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{-# LANGUAGE OverloadedStrings #-}
{-# LANGUAGE ScopedTypeVariables #-}
module KAT_PubKey.P256 (tests) where
import qualified Crypto.PubKey.ECC.Types as ECC
import qualified Crypto.PubKey.ECC.Prim as ECC
import qualified Crypto.PubKey.ECC.P256 as P256
import Data.ByteArray (Bytes)
import Crypto.Number.Serialize (i2ospOf, os2ip)
import Crypto.Number.ModArithmetic (inverseCoprimes)
import Crypto.Error
import Imports
newtype P256Scalar = P256Scalar Integer
deriving (Show,Eq,Ord)
instance Arbitrary P256Scalar where
-- Cover the full range up to 2^256-1 except 0 and curveN. To test edge
-- cases with arithmetic functions, some values close to 0, curveN and
-- 2^256 are given higher frequency.
arbitrary = P256Scalar <$> oneof
[ choose (1, w)
, choose (w + 1, curveN - w - 1)
, choose (curveN - w, curveN - 1)
, choose (curveN + 1, curveN + w)
, choose (curveN + w + 1, high - w - 1)
, choose (high - w, high - 1)
]
where high = 2^(256 :: Int)
w = 100
curve = ECC.getCurveByName ECC.SEC_p256r1
curveN = ECC.ecc_n . ECC.common_curve $ curve
curveGen = ECC.ecc_g . ECC.common_curve $ curve
pointP256ToECC :: P256.Point -> ECC.Point
pointP256ToECC = uncurry ECC.Point . P256.pointToIntegers
i2ospScalar :: Integer -> Bytes
i2ospScalar i =
case i2ospOf 32 i of
Nothing -> error "invalid size of P256 scalar"
Just b -> b
unP256Scalar :: P256Scalar -> P256.Scalar
unP256Scalar (P256Scalar r) =
let rBytes = i2ospScalar r
in case P256.scalarFromBinary rBytes of
CryptoFailed err -> error ("cannot convert scalar: " ++ show err)
CryptoPassed scalar -> scalar
unP256 :: P256Scalar -> Integer
unP256 (P256Scalar r) = r
modP256Scalar :: P256Scalar -> P256Scalar
modP256Scalar (P256Scalar r) = P256Scalar (r `mod` curveN)
p256ScalarToInteger :: P256.Scalar -> Integer
p256ScalarToInteger s = os2ip (P256.scalarToBinary s :: Bytes)
xS = 0xde2444bebc8d36e682edd27e0f271508617519b3221a8fa0b77cab3989da97c9
yS = 0xc093ae7ff36e5380fc01a5aad1e66659702de80f53cec576b6350b243042a256
xT = 0x55a8b00f8da1d44e62f6b3b25316212e39540dc861c89575bb8cf92e35e0986b
yT = 0x5421c3209c2d6c704835d82ac4c3dd90f61a8a52598b9e7ab656e9d8c8b24316
xR = 0x72b13dd4354b6b81745195e98cc5ba6970349191ac476bd4553cf35a545a067e
yR = 0x8d585cbb2e1327d75241a8a122d7620dc33b13315aa5c9d46d013011744ac264
tests = testGroup "P256"
[ testGroup "scalar"
[ testProperty "marshalling" $ \(QAInteger r) ->
let rBytes = i2ospScalar r
in case P256.scalarFromBinary rBytes of
CryptoFailed err -> error (show err)
CryptoPassed scalar -> rBytes `propertyEq` P256.scalarToBinary scalar
, testProperty "add" $ \r1 r2 ->
let r = (unP256 r1 + unP256 r2) `mod` curveN
r' = P256.scalarAdd (unP256Scalar r1) (unP256Scalar r2)
in r `propertyEq` p256ScalarToInteger r'
, testProperty "add0" $ \r ->
let v = unP256 r `mod` curveN
v' = P256.scalarAdd (unP256Scalar r) P256.scalarZero
in v `propertyEq` p256ScalarToInteger v'
, testProperty "sub" $ \r1 r2 ->
let r = (unP256 r1 - unP256 r2) `mod` curveN
r' = P256.scalarSub (unP256Scalar r1) (unP256Scalar r2)
v = (unP256 r2 - unP256 r1) `mod` curveN
v' = P256.scalarSub (unP256Scalar r2) (unP256Scalar r1)
in propertyHold
[ eqTest "r1-r2" r (p256ScalarToInteger r')
, eqTest "r2-r1" v (p256ScalarToInteger v')
]
, testProperty "sub0" $ \r ->
let v = unP256 r `mod` curveN
v' = P256.scalarSub (unP256Scalar r) P256.scalarZero
in v `propertyEq` p256ScalarToInteger v'
, testProperty "mul" $ \r1 r2 ->
