{-# LANGUAGE AllowAmbiguousTypes #-}
{-# LANGUAGE TypeOperators       #-}

module Tests.Algebra.EllipticCurve (specEllipticCurve) where

import           Data.Foldable
import           Data.Proxy
import           GHC.TypeLits
import           Prelude                                     hiding (Num (..))
import           Test.Hspec
import           Test.QuickCheck                             hiding (scale)

import           ZkFold.Base.Algebra.Basic.Class
import           ZkFold.Base.Algebra.EllipticCurve.BLS12_381
import           ZkFold.Base.Algebra.EllipticCurve.BN254
import           ZkFold.Base.Algebra.EllipticCurve.Class
import           ZkFold.Base.Algebra.EllipticCurve.Ed25519
import           ZkFold.Base.Algebra.EllipticCurve.Pasta
import           ZkFold.Base.Algebra.EllipticCurve.PlutoEris
import           ZkFold.Base.Algebra.EllipticCurve.Secp256k1
import           ZkFold.Symbolic.Data.Eq                     (BooleanOf)

specEllipticCurve :: Spec
specEllipticCurve = do
  describe "secp256k1" $
    for_ secp256k1testVectors $ \(TestVector k x y) ->
      it "should match test vector" $ do
        let p, q :: Secp256k1_Point
            p = pointXY (fromConstant x) (fromConstant y)
            q = scale k pointGen
        p `shouldBe` q

  specEllipticCurveGenerator @Secp256k1_Point
  specEllipticCurveGenerator @BLS12_381_G1_Point
  specEllipticCurveGenerator @BLS12_381_G2_Point
  specEllipticCurveGenerator @BN254_G1_Point
  specEllipticCurveGenerator @BN254_G2_Point
  specEllipticCurveGenerator @Ed25519_Point
  specEllipticCurveGenerator @Pallas_Point
  specEllipticCurveGenerator @Vesta_Point
  specEllipticCurveGenerator @Pluto_Point
  specEllipticCurveGenerator @Eris_Point

specEllipticCurveGenerator
  :: forall point .
    ( EllipticCurve point
    , CyclicGroup point
    , Eq point
    , Show point
    , Arbitrary (ScalarFieldOf point)
    , Show (ScalarFieldOf point)
    , KnownSymbol (CurveOf point)
    , BooleanOf (BaseFieldOf point) ~ Bool
    ) => Spec
specEllipticCurveGenerator = do
  let curve = symbolVal (Proxy @(CurveOf point))
  describe (curve <> " curve specification") $ do
    describe "cyclic group generator" $ do
      let g = pointGen @point
      it "should be on the curve" $
        g `shouldSatisfy` isOnCurve
      it "should have the same order as the scalar field" $ do
        let coef = order @(ScalarFieldOf point)
        scale coef g `shouldBe` zero
      it "should be closed under scalar multiplication" $
        property $ \ (coef :: ScalarFieldOf point) ->
          isOnCurve (coef `scale` g)

data TestVector = TestVector
  { _k :: Natural -- scalar
  , _x :: Natural -- x coordinate of scaled generator point
  , _y :: Natural -- y coordinate of scaled generator point
  }

-- https://chuckbatson.wordpress.com/2014/11/26/secp256k1-test-vectors/
secp256k1testVectors :: [TestVector]
secp256k1testVectors =
  [ TestVector
    { _k = 1
    , _x = 0x79BE667EF9DCBBAC55A06295CE870B07029BFCDB2DCE28D959F2815B16F81798
    , _y = 0x483ADA7726A3C4655DA4FBFC0E1108A8FD17B448A68554199C47D08FFB10D4B8
    }

  , TestVector
    { _k = 2
    , _x = 0xC6047F9441ED7D6D3045406E95C07CD85C778E4B8CEF3CA7ABAC09B95C709EE5
    , _y = 0x1AE168FEA63DC339A3C58419466CEAEEF7F632653266D0E1236431A950CFE52A
    }

  , TestVector
    { _k = 3
    , _x = 0xF9308A019258C31049344F85F89D5229B531C845836F99B08601F113BCE036F9
    , _y = 0x388F7B0F632DE8140FE337E62A37F3566500A99934C2231B6CB9FD7584B8E672
    }

  , TestVector
    { _k = 4
    , _x = 0xE493DBF1C10D80F3581E4904930B1404CC6C13900EE0758474FA94ABE8C4CD13
    , _y = 0x51ED993EA0D455B75642E2098EA51448D967AE33BFBDFE40CFE97BDC47739922
    }

