```{-# LANGUAGE DeriveDataTypeable #-}
-- |
-- Module      : Crypto.Types.PubKey.ECC
-- Maintainer  : Vincent Hanquez <vincent@snarc.org>
-- Stability   : Experimental
-- Portability : Excellent
--
module Crypto.Types.PubKey.ECC
( Curve(..)
, Point(..)
, CurveBinary(..)
, CurvePrime(..)
, ecc_fx
, ecc_p
, CurveCommon(..)
-- * recommended curves definition
, CurveName(..)
, getCurveByName
) where

import Data.Data

-- | Define either a binary curve or a prime curve.
data Curve = CurveF2M CurveBinary -- ^ 𝔽(2^m)
| CurveFP  CurvePrime  -- ^ 𝔽p

-- | Define a point on a curve
data Point = Point
{ point_x :: Integer
, point_y :: Integer

-- | Define an elliptic curve in 𝔽(2^m)
-- The first parameter is a bitfield representing the
-- f(x) polynomial.
data CurveBinary = CurveBinary Integer CurveCommon

-- | Define an elliptic curve in 𝔽p
--
-- the first parameter is a prime number
data CurvePrime = CurvePrime Integer CurveCommon

-- | Polynomial representing the characteristic of a CurveBinary.
ecc_fx :: CurveBinary -> Integer
ecc_fx (CurveBinary fx _) = fx

-- | Prime number representing the characteristic of a CurvePrime.
ecc_p :: CurvePrime -> Integer
ecc_p (CurvePrime p _) = p

-- | Define common parameters in a curve definition
-- of the form: y^2 = x^3 + ax + b
data CurveCommon = CurveCommon
{ ecc_a :: Integer -- ^ curve parameter a
, ecc_b :: Integer -- ^ curve parameter b
, ecc_g :: Point   -- ^ base point
, ecc_n :: Integer -- ^ order of G
, ecc_h :: Integer -- ^ cofactor

-- | Define names for known recommended curves
data CurveName =
SEC_p112r1
| SEC_p112r2
| SEC_p128r1
| SEC_p128r2
| SEC_p160k1
| SEC_p160r1
| SEC_p160r2
| SEC_p192k1
| SEC_p192r1
| SEC_p224k1
| SEC_p224r1
| SEC_p256k1
| SEC_p256r1
| SEC_p384r1
| SEC_p521r1
| SEC_t113r1
| SEC_t113r2
| SEC_t131r1
| SEC_t131r2
| SEC_t163k1
| SEC_t163r1
| SEC_t163r2
| SEC_t193r1
| SEC_t193r2
| SEC_t233k1
| SEC_t233r1
| SEC_t239k1
| SEC_t283k1
| SEC_t283r1
| SEC_t409k1
| SEC_t409r1
| SEC_t571k1
| SEC_t571r1
deriving (Show,Eq,Ord)

-- | get the curve definition associated with a recommended known curve name.