let r = (unP256 r1 * unP256 r2) `mod` curveN
r' = P256.scalarMul (unP256Scalar r1) (unP256Scalar r2)
in r `propertyEq` p256ScalarToInteger r'
, testProperty "inv" $ \r' ->
let inv = inverseCoprimes (unP256 r') curveN
inv' = P256.scalarInv (unP256Scalar r')
in unP256 r' /= 0 ==> inv `propertyEq` p256ScalarToInteger inv'
, testProperty "inv-safe" $ \r' ->
let inv = P256.scalarInv (unP256Scalar r')
inv' = P256.scalarInvSafe (unP256Scalar r')
in unP256 r' /= 0 ==> inv `propertyEq` inv'
, testProperty "inv-safe-mul" $ \r' ->
let inv = P256.scalarInvSafe (unP256Scalar r')
res = P256.scalarMul (unP256Scalar r') inv
in unP256 r' /= 0 ==> 1 `propertyEq` p256ScalarToInteger res
, testProperty "inv-safe-zero" $
let inv0 = P256.scalarInvSafe P256.scalarZero
invN = P256.scalarInvSafe P256.scalarN
in propertyHold [ eqTest "scalarZero" P256.scalarZero inv0
, eqTest "scalarN" P256.scalarZero invN
]
]
, testGroup "point"
[ testProperty "marshalling" $ \rx ry ->
let p = P256.pointFromIntegers (unP256 rx, unP256 ry)
b = P256.pointToBinary p :: Bytes
p' = P256.unsafePointFromBinary b
in propertyHold [ eqTest "point" (CryptoPassed p) p' ]
, testProperty "marshalling-integer" $ \rx ry ->
let p = P256.pointFromIntegers (unP256 rx, unP256 ry)
(x,y) = P256.pointToIntegers p
in propertyHold [ eqTest "x" (unP256 rx) x, eqTest "y" (unP256 ry) y ]
, testCase "valid-point-1" $ casePointIsValid (xS,yS)
, testCase "valid-point-2" $ casePointIsValid (xR,yR)
, testCase "valid-point-3" $ casePointIsValid (xT,yT)
, testCase "point-add-1" $
let s = P256.pointFromIntegers (xS, yS)
t = P256.pointFromIntegers (xT, yT)
r = P256.pointFromIntegers (xR, yR)
in r @=? P256.pointAdd s t
, testProperty "lift-to-curve" propertyLiftToCurve
, testProperty "point-add" propertyPointAdd
, testProperty "point-negate" propertyPointNegate
, testProperty "point-mul" propertyPointMul
, testProperty "infinity" $
let gN = P256.toPoint P256.scalarN
g1 = P256.pointBase
in propertyHold [ eqTest "zero" True (P256.pointIsAtInfinity gN)
, eqTest "base" False (P256.pointIsAtInfinity g1)
]
]
]
where
casePointIsValid pointTuple =
let s = P256.pointFromIntegers pointTuple in True @=? P256.pointIsValid s
propertyLiftToCurve r =
let p = P256.toPoint (unP256Scalar r)
(x,y) = P256.pointToIntegers p
pEcc = ECC.pointMul curve (unP256 r) curveGen
in pEcc `propertyEq` ECC.Point x y
propertyPointAdd r1 r2 =
let p1 = P256.toPoint (unP256Scalar r1)
p2 = P256.toPoint (unP256Scalar r2)
pe1 = ECC.pointMul curve (unP256 r1) curveGen
pe2 = ECC.pointMul curve (unP256 r2) curveGen
pR = P256.toPoint (P256.scalarAdd (unP256Scalar r1) (unP256Scalar r2))
peR = ECC.pointAdd curve pe1 pe2
in (unP256 r1 + unP256 r2) `mod` curveN /= 0 ==>
propertyHold [ eqTest "p256" pR (P256.pointAdd p1 p2)
, eqTest "ecc" peR (pointP256ToECC pR)
]
propertyPointNegate r =
let p = P256.toPoint (unP256Scalar r)
pe = ECC.pointMul curve (unP256 r) curveGen
pR = P256.pointNegate p
in ECC.pointNegate curve pe `propertyEq` pointP256ToECC pR
propertyPointMul s' r' =
let s = modP256Scalar s'
r = modP256Scalar r'
p = P256.toPoint (unP256Scalar r)
pe = ECC.pointMul curve (unP256 r) curveGen
pR = P256.toPoint (P256.scalarMul (unP256Scalar s) (unP256Scalar r))
peR = ECC.pointMul curve (unP256 s) pe
in propertyHold [ eqTest "p256" pR (P256.pointMul (unP256Scalar s) p)
, eqTest "ecc" peR (pointP256ToECC pR)
]
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