate + ) where + +import Protolude + +import Data.Text (toLower) +import Text.PrettyPrint.Leijen.Text + +import Generate.Edwards.Types +import Generate.Generate +import Generate.Pretty + +------------------------------------------------------------------------------- +-- Generate +------------------------------------------------------------------------------- + +prettyImports :: Doc +prettyImports + = "module Generate.Edwards.Parameters" + <$$> 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 diff --git a/generate/Generate/Edwards/Parameters.hs b/generate/Generate/Edwards/Parameters.hs new file mode 100644 --- /dev/null +++ b/generate/Generate/Edwards/Parameters.hs @@ -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 + } + } diff --git a/generate/Generate/Edwards/Types.hs b/generate/Generate/Edwards/Types.hs new file mode 100644 --- /dev/null +++ b/generate/Generate/Edwards/Types.hs @@ -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 + } diff --git a/generate/Generate/Generate.hs b/generate/Generate/Generate.hs new file mode 100644 --- /dev/null +++ b/generate/Generate/Generate.hs @@ -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 diff --git a/generate/Generate/Montgomery/Curve.hs b/generate/Generate/Montgomery/Curve.hs new file mode 100644 --- /dev/null +++ b/generate/Generate/Montgomery/Curve.hs @@ -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 diff --git a/generate/Generate/Montgomery/Generate.hs b/generate/Generate/Montgomery/Generate.hs new file mode 100644 --- /dev/null +++ b/generate/Generate/Montgomery/Generate.hs @@ -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 diff --git a/generate/Generate/Montgomery/Parameters.hs b/generate/Generate/Montgomery/Parameters.hs new file mode 100644 --- /dev/null +++ b/generate/Generate/Montgomery/Parameters.hs @@ -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 + } + } diff --git a/generate/Generate/Montgomery/Types.hs b/generate/Generate/Montgomery/Types.hs new file mode 100644 --- /dev/null +++ b/generate/Generate/Montgomery/Types.hs @@ -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 + } diff --git a/generate/Generate/Pretty.hs b/generate/Generate/Pretty.hs new file mode 100644 --- /dev/null +++ b/generate/Generate/Pretty.hs @@ -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 <$$> "-- ") (prettyBreak <> prettyLine <> prettyBreak) + +prettyText :: Text -> Doc +prettyText + = dquotes . pretty diff --git a/generate/Generate/Types.hs b/generate/Generate/Types.hs new file mode 100644 --- /dev/null +++ b/generate/Generate/Types.hs @@ -0,0 +1,24 @@ +module Generate.Types + ( module Generate.Types + ) where + +import Protolude + +------------------------------------------------------------------------------- +-- Types +------------------------------------------------------------------------------- + +data Element = BF Integer + | EF [Element] + | PF Integer + +data Field = BinaryField Text Integer + | ExtensionField Text Text Text Text (Maybe Field) + | PrimeField Text Integer + +data Types = Types + { curve :: Text + , field :: Field + , field' :: Field + , imports :: Maybe Text + } diff --git a/generate/Generate/Weierstrass/Curve.hs b/generate/Generate/Weierstrass/Curve.hs new file mode 100644 --- /dev/null +++ b/generate/Generate/Weierstrass/Curve.hs @@ -0,0 +1,159 @@ +module Generate.Weierstrass.Curve + ( prettyCurve + ) where + +import Protolude + +import Text.PrettyPrint.Leijen.Text + +import Generate.Curve +import Generate.Pretty +import Generate.Weierstrass.Types + +------------------------------------------------------------------------------- +-- Curve +------------------------------------------------------------------------------- + +prettyImports :: Types -> Doc +prettyImports Types{..