spake2-0.2.0: tests/Groups.hs

{-# LANGUAGE TypeFamilies #-}
{-# LANGUAGE FlexibleContexts #-}
module Groups (tests) where

import Protolude hiding (group)

import Crypto.Error (CryptoFailable(..))
import Test.QuickCheck (Gen, (===), arbitrary, forAll, property)
import Test.Tasty (TestTree)
import Test.Tasty.Hspec (Spec, testSpec, describe, it, shouldBe)

import Crypto.Spake2.Group (AbelianGroup(..), Group(..))
import Crypto.Spake2.Groups
  ( IntegerGroup(..)
  , Ed25519(..)
  , i1024)
import qualified Crypto.Spake2.Groups.Ed25519 as Ed25519
import qualified Crypto.Spake2.Groups.IntegerGroup as IntegerGroup

tests :: IO TestTree
tests = testSpec "Groups" $ do
  describe "integer group" $
    allGroupProperties i1024 (makeScalar (subgroupOrder i1024)) (IntegerGroup.generator i1024)
  describe "Ed25519" $
    allGroupProperties Ed25519 (makeScalar Ed25519.l) Ed25519.generator

allGroupProperties
  :: (Show (Scalar group), Show (Element group), Eq (Scalar group), Eq (Element group), AbelianGroup group)
  => group
  -> Gen (Scalar group)
  -> Element group
  -> Spec
allGroupProperties group scalars base = do
  describe "is a group" $ groupProperties group (makeElement group scalars base)
  describe "is an abelian group" $ abelianGroupProperties group scalars base

groupProperties
  :: (Group group, Eq (Element group), Show (Element group))
  => group
  -> Gen (Element group)
  -> Spec
groupProperties group elements = do
  it "addition is associative" $ property $
    forAll (triples elements) $ \(x, y, z) -> elementAdd group (elementAdd group x y) z === elementAdd group x (elementAdd group y z)

  it "addition with inverse yields identity" $ property $
    forAll elements $ \x -> elementAdd group x (elementNegate group x) === groupIdentity group

  it "double negative is no-op" $ property $
    forAll elements $ \x -> elementNegate group (elementNegate group x) === x

  it "identity is its own inverse" $
    elementNegate group (groupIdentity group) `shouldBe` groupIdentity group

  it "subtraction is negated addition" $ property $
    forAll (pairs elements) $ \(x, y) -> elementSubtract group x y === elementAdd group x (elementNegate group y)

  it "right-hand addition with identity yields original" $ property $
    forAll elements $ \x -> elementAdd group x (groupIdentity group) === x

  it "left-hand addition with identity yields original" $ property $
    forAll elements $ \x -> elementAdd group (groupIdentity group) x === x

  it "element codec roundtrips" $ property $
    forAll elements $ \x -> let bytes = encodeElement group x :: ByteString
                            in decodeElement group bytes == CryptoPassed x


abelianGroupProperties
  :: (AbelianGroup group, Eq (Element group), Eq (Scalar group), Show (Element group), Show (Scalar group))
  => group
  -> Gen (Scalar group)
  -> Element group
  -> Spec
abelianGroupProperties group scalars base = do
  it "addition is commutative" $ property $
    forAll (pairs elements) $ \(x, y) -> elementAdd group x y === elementAdd group y x

  it "scalar to integer roundtrips" $ property $
    forAll scalars $ \n -> integerToScalar group (scalarToInteger group n) === n

  it "integer to scalar conversion" $ property $
    -- Doesn't roundtrip per se, because negative integers (for example) get
    -- turned into scalars within the subgroup range, losing the original
    -- information.
    \i -> integerToScalar group (scalarToInteger group (integerToScalar group i)) === integerToScalar group i

  it "scalar multiply by 0 is identity" $ property $
    forAll elements $ \x -> scalarMultiply group (integerToScalar group 0) x === groupIdentity group

  it "scalar multiply by 1 is original" $ property $
    forAll elements $ \x -> scalarMultiply group (integerToScalar group 1) x === x

  it "scalar multiply by 2 is equivalent to addition" $ property $
    forAll elements $ \x -> scalarMultiply group (integerToScalar group 2) x === elementAdd group x x

  where
    elements = makeElement group scalars base

-- | Generate pairs of a thing.
pairs :: Gen a -> Gen (a, a)
pairs gen = do
  x <- gen
  y <- gen
  pure (x, y)

-- | Generate triples of a thing.
triples :: Gen a -> Gen (a, a, a)
triples gen = do
  x <- gen
  y <- gen
  z <- gen
  pure (x, y, z)

makeScalar :: Integer -> Gen Integer
makeScalar k = do
  i <- arbitrary
  pure $ i `mod` k

makeElement :: AbelianGroup group => group -> Gen (Scalar group) -> Element group -> Gen (Element group)
makeElement group scalars base = do
  scalar <- scalars
  pure (scalarMultiply group scalar base)