getCurveByName :: CurveName -> Curve
getCurveByName SEC_p112r1 = CurveFP  \$ CurvePrime
(CurveCommon
, ecc_b = 0x659ef8ba043916eede8911702b22
, ecc_g = Point { point_x = 0x09487239995a5ee76b55f9c2f098
, point_y = 0xa89ce5af8724c0a23e0e0ff77500
}
, ecc_n = 0xdb7c2abf62e35e7628dfac6561c5
, ecc_h = 1
})
getCurveByName SEC_p112r2 = CurveFP  \$ CurvePrime
(CurveCommon
{ ecc_a = 0x6127c24c05f38a0aaaf65c0ef02c
, ecc_b = 0x51def1815db5ed74fcc34c85d709
, ecc_g = Point { point_x = 0x4ba30ab5e892b4e1649dd0928643
}
, ecc_n = 0x36df0aafd8b8d7597ca10520d04b
, ecc_h = 4
})
getCurveByName SEC_p128r1 = CurveFP  \$ CurvePrime
0xfffffffdffffffffffffffffffffffff
(CurveCommon
{ ecc_a = 0xfffffffdfffffffffffffffffffffffc
, ecc_b = 0xe87579c11079f43dd824993c2cee5ed3
, ecc_g = Point { point_x = 0x161ff7528b899b2d0c28607ca52c5b86
, point_y = 0xcf5ac8395bafeb13c02da292dded7a83
}
, ecc_n = 0xfffffffe0000000075a30d1b9038a115
, ecc_h = 1
})
getCurveByName SEC_p128r2 = CurveFP  \$ CurvePrime
0xfffffffdffffffffffffffffffffffff
(CurveCommon
{ ecc_a = 0xd6031998d1b3bbfebf59cc9bbff9aee1
, ecc_b = 0x5eeefca380d02919dc2c6558bb6d8a5d
, ecc_g = Point { point_x = 0x7b6aa5d85e572983e6fb32a7cdebc140
, point_y = 0x27b6916a894d3aee7106fe805fc34b44
}
, ecc_n = 0x3fffffff7fffffffbe0024720613b5a3
, ecc_h = 4
})
getCurveByName SEC_p160k1 = CurveFP  \$ CurvePrime
0x00fffffffffffffffffffffffffffffffeffffac73
(CurveCommon
{ ecc_a = 0x000000000000000000000000000000000000000000
, ecc_b = 0x000000000000000000000000000000000000000007
, ecc_g = Point { point_x = 0x003b4c382ce37aa192a4019e763036f4f5dd4d7ebb
, point_y = 0x00938cf935318fdced6bc28286531733c3f03c4fee
}
, ecc_n = 0x0100000000000000000001b8fa16dfab9aca16b6b3
, ecc_h = 1
})
getCurveByName SEC_p160r1 = CurveFP  \$ CurvePrime
0x00ffffffffffffffffffffffffffffffff7fffffff
(CurveCommon
{ ecc_a = 0x00ffffffffffffffffffffffffffffffff7ffffffc
, ecc_g = Point { point_x = 0x004a96b5688ef573284664698968c38bb913cbfc82
, point_y = 0x0023a628553168947d59dcc912042351377ac5fb32
}
, ecc_n = 0x0100000000000000000001f4c8f927aed3ca752257
, ecc_h = 1
})
getCurveByName SEC_p160r2 = CurveFP  \$ CurvePrime
0x00fffffffffffffffffffffffffffffffeffffac73
(CurveCommon
{ ecc_a = 0x00fffffffffffffffffffffffffffffffeffffac70
, ecc_b = 0x00b4e134d3fb59eb8bab57274904664d5af50388ba
, ecc_g = Point { point_x = 0x0052dcb034293a117e1f4ff11b30f7199d3144ce6d
, point_y = 0x00feaffef2e331f296e071fa0df9982cfea7d43f2e
}
, ecc_n = 0x0100000000000000000000351ee786a818f3a1a16b
, ecc_h = 1
})
getCurveByName SEC_p192k1 = CurveFP  \$ CurvePrime
0xfffffffffffffffffffffffffffffffffffffffeffffee37
(CurveCommon
{ ecc_a = 0x000000000000000000000000000000000000000000000000
, ecc_b = 0x000000000000000000000000000000000000000000000003
, ecc_g = Point { point_x = 0xdb4ff10ec057e9ae26b07d0280b7f4341da5d1b1eae06c7d