} + = "module Curve.Weierstrass." <> pretty curve + <$$> 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 + <$$> prettyParameters types parameters + <> prettyBreak diff --git a/generate/Generate/Weierstrass/Generate.hs b/generate/Generate/Weierstrass/Generate.hs new file mode 100644 --- /dev/null +++ b/generate/Generate/Weierstrass/Generate.hs @@ -0,0 +1,84 @@ +module Generate.Weierstrass.Generate + ( prettyGenerate + ) where + +import Protolude + +import Data.Text (toLower) +import Text.PrettyPrint.Leijen.Text + +import Generate.Generate +import Generate.Pretty +import Generate.Weierstrass.Types + +------------------------------------------------------------------------------- +-- Generate +------------------------------------------------------------------------------- + +prettyImports :: Doc +prettyImports + = "module Generate.Weierstrass.Parameters" + <$$> 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 diff --git a/generate/Generate/Weierstrass/Parameters.hs b/generate/Generate/Weierstrass/Parameters.hs new file mode 100644 --- /dev/null +++ b/generate/Generate/Weierstrass/Parameters.hs @@ -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 + } + } diff --git a/generate/Generate/Weierstrass/Types.hs b/generate/Generate/Weierstrass/Types.hs new file mode 100644 --- /dev/null +++ b/generate/Generate/Weierstrass/Types.hs @@ -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 + } diff --git a/generate/Main.hs b/generate/Main.hs new file mode 100644 --- /dev/null +++ b/generate/Main.hs @@ -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 diff --git a/src/Curve.hs b/src/Curve.hs --- a/src/Curve.hs +++ b/src/Curve.hs @@ -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." diff --git a/src/Curve/Binary.hs b/src/Curve/Binary.hs --- a/src/Curve/Binary.hs +++ b/src/Curve/Binary.hs @@ -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) diff --git a/src/Curve/Binary/SECT113R1.hs b/src/Curve/Binary/SECT113R1.hs --- a/src/Curve/Binary/SECT113R1.hs +++ b/src/Curve/Binary/SECT113R1.hs @@ -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 #-} diff --git a/src/Curve/Binary/SECT113R2.hs b/src/Curve/Binary/SECT113R2.hs --- a/src/Curve/Binary/SECT113R2.hs +++ b/src/Curve/Binary/SECT113R2.hs @@ -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 #-} diff --git a/src/Curve/Binary/SECT131R1.hs b/src/Curve/Binary/SECT131R1.hs --- a/src/Curve/Binary/SECT131R1.hs +++ b/src/Curve/Binary/SECT131R1.hs @@ -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 #-} diff --git a/src/Curve/Binary/SECT131R2.hs b/src/Curve/Binary/SECT131R2.hs --- a/src/Curve/Binary/SECT131R2.hs +++ b/src/Curve/Binary/SECT131R2.hs @@ -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 #-} diff --git a/src/Curve/Binary/SECT163K1.hs b/src/Curve/Binary/SECT163K1.hs --- a/src/Curve/Binary/SECT163K1.hs +++ b/src/Curve/Binary/SECT163K1.hs @@ -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 #-} diff --git