  , TestVector
    { _k = 5
    , _x = 0x2F8BDE4D1A07209355B4A7250A5C5128E88B84BDDC619AB7CBA8D569B240EFE4
    , _y = 0xD8AC222636E5E3D6D4DBA9DDA6C9C426F788271BAB0D6840DCA87D3AA6AC62D6
    }

  , TestVector
    { _k = 6
    , _x = 0xFFF97BD5755EEEA420453A14355235D382F6472F8568A18B2F057A1460297556
    , _y = 0xAE12777AACFBB620F3BE96017F45C560DE80F0F6518FE4A03C870C36B075F297
    }

  , TestVector
    { _k = 7
    , _x = 0x5CBDF0646E5DB4EAA398F365F2EA7A0E3D419B7E0330E39CE92BDDEDCAC4F9BC
    , _y = 0x6AEBCA40BA255960A3178D6D861A54DBA813D0B813FDE7B5A5082628087264DA
    }

  , TestVector
    { _k = 8
    , _x = 0x2F01E5E15CCA351DAFF3843FB70F3C2F0A1BDD05E5AF888A67784EF3E10A2A01
    , _y = 0x5C4DA8A741539949293D082A132D13B4C2E213D6BA5B7617B5DA2CB76CBDE904
    }

  , TestVector
    { _k = 9
    , _x = 0xACD484E2F0C7F65309AD178A9F559ABDE09796974C57E714C35F110DFC27CCBE
    , _y = 0xCC338921B0A7D9FD64380971763B61E9ADD888A4375F8E0F05CC262AC64F9C37
    }

  , TestVector
    { _k = 10
    , _x = 0xA0434D9E47F3C86235477C7B1AE6AE5D3442D49B1943C2B752A68E2A47E247C7
    , _y = 0x893ABA425419BC27A3B6C7E693A24C696F794C2ED877A1593CBEE53B037368D7
    }

  , TestVector
    { _k = 11
    , _x = 0x774AE7F858A9411E5EF4246B70C65AAC5649980BE5C17891BBEC17895DA008CB
    , _y = 0xD984A032EB6B5E190243DD56D7B7B365372DB1E2DFF9D6A8301D74C9C953C61B
    }

  , TestVector
    { _k = 12
    , _x = 0xD01115D548E7561B15C38F004D734633687CF4419620095BC5B0F47070AFE85A
    , _y = 0xA9F34FFDC815E0D7A8B64537E17BD81579238C5DD9A86D526B051B13F4062327
    }

  , TestVector
    { _k = 13
    , _x = 0xF28773C2D975288BC7D1D205C3748651B075FBC6610E58CDDEEDDF8F19405AA8
    , _y = 0x0AB0902E8D880A89758212EB65CDAF473A1A06DA521FA91F29B5CB52DB03ED81
    }

  , TestVector
    { _k = 14
    , _x = 0x499FDF9E895E719CFD64E67F07D38E3226AA7B63678949E6E49B241A60E823E4
    , _y = 0xCAC2F6C4B54E855190F044E4A7B3D464464279C27A3F95BCC65F40D403A13F5B
    }

  , TestVector
    { _k = 15
    , _x = 0xD7924D4F7D43EA965A465AE3095FF41131E5946F3C85F79E44ADBCF8E27E080E
    , _y = 0x581E2872A86C72A683842EC228CC6DEFEA40AF2BD896D3A5C504DC9FF6A26B58
    }

  , TestVector
    { _k = 16
    , _x = 0xE60FCE93B59E9EC53011AABC21C23E97B2A31369B87A5AE9C44EE89E2A6DEC0A
    , _y = 0xF7E3507399E595929DB99F34F57937101296891E44D23F0BE1F32CCE69616821
    }

  , TestVector
    { _k = 17
    , _x = 0xDEFDEA4CDB677750A420FEE807EACF21EB9898AE79B9768766E4FAA04A2D4A34
    , _y = 0x4211AB0694635168E997B0EAD2A93DAECED1F4A04A95C0F6CFB199F69E56EB77
    }

  , TestVector
    { _k = 18
    , _x = 0x5601570CB47F238D2B0286DB4A990FA0F3BA28D1A319F5E7CF55C2A2444DA7CC
    , _y = 0xC136C1DC0CBEB930E9E298043589351D81D8E0BC736AE2A1F5192E5E8B061D58
    }

  , TestVector
    { _k = 19
    , _x = 0x2B4EA0A797A443D293EF5CFF444F4979F06ACFEBD7E86D277475656138385B6C
    , _y = 0x85E89BC037945D93B343083B5A1C86131A01F60C50269763B570C854E5C09B7A
    }

  , TestVector
    { _k = 20
    , _x = 0x4CE119C96E2FA357200B559B2F7DD5A5F02D5290AFF74B03F3E471B273211C97
    , _y = 0x12BA26DCB10EC1625DA61FA10A844C676162948271D96967450288EE9233DC3A
    }

