module Crypto.Lol.Tests.ZqTests where
import Crypto.Lol
import Crypto.Lol.CRTrans
import Crypto.Lol.Tests
import Crypto.Lol.Utils.ShowType
import Control.Applicative
import Control.Monad.Random
import qualified Test.Framework as TF
zqTests :: _ => Proxy r -> TF.Test
zqTests p = testGroup (showType p) $ ($ p) <$> [
genTestArgs "(+)" prop_add,
genTestArgs "(*)" prop_mul,
genTestArgs "^-1" prop_recip,
genTestArgs "extension ring (*)" prop_mul_ext
]
prop_add :: forall r . (Ring r, Eq r) => LiftedMod r -> LiftedMod r -> Test r
prop_add (LMod x) (LMod y) = test $ fromIntegral (x + y) == (fromIntegral x + fromIntegral y :: r)
prop_mul :: forall r . (Ring r, Eq r) => LiftedInvertible r -> LiftedInvertible r -> Test r
prop_mul (LInv x) (LInv y) = test $ fromIntegral (x * y) == (fromIntegral x * fromIntegral y :: r)
prop_recip :: (Field r, Eq r) => Invertible r -> Test r
prop_recip (Invertible x) = test $ one == (x * recip x)
prop_mul_ext :: (CRTEmbed r, Eq r) => Invertible r -> Invertible r -> Test r
prop_mul_ext (Invertible x) (Invertible y) = test $
let z = x * y
z' = fromExt $ toExt x * toExt y
in z == z'
data LiftedMod r where
LMod :: (ToInteger (ModRep r)) => ModRep r -> LiftedMod r
instance (Mod r, Random (ModRep r), ToInteger (ModRep r))
=> Random (LiftedMod r) where
random =
let q = proxy modulus (Proxy::Proxy r)
in \g -> let (x,g') = randomR (0,q1) g in (LMod x, g')
randomR = error "randomR not defined for `LiftedMod`"
data LiftedInvertible r where
LInv :: (ToInteger (ModRep r)) => ModRep r -> LiftedInvertible r
instance (Mod r, Random (ModRep r), PID (ModRep r), ToInteger (ModRep r))
=> Random (LiftedInvertible r) where
random =
let q = proxy modulus (Proxy::Proxy r)
in \g -> let (x,g') = randomR (1,q1) g
in if gcd x q == 1 then (LInv x, g') else random g'
randomR = error "randomR not defined for `LiftedInvertible`"
newtype Invertible r = Invertible r
instance (Random (LiftedInvertible r), Ring r, ToInteger (ModRep r))
=> Random (Invertible r) where
random g =
let (LInv x :: LiftedInvertible r, g') = random g
in (Invertible $ fromIntegral x, g')
randomR = error "randomR not defined for `Invertible`"