a/src/Curve/Binary/SECT163R1.hs b/src/Curve/Binary/SECT163R1.hs --- a/src/Curve/Binary/SECT163R1.hs +++ b/src/Curve/Binary/SECT163R1.hs @@ -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 #-} diff --git a/src/Curve/Binary/SECT163R2.hs b/src/Curve/Binary/SECT163R2.hs --- a/src/Curve/Binary/SECT163R2.hs +++ b/src/Curve/Binary/SECT163R2.hs @@ -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 #-} diff --git a/src/Curve/Binary/SECT193R1.hs b/src/Curve/Binary/SECT193R1.hs --- a/src/Curve/Binary/SECT193R1.hs +++ b/src/Curve/Binary/SECT193R1.hs @@ -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 #-} diff --git a/src/Curve/Binary/SECT193R2.hs b/src/Curve/Binary/SECT193R2.hs --- a/src/Curve/Binary/SECT193R2.hs +++ b/src/Curve/Binary/SECT193R2.hs @@ -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 #-} diff --git a/src/Curve/Binary/SECT233K1.hs b/src/Curve/Binary/SECT233K1.hs --- a/src/Curve/Binary/SECT233K1.hs +++ b/src/Curve/Binary/SECT233K1.hs @@ -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 #-} diff --git a/src/Curve/Binary/SECT233R1.hs b/src/Curve/Binary/SECT233R1.hs --- a/src/Curve/Binary/SECT233R1.hs +++ b/src/Curve/Binary/SECT233R1.hs @@ -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 #-} diff --git a/src/Curve/Binary/SECT239K1.hs b/src/Curve/Binary/SECT239K1.hs --- a/src/Curve/Binary/SECT239K1.hs +++ b/src/Curve/Binary/SECT239K1.hs @@ -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 #-} diff --git a/src/Curve/Binary/SECT283K1.hs b/src/Curve/Binary/SECT283K1.hs --- a/src/Curve/Binary/SECT283K1.hs +++ b/src/Curve/Binary/SECT283K1.hs @@ -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 #-} diff --git a/src/Curve/Binary/SECT283R1.hs b/src/Curve/Binary/SECT283R1.hs --- a/src/Curve/Binary/SECT283R1.hs +++ b/src/Curve/Binary/SECT283R1.hs @@ -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 #-} diff --git a/src/Curve/Binary/SECT409K1.hs b/src/Curve/Binary/SECT409K1.hs --- a/src/Curve/Binary/SECT409K1.hs +++ b/src/Curve/Binary/SECT409K1.hs @@ -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 #-} diff --git a/src/Curve/Binary/SECT409R1.hs b/src/Curve/Binary/SECT409R1.hs --- a/src/Curve/Binary/SECT409R1.hs +++ b/src/Curve/Binary/SECT409R1.hs @@ -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 #-} diff --git a/src/Curve/Binary/SECT571K1.hs b/src/Curve/Binary/SECT571K1.hs --- a/src/Curve/Binary/SECT571K1.hs +++ b/src/Curve/Binary/SECT571K1.hs @@ -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 #-} diff --git a/src/Curve/Binary/SECT571R1.hs b/src/Curve/Binary/SECT571R1.hs --- a/src/Curve/Binary/SECT571R1.hs +++ b/src/Curve/Binary/SECT571R1.hs @@ -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 #-} diff --git a/src/Curve/Edwards.hs b/src/Curve/Edwards.hs --- a/src/Curve/Edwards.hs +++ b/src/Curve/Edwards.hs @@ -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) diff --git a/src/Curve/Edwards/Curve1174.hs b/src/Curve/Edwards/Curve1174.hs --- a/src/Curve/Edwards/Curve1174.hs +++ b/src/Curve/Edwards/Curve1174.hs @@ -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 #-} diff --git a/src/Curve/Edwards/Curve41417.hs b/src/Curve/Edwards/Curve41417.hs --- a/src/Curve/Edwards/Curve41417.hs +++ b/src/Curve/Edwards/Curve41417.hs @@ -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 #-} diff --git a/src/Curve/Edwards/E222.hs