  , TestVector
    { _k = 112233445566778899
    , _x = 0xA90CC3D3F3E146DAADFC74CA1372207CB4B725AE708CEF713A98EDD73D99EF29
    , _y = 0x5A79D6B289610C68BC3B47F3D72F9788A26A06868B4D8E433E1E2AD76FB7DC76
    }

  , TestVector
    { _k = 112233445566778899112233445566778899
    , _x = 0xE5A2636BCFD412EBF36EC45B19BFB68A1BC5F8632E678132B885F7DF99C5E9B3
    , _y = 0x736C1CE161AE27B405CAFD2A7520370153C2C861AC51D6C1D5985D9606B45F39
    }

  , TestVector
    { _k = 28948022309329048855892746252171976963209391069768726095651290785379540373584
    , _x = 0xA6B594B38FB3E77C6EDF78161FADE2041F4E09FD8497DB776E546C41567FEB3C
    , _y = 0x71444009192228730CD8237A490FEBA2AFE3D27D7CC1136BC97E439D13330D55
    }

  , TestVector
    { _k = 57896044618658097711785492504343953926418782139537452191302581570759080747168
    , _x = 0x00000000000000000000003B78CE563F89A0ED9414F5AA28AD0D96D6795F9C63
    , _y = 0x3F3979BF72AE8202983DC989AEC7F2FF2ED91BDD69CE02FC0700CA100E59DDF3
    }

  , TestVector
    { _k = 86844066927987146567678238756515930889628173209306178286953872356138621120752
    , _x = 0xE24CE4BEEE294AA6350FAA67512B99D388693AE4E7F53D19882A6EA169FC1CE1
    , _y = 0x8B71E83545FC2B5872589F99D948C03108D36797C4DE363EBD3FF6A9E1A95B10
    }

  , TestVector
    { _k = 115792089237316195423570985008687907852837564279074904382605163141518161494317
    , _x = 0x4CE119C96E2FA357200B559B2F7DD5A5F02D5290AFF74B03F3E471B273211C97
    , _y = 0xED45D9234EF13E9DA259E05EF57BB3989E9D6B7D8E269698BAFD77106DCC1FF5
    }

  , TestVector
    { _k = 115792089237316195423570985008687907852837564279074904382605163141518161494318
    , _x = 0x2B4EA0A797A443D293EF5CFF444F4979F06ACFEBD7E86D277475656138385B6C
    , _y = 0x7A17643FC86BA26C4CBCF7C4A5E379ECE5FE09F3AFD9689C4A8F37AA1A3F60B5
    }

  , TestVector
    { _k = 115792089237316195423570985008687907852837564279074904382605163141518161494319
    , _x = 0x5601570CB47F238D2B0286DB4A990FA0F3BA28D1A319F5E7CF55C2A2444DA7CC
    , _y = 0x3EC93E23F34146CF161D67FBCA76CAE27E271F438C951D5E0AE6D1A074F9DED7
    }

  , TestVector
    { _k = 115792089237316195423570985008687907852837564279074904382605163141518161494320
    , _x = 0xDEFDEA4CDB677750A420FEE807EACF21EB9898AE79B9768766E4FAA04A2D4A34
    , _y = 0xBDEE54F96B9CAE9716684F152D56C251312E0B5FB56A3F09304E660861A910B8
    }

  , TestVector
    { _k = 115792089237316195423570985008687907852837564279074904382605163141518161494321
    , _x = 0xE60FCE93B59E9EC53011AABC21C23E97B2A31369B87A5AE9C44EE89E2A6DEC0A
    , _y = 0x081CAF8C661A6A6D624660CB0A86C8EFED6976E1BB2DC0F41E0CD330969E940E
    }

  , TestVector
    { _k = 115792089237316195423570985008687907852837564279074904382605163141518161494322
    , _x = 0xD7924D4F7D43EA965A465AE3095FF41131E5946F3C85F79E44ADBCF8E27E080E
    , _y = 0xA7E1D78D57938D597C7BD13DD733921015BF50D427692C5A3AFB235F095D90D7
    }

  , TestVector
    { _k = 115792089237316195423570985008687907852837564279074904382605163141518161494323
    , _x = 0x499FDF9E895E719CFD64E67F07D38E3226AA7B63678949E6E49B241A60E823E4
    , _y = 0x353D093B4AB17AAE6F0FBB1B584C2B9BB9BD863D85C06A4339A0BF2AFC5EBCD4
    }