, point_y = 0x9b2f2f6d9c5628a7844163d015be86344082aa88d95e2f9d
}
, ecc_n = 0xfffffffffffffffffffffffe26f2fc170f69466a74defd8d
, ecc_h = 1
})
getCurveByName SEC_p224k1 = CurveFP  \$ CurvePrime
0x00fffffffffffffffffffffffffffffffffffffffffffffffeffffe56d
(CurveCommon
{ ecc_a = 0x0000000000000000000000000000000000000000000000000000000000
, ecc_b = 0x0000000000000000000000000000000000000000000000000000000005
, ecc_g = Point { point_x = 0x00a1455b334df099df30fc28a169a467e9e47075a90f7e650eb6b7a45c
, point_y = 0x007e089fed7fba344282cafbd6f7e319f7c0b0bd59e2ca4bdb556d61a5
}
, ecc_n = 0x010000000000000000000000000001dce8d2ec6184caf0a971769fb1f7
, ecc_h = 1
})
getCurveByName SEC_p224r1 = CurveFP  \$ CurvePrime
0xffffffffffffffffffffffffffffffff000000000000000000000001
(CurveCommon
{ ecc_a = 0xfffffffffffffffffffffffffffffffefffffffffffffffffffffffe
, ecc_b = 0xb4050a850c04b3abf54132565044b0b7d7bfd8ba270b39432355ffb4
, ecc_g = Point { point_x = 0xb70e0cbd6bb4bf7f321390b94a03c1d356c21122343280d6115c1d21
, point_y = 0xbd376388b5f723fb4c22dfe6cd4375a05a07476444d5819985007e34
}
, ecc_n = 0xffffffffffffffffffffffffffff16a2e0b8f03e13dd29455c5c2a3d
, ecc_h = 1
})
getCurveByName SEC_p256k1 = CurveFP  \$ CurvePrime
0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f
(CurveCommon
{ ecc_a = 0x0000000000000000000000000000000000000000000000000000000000000000
, ecc_b = 0x0000000000000000000000000000000000000000000000000000000000000007
, ecc_g = Point { point_x = 0x79be667ef9dcbbac55a06295ce870b07029bfcdb2dce28d959f2815b16f81798
}
, ecc_n = 0xfffffffffffffffffffffffffffffffebaaedce6af48a03bbfd25e8cd0364141
, ecc_h = 1
})
getCurveByName SEC_p384r1 = CurveFP  \$ CurvePrime
0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffeffffffff0000000000000000ffffffff
(CurveCommon
{ ecc_a = 0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffeffffffff0000000000000000fffffffc
, ecc_b = 0xb3312fa7e23ee7e4988e056be3f82d19181d9c6efe8141120314088f5013875ac656398d8a2ed19d2a85c8edd3ec2aef
, ecc_g = Point { point_x = 0xaa87ca22be8b05378eb1c71ef320ad746e1d3b628ba79b9859f741e082542a385502f25dbf55296c3a545e3872760ab7
, point_y = 0x3617de4a96262c6f5d9e98bf9292dc29f8f41dbd289a147ce9da3113b5f0b8c00a60b1ce1d7e819d7a431d7c90ea0e5f
}
, ecc_n = 0xffffffffffffffffffffffffffffffffffffffffffffffffc7634d81f4372ddf581a0db248b0a77aecec196accc52973
, ecc_h = 1
})
getCurveByName SEC_p521r1 = CurveFP  \$ CurvePrime
0x01ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
(CurveCommon
{ ecc_a = 0x01fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffc
, ecc_b = 0x0051953eb9618e1c9a1f929a21a0b68540eea2da725b99b315f3b8b489918ef109e156193951ec7e937b1652c0bd3bb1bf073573df883d2c34f1ef451fd46b503f00
, ecc_g = Point { point_x = 0x00c6858e06b70404e9cd9e3ecb662395b4429c648139053fb521f828af606b4d3dbaa14b5e77efe75928fe1dc127a2ffa8de3348b3c1856a429bf97e7e31c2e5bd66