b/src/Curve/Edwards/E222.hs --- a/src/Curve/Edwards/E222.hs +++ b/src/Curve/Edwards/E222.hs @@ -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 #-} diff --git a/src/Curve/Edwards/E382.hs b/src/Curve/Edwards/E382.hs --- a/src/Curve/Edwards/E382.hs +++ b/src/Curve/Edwards/E382.hs @@ -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 #-} diff --git a/src/Curve/Edwards/E521.hs b/src/Curve/Edwards/E521.hs --- a/src/Curve/Edwards/E521.hs +++ b/src/Curve/Edwards/E521.hs @@ -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 #-} diff --git a/src/Curve/Edwards/Ed25519.hs b/src/Curve/Edwards/Ed25519.hs --- a/src/Curve/Edwards/Ed25519.hs +++ b/src/Curve/Edwards/Ed25519.hs @@ -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 #-} diff --git a/src/Curve/Edwards/Ed3363.hs b/src/Curve/Edwards/Ed3363.hs --- a/src/Curve/Edwards/Ed3363.hs +++ b/src/Curve/Edwards/Ed3363.hs @@ -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 #-} diff --git a/src/Curve/Edwards/Ed448.hs b/src/Curve/Edwards/Ed448.hs --- a/src/Curve/Edwards/Ed448.hs +++ b/src/Curve/Edwards/Ed448.hs @@ -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 #-} diff --git a/src/Curve/Edwards/JubJub.hs b/src/Curve/Edwards/JubJub.hs --- a/src/Curve/Edwards/JubJub.hs +++ b/src/Curve/Edwards/JubJub.hs @@ -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 #-} diff --git a/src/Curve/Montgomery.hs b/src/Curve/Montgomery.hs --- a/src/Curve/Montgomery.hs +++ b/src/Curve/Montgomery.hs @@ -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" diff --git a/src/Curve/Montgomery/Curve25519.hs b/src/Curve/Montgomery/Curve25519.hs --- a/src/Curve/Montgomery/Curve25519.hs +++ b/src/Curve/Montgomery/Curve25519.hs @@ -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 #-} diff --git a/src/Curve/Montgomery/Curve383187.hs b/src/Curve/Montgomery/Curve383187.hs --- a/src/Curve/Montgomery/Curve383187.hs +++ b/src/Curve/Montgomery/Curve383187.hs @@ -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 #-} diff --git a/src/Curve/Montgomery/Curve448.hs b/src/Curve/Montgomery/Curve448.hs --- a/src/Curve/Montgomery/Curve448.hs +++ b/src/Curve/Montgomery/Curve448.hs @@ -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 #-} diff --git a/src/Curve/Montgomery/M221.hs b/src/Curve/Montgomery/M221.hs --- a/src/Curve/Montgomery/M221.hs +++ b/src/Curve/Montgomery/M221.hs @@ -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 #-} diff --git a/src/Curve/Montgomery/M383.hs b/src/Curve/Montgomery/M383.hs --- a/src/Curve/Montgomery/M383.hs +++ b/src/Curve/Montgomery/M383.hs @@ -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 #-} diff --git a/src/Curve/Montgomery/M511.hs b/src/Curve/Montgomery/M511.hs --- a/src/Curve/Montgomery/M511.hs +++ b/src/Curve/Montgomery/M511.hs @@ -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 #-} diff --git a/src/Curve/Weierstrass.hs b/src/Curve/Weierstrass.hs --- a/src/Curve/Weierstrass.hs +++ b/src/Curve/Weierstrass.hs @@ -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) diff --git a/src/Curve/Weierstrass/ANSSIFRP256V1.hs b/src/Curve/Weierstrass/ANSSIFRP256V1.hs --- a/src/Curve/Weierstrass/ANSSIFRP256V1.hs +++ b/src/Curve/Weierstrass/ANSSIFRP256V1.hs @@ -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 #-} diff --git a/src/Curve/Weierstrass/Anomalous.hs b/src/Curve/Weierstrass/Anomalous.hs --- a/src/Curve/Weierstrass/Anomalous.hs +++ b/src/Curve/Weierstrass/Anomalous.hs @@ -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 #-} diff --git a/src/Curve/Weierstrass/BLS12381.hs b/src/Curve/Weierstrass/BLS12381.hs new file mode 100644 --- /dev/null +++ b/src/Curve/Weierstrass/BLS12381.hs @@ -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 #-} diff --git a/src/Curve/Weierstrass/BLS12381T.hs b/src/Curve/Weierstrass/BLS12381T.hs new file mode 100644 --- /dev/null +++ b/src/Curve/Weierstrass/BLS12381T.hs @@ -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 #-} diff --git a/src/Curve/Weierstrass/BLS12_381.hs b/src/Curve/Weierstrass/BLS12_381.hs deleted file mode 100644 --- a/src/Curve/Weierstrass/BLS12_381.hs +++ /dev/null @@ -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 #-} diff --git a/src/Curve/Weierstrass/BLS12_381T.hs b/src/Curve/Weierstrass/BLS12_381T.hs deleted file mode 100644 --- a/src/Curve/Weierstrass/BLS12_381T.hs +++ /dev/null @@ -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 #-} diff --git a/src/Curve/Weierstrass/BLS48581.hs b/src/Curve/Weierstrass/BLS48581.hs new file mode 100644 --- /dev/null +++ b/src/Curve/Weierstrass/BLS48581.hs @@ -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 #-} diff --git a/src/Curve/Weierstrass/BLS48581T.hs b/src/Curve/Weierstrass/BLS48581T.hs new file mode 100644 --- /dev/null +++ b/src/Curve/Weierstrass/BLS48581T.hs @@ -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 #-} diff --git a/src/Curve/Weierstrass/BLS48_581.hs b/src/Curve/Weierstrass/BLS48_581.hs deleted file mode 100644 --- a/src/Curve/Weierstrass/BLS48_581.hs +++ /dev/null @@ -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 #-} diff --git a/src/Curve/Weierstrass/BLS48_581T.hs b/src/Curve/Weierstrass/BLS48_581T.hs deleted file mode 100644 --- a/src/Curve/Weierstrass/BLS48_581T.hs +++ /dev/null @@ -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 #-} diff --git a/src/Curve/Weierstrass/BN224.hs b/src/Curve/Weierstrass/BN224.hs --- a/src/Curve/Weierstrass/BN224.hs +++ b/src/Curve/Weierstrass/BN224.hs @@ -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 #-} diff --git a/src/Curve/Weierstrass/BN254.hs b/src/Curve/Weierstrass/BN254.hs --- a/src/Curve/Weierstrass/BN254.hs +++ b/src/Curve/Weierstrass/BN254.hs @@ -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 #-} diff --git a/src/Curve/Weierstrass/BN254A.hs b/src/Curve/Weierstrass/BN254A.hs --- a/src/Curve/Weierstrass/BN254A.hs +++ b/src/Curve/Weierstrass/BN254A.hs @@ -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 #-} diff --git a/src/Curve/Weierstrass/BN254AT.hs b/src/Curve/Weierstrass/BN254AT.hs --- a/src/Curve/Weierstrass/BN254AT.hs +++ b/src/Curve/Weierstrass/BN254AT.hs @@ -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 #-} diff --git a/src/Curve/Weierstrass/BN254B.hs b/src/Curve/Weierstrass/BN254B.hs --- a/src/Curve/Weierstrass/BN254B.hs +++ b/src/Curve/Weierstrass/BN254B.hs @@ -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 #-} diff --git a/src/Curve/Weierstrass/BN254BT.hs b/src/Curve/Weierstrass/BN254BT.hs --- a/src/Curve/Weierstrass/BN254BT.hs +++ b/src/Curve/Weierstrass/BN254BT.hs @@ -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 #-} diff --git a/src/Curve/Weierstrass/BN254T.hs b/src/Curve/Weierstrass/BN254T.hs --- a/src/Curve/Weierstrass/BN254T.hs +++ b/src/Curve/Weierstrass/BN254T.hs @@ -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 #-} diff --git a/src/Curve/Weierstrass/BN256.hs b/src/Curve/Weierstrass/BN256.hs --- a/src/Curve/Weierstrass/BN256.hs +++ b/src/Curve/Weierstrass/BN256.hs @@ -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 #-} diff --git a/src/Curve/Weierstrass/BN384.hs b/src/Curve/Weierstrass/BN384.hs --- a/src/Curve/Weierstrass/BN384.hs +++ b/src/Curve/Weierstrass/BN384.hs @@ -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 #-} diff --git a/src/Curve/Weierstrass/BN462.hs b/src/Curve/Weierstrass/BN462.hs --- a/src/Curve/Weierstrass/BN462.hs +++ b/src/Curve/Weierstrass/BN462.hs @@ -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 #-} diff --git a/src/Curve/Weierstrass/BN462T.hs b/src/Curve/Weierstrass/BN462T.hs --- a/src/Curve/Weierstrass/BN462T.hs +++ b/src/Curve/Weierstrass/BN462T.hs @@ -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 #-} diff --git a/src/Curve/Weierstrass/BN512.hs b/src/Curve/Weierstrass/BN512.hs --- a/src/Curve/Weierstrass/BN512.hs +++ b/src/Curve/Weierstrass/BN512.hs @@ -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 #-} diff --git a/src/Curve/Weierstrass/BrainpoolP160R1.hs b/src/Curve/Weierstrass/BrainpoolP160R1.hs --- a/src/Curve/Weierstrass/BrainpoolP160R1.hs +++ b/src/Curve/Weierstrass/BrainpoolP160R1.hs @@ -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 #-} diff --git a/src/Curve/Weierstrass/BrainpoolP160T1.hs b/src/Curve/Weierstrass/BrainpoolP160T1.hs --- a/src/Curve/Weierstrass/BrainpoolP160T1.hs +++ b/src/Curve/Weierstrass/BrainpoolP160T1.hs @@ -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 #-} diff --git a/src/Curve/Weierstrass/BrainpoolP192R1.hs b/src/Curve/Weierstrass/BrainpoolP192R1.hs --- a/src/Curve/Weierstrass/BrainpoolP192R1.hs +++ b/src/Curve/Weierstrass/BrainpoolP192R1.hs @@ -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 #-} diff --git a/src/Curve/Weierstrass/BrainpoolP192T1.hs b/src/Curve/Weierstrass/BrainpoolP192T1.hs --- a/src/Curve/Weierstrass/BrainpoolP192T1.hs +++ b/src/Curve/Weierstrass/BrainpoolP192T1.hs @@ -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 #-} diff --git a/src/Curve/Weierstrass/BrainpoolP224R1.hs b/src/Curve/Weierstrass/BrainpoolP224R1.hs --- a/src/Curve/Weierstrass/BrainpoolP224R1.hs +++ b/src/Curve/Weierstrass/BrainpoolP224R1.hs @@ -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 #-} diff --git a/src/Curve/Weierstrass/BrainpoolP224T1.hs b/src/Curve/Weierstrass/BrainpoolP224T1.hs --- a/src/Curve/Weierstrass/BrainpoolP224T1.hs +++ b/src/Curve/Weierstrass/BrainpoolP224T1.hs @@ -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 #-} diff --git a/src/Curve/Weierstrass/BrainpoolP256R1.hs b/src/Curve/Weierstrass/BrainpoolP256R1.hs --- a/src/Curve/Weierstrass/BrainpoolP256R1.hs +++ b/src/Curve/Weierstrass/BrainpoolP256R1.hs @@ -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 #-} diff --git a/src/Curve/Weierstrass/BrainpoolP256T1.hs b/src/Curve/Weierstrass/BrainpoolP256T1.hs --- a/src/Curve/Weierstrass/BrainpoolP256T1.hs +++ b/src/Curve/Weierstrass/BrainpoolP256T1.hs @@ -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 #-} diff --git a/src/Curve/Weierstrass/BrainpoolP320R1.hs b/src/Curve/Weierstrass/BrainpoolP320R1.hs --- a/src/Curve/Weierstrass/BrainpoolP320R1.hs +++ b/src/Curve/Weierstrass/BrainpoolP320R1.hs @@ -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 #-} diff --git a/src/Curve/Weierstrass/BrainpoolP320T1.hs b/src/Curve/Weierstrass/BrainpoolP320T1.hs --- a/src/Curve/Weierstrass/BrainpoolP320T1.hs +++ b/src/Curve/Weierstrass/BrainpoolP320T1.hs @@ -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 #-} diff --git a/src/Curve/Weierstrass/BrainpoolP384R1.hs b/src/Curve/Weierstrass/BrainpoolP384R1.hs --- a/src/Curve/Weierstrass/BrainpoolP384R1.hs +++ b/src/Curve/Weierstrass/BrainpoolP384R1.hs @@ -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 #-} diff --git a/src/Curve/Weierstrass/BrainpoolP384T1.hs b/src/Curve/Weierstrass/BrainpoolP384T1.hs --- a/src/Curve/Weierstrass/BrainpoolP384T1.hs +++ b/src/Curve/Weierstrass/BrainpoolP384T1.hs @@ -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 #-} diff --git a/src/Curve/Weierstrass/BrainpoolP512R1.hs b/src/Curve/Weierstrass/BrainpoolP512R1.hs --- a/src/Curve/Weierstrass/BrainpoolP512R1.hs +++ b/src/Curve/Weierstrass/BrainpoolP512R1.hs @@ -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 #-} diff --git a/src/Curve/Weierstrass/BrainpoolP512T1.hs b/src/Curve/Weierstrass/BrainpoolP512T1.hs --- a/src/Curve/Weierstrass/BrainpoolP512T1.hs +++ b/src/Curve/Weierstrass/BrainpoolP512T1.hs @@ -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 #-} diff --git a/src/Curve/Weierstrass/SECP112R1.hs b/src/Curve/Weierstrass/SECP112R1.hs --- a/src/Curve/Weierstrass/SECP112R1.hs +++ b/src/Curve/Weierstrass/SECP112R1.hs @@ -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 #-} diff --git a/src/Curve/Weierstrass/SECP112R2.hs b/src/Curve/Weierstrass/SECP112R2.hs --- a/src/Curve/Weierstrass/SECP112R2.hs +++ b/src/Curve/Weierstrass/SECP112R2.hs @@ -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 #-} diff --git a/src/Curve/Weierstrass/SECP128R1.hs b/src/Curve/Weierstrass/SECP128R1.hs --- a/src/Curve/Weierstrass/SECP128R1.hs +++ b/src/Curve/Weierstrass/SECP128R1.hs @@ -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 #-} diff --git a/src/Curve/Weierstrass/SECP128R2.hs b/src/Curve/Weierstrass/SECP128R2.hs --- a/src/Curve/Weierstrass/SECP128R2.hs +++ b/src/Curve/Weierstrass/SECP128R2.hs @@ -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 #-} diff --git a/src/Curve/Weierstrass/SECP160K1.hs b/src/Curve/Weierstrass/SECP160K1.hs --- a/src/Curve/Weierstrass/SECP160K1.hs +++ b/src/Curve/Weierstrass/SECP160K1.hs @@ -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 #-} diff --git a/src/Curve/Weierstrass/SECP160R1.hs b/src/Curve/Weierstrass/SECP160R1.hs --- a/src/Curve/Weierstrass/SECP160R1.hs +++ b/src/Curve/Weierstrass/SECP160R1.hs @@ -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 #-} diff --git a/src/Curve/Weierstrass/SECP160R2.hs b/src/Curve/Weierstrass/SECP160R2.hs --- a/src/Curve/Weierstrass/SECP160R2.hs +++ b/src/Curve/Weierstrass/SECP160R2.hs @@ -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 #-} diff --git a/src/Curve/Weierstrass/SECP192K1.hs b/src/Curve/Weierstrass/SECP192K1.hs --- a/src/Curve/Weierstrass/SECP192K1.hs +++ b/src/Curve/Weierstrass/SECP192K1.hs @@ -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 #-} diff --git a/src/Curve/Weierstrass/SECP192R1.hs b/src/Curve/Weierstrass/SECP192R1.hs --- a/src/Curve/Weierstrass/SECP192R1.hs +++ b/src/Curve/Weierstrass/SECP192R1.hs @@ -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 #-} diff --git a/src/Curve/Weierstrass/SECP224K1.hs b/src/Curve/Weierstrass/SECP224K1.hs --- a/src/Curve/Weierstrass/SECP224K1.hs +++ b/src/Curve/Weierstrass/SECP224K1.hs @@ -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 #-} diff --git a/src/Curve/Weierstrass/SECP224R1.hs b/src/Curve/Weierstrass/SECP224R1.hs --- a/src/Curve/Weierstrass/SECP224R1.hs +++ b/src/Curve/Weierstrass/SECP224R1.hs @@ -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 #-} diff --git a/src/Curve/Weierstrass/SECP256K1.hs b/src/Curve/Weierstrass/SECP256K1.hs --- a/src/Curve/Weierstrass/SECP256K1.hs +++ b/src/Curve/Weierstrass/SECP256K1.hs @@ -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 #-} diff --git a/src/Curve/Weierstrass/SECP256R1.hs b/src/Curve/Weierstrass/SECP256R1.hs --- a/src/Curve/Weierstrass/SECP256R1.hs +++ b/src/Curve/Weierstrass/SECP256R1.hs @@ -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 #-} diff --git a/src/Curve/Weierstrass/SECP384R1.hs b/src/Curve/Weierstrass/SECP384R1.hs --- a/src/Curve/Weierstrass/SECP384R1.hs +++ b/src/Curve/Weierstrass/SECP384R1.hs @@ -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 #-} diff --git a/src/Curve/Weierstrass/SECP521R1.hs b/src/Curve/Weierstrass/SECP521R1.hs --- a/src/Curve/Weierstrass/SECP521R1.hs +++ b/src/Curve/Weierstrass/SECP521R1.hs @@ -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 #-} diff --git a/src/Group.hs b/src/Group.hs new file mode 100644 --- /dev/null +++ b/src/Group.hs @@ -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 #-} diff --git a/src/Group/Field.hs b/src/Group/Field.hs new file mode 100644 --- /dev/null +++ b/src/Group/Field.hs @@ -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." diff --git a/src/Group/Field/BN254TF.hs b/src/Group/Field/BN254TF.hs new file mode 100644 --- /dev/null +++ b/src/Group/Field/BN254TF.hs @@ -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 #-} diff --git a/tests/BinaryTests.hs b/tests/BinaryTests.hs --- a/tests/BinaryTests.hs +++ b/tests/BinaryTests.hs @@ -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 + ] diff --git a/tests/CurveTests.hs b/tests/CurveTests.hs deleted file mode 100644 --- a/tests/CurveTests.hs +++ /dev/null @@ -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] diff --git a/tests/EdwardsTests.hs b/tests/EdwardsTests.hs --- a/tests/EdwardsTests.hs +++ b/tests/EdwardsTests.hs @@ -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 + ] diff --git a/tests/FieldTests.hs b/tests/FieldTests.hs new file mode 100644 --- /dev/null +++ b/tests/FieldTests.hs @@ -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 + ] diff --git a/tests/GroupTests.hs b/tests/GroupTests.hs new file mode 100644 --- /dev/null +++ b/tests/GroupTests.hs @@ -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] diff --git a/tests/Main.hs b/tests/Main.hs --- a/tests/Main.hs +++ b/tests/Main.hs @@ -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] diff --git a/tests/MontgomeryTests.hs b/tests/MontgomeryTests.hs --- a/tests/MontgomeryTests.hs +++ b/tests/MontgomeryTests.hs @@ -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 + ] diff --git a/tests/WeierstrassTests.hs b/tests/WeierstrassTests.hs --- a/tests/WeierstrassTests.hs +++ b/tests/WeierstrassTests.hs @@ -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 + ]