  , TestVector
    { _k = 115792089237316195423570985008687907852837564279074904382605163141518161494324
    , _x = 0xF28773C2D975288BC7D1D205C3748651B075FBC6610E58CDDEEDDF8F19405AA8
    , _y = 0xF54F6FD17277F5768A7DED149A3250B8C5E5F925ADE056E0D64A34AC24FC0EAE
    }

  , TestVector
    { _k = 115792089237316195423570985008687907852837564279074904382605163141518161494325
    , _x = 0xD01115D548E7561B15C38F004D734633687CF4419620095BC5B0F47070AFE85A
    , _y = 0x560CB00237EA1F285749BAC81E8427EA86DC73A2265792AD94FAE4EB0BF9D908
    }

  , TestVector
    { _k = 115792089237316195423570985008687907852837564279074904382605163141518161494326
    , _x = 0x774AE7F858A9411E5EF4246B70C65AAC5649980BE5C17891BBEC17895DA008CB
    , _y = 0x267B5FCD1494A1E6FDBC22A928484C9AC8D24E1D20062957CFE28B3536AC3614
    }

  , TestVector
    { _k = 115792089237316195423570985008687907852837564279074904382605163141518161494327
    , _x = 0xA0434D9E47F3C86235477C7B1AE6AE5D3442D49B1943C2B752A68E2A47E247C7
    , _y = 0x76C545BDABE643D85C4938196C5DB3969086B3D127885EA6C3411AC3FC8C9358
    }

  , TestVector
    { _k = 115792089237316195423570985008687907852837564279074904382605163141518161494328
    , _x = 0xACD484E2F0C7F65309AD178A9F559ABDE09796974C57E714C35F110DFC27CCBE
    , _y = 0x33CC76DE4F5826029BC7F68E89C49E165227775BC8A071F0FA33D9D439B05FF8
    }

  , TestVector
    { _k = 115792089237316195423570985008687907852837564279074904382605163141518161494329
    , _x = 0x2F01E5E15CCA351DAFF3843FB70F3C2F0A1BDD05E5AF888A67784EF3E10A2A01
    , _y = 0xA3B25758BEAC66B6D6C2F7D5ECD2EC4B3D1DEC2945A489E84A25D3479342132B
    }

  , TestVector
    { _k = 115792089237316195423570985008687907852837564279074904382605163141518161494330
    , _x = 0x5CBDF0646E5DB4EAA398F365F2EA7A0E3D419B7E0330E39CE92BDDEDCAC4F9BC
    , _y = 0x951435BF45DAA69F5CE8729279E5AB2457EC2F47EC02184A5AF7D9D6F78D9755
    }

  , TestVector
    { _k = 115792089237316195423570985008687907852837564279074904382605163141518161494331
    , _x = 0xFFF97BD5755EEEA420453A14355235D382F6472F8568A18B2F057A1460297556
    , _y = 0x51ED8885530449DF0C4169FE80BA3A9F217F0F09AE701B5FC378F3C84F8A0998
    }

  , TestVector
    { _k = 115792089237316195423570985008687907852837564279074904382605163141518161494332
    , _x = 0x2F8BDE4D1A07209355B4A7250A5C5128E88B84BDDC619AB7CBA8D569B240EFE4
    , _y = 0x2753DDD9C91A1C292B24562259363BD90877D8E454F297BF235782C459539959
    }

  , TestVector
    { _k = 115792089237316195423570985008687907852837564279074904382605163141518161494333
    , _x = 0xE493DBF1C10D80F3581E4904930B1404CC6C13900EE0758474FA94ABE8C4CD13
    , _y = 0xAE1266C15F2BAA48A9BD1DF6715AEBB7269851CC404201BF30168422B88C630D
    }

  , TestVector
    { _k = 115792089237316195423570985008687907852837564279074904382605163141518161494334
    , _x = 0xF9308A019258C31049344F85F89D5229B531C845836F99B08601F113BCE036F9
    , _y = 0xC77084F09CD217EBF01CC819D5C80CA99AFF5666CB3DDCE4934602897B4715BD
    }

  , TestVector
    { _k = 115792089237316195423570985008687907852837564279074904382605163141518161494335
    , _x = 0xC6047F9441ED7D6D3045406E95C07CD85C778E4B8CEF3CA7ABAC09B95C709EE5
    , _y = 0xE51E970159C23CC65C3A7BE6B99315110809CD9ACD992F1EDC9BCE55AF301705
    }

  , TestVector
    { _k = 115792089237316195423570985008687907852837564279074904382605163141518161494336
    , _x = 0x79BE667EF9DCBBAC55A06295CE870B07029BFCDB2DCE28D959F2815B16F81798
    , _y = 0xB7C52588D95C3B9AA25B0403F1EEF75702E84BB7597AABE663B82F6F04EF2777
    }
  ]