}
, ecc_n = 0x01fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffa51868783bf2f966b7fcc0148f709a5d03bb5c9b8899c47aebb6fb71e91386409
, ecc_h = 1
})
getCurveByName SEC_t113r1 = CurveF2M \$ CurveBinary
0x020000000000000000000000000201
(CurveCommon
{ ecc_a = 0x003088250ca6e7c7fe649ce85820f7
, ecc_b = 0x00e8bee4d3e2260744188be0e9c723
, ecc_g = Point { point_x = 0x009d73616f35f4ab1407d73562c10f
, point_y = 0x00a52830277958ee84d1315ed31886
}
, ecc_n = 0x0100000000000000d9ccec8a39e56f
, ecc_h = 2
})
getCurveByName SEC_t113r2 = CurveF2M \$ CurveBinary
0x020000000000000000000000000201
(CurveCommon
{ ecc_a = 0x00689918dbec7e5a0dd6dfc0aa55c7
, ecc_b = 0x0095e9a9ec9b297bd4bf36e059184f
, ecc_g = Point { point_x = 0x01a57a6a7b26ca5ef52fcdb8164797
}
, ecc_n = 0x010000000000000108789b2496af93
, ecc_h = 2
})
getCurveByName SEC_t131r1 = CurveF2M \$ CurveBinary
0x080000000000000000000000000000010d
(CurveCommon
{ ecc_a = 0x07a11b09a76b562144418ff3ff8c2570b8
, ecc_b = 0x0217c05610884b63b9c6c7291678f9d341
, ecc_g = Point { point_x = 0x0081baf91fdf9833c40f9c181343638399
, point_y = 0x078c6e7ea38c001f73c8134b1b4ef9e150
}
, ecc_n = 0x0400000000000000023123953a9464b54d
, ecc_h = 2
})
getCurveByName SEC_t131r2 = CurveF2M \$ CurveBinary
0x080000000000000000000000000000010d
(CurveCommon
{ ecc_a = 0x03e5a88919d7cafcbf415f07c2176573b2
, ecc_b = 0x04b8266a46c55657ac734ce38f018f2192
, ecc_g = Point { point_x = 0x0356dcd8f2f95031ad652d23951bb366a8
, point_y = 0x0648f06d867940a5366d9e265de9eb240f
}
, ecc_n = 0x0400000000000000016954a233049ba98f
, ecc_h = 2
})
getCurveByName SEC_t163k1 = CurveF2M \$ CurveBinary
0x0800000000000000000000000000000000000000c9
(CurveCommon
{ ecc_a = 0x000000000000000000000000000000000000000001
, ecc_b = 0x000000000000000000000000000000000000000001
, ecc_g = Point { point_x = 0x02fe13c0537bbc11acaa07d793de4e6d5e5c94eee8
, point_y = 0x0289070fb05d38ff58321f2e800536d538ccdaa3d9
}
, ecc_n = 0x04000000000000000000020108a2e0cc0d99f8a5ef
, ecc_h = 2
})
getCurveByName SEC_t163r1 = CurveF2M \$ CurveBinary
0x0800000000000000000000000000000000000000c9
(CurveCommon
{ ecc_a = 0x07b6882caaefa84f9554ff8428bd88e246d2782ae2
, ecc_b = 0x0713612dcddcb40aab946bda29ca91f73af958afd9
, ecc_g = Point { point_x = 0x0369979697ab43897789566789567f787a7876a654
, point_y = 0x00435edb42efafb2989d51fefce3c80988f41ff883
}
, ecc_n = 0x03ffffffffffffffffffff48aab689c29ca710279b
, ecc_h = 2
})
getCurveByName SEC_t163r2 = CurveF2M \$ CurveBinary
0x0800000000000000000000000000000000000000c9
(CurveCommon
{ ecc_a = 0x000000000000000000000000000000000000000001
, ecc_b = 0x020a601907b8c953ca1481eb10512f78744a3205fd
, ecc_g = Point { point_x = 0x03f0eba16286a2d57ea0991168d4994637e8343e36
, point_y = 0x00d51fbc6c71a0094fa2cdd545b11c5c0c797324f1
}
, ecc_n = 0x040000000000000000000292fe77e70c12a4234c33
, ecc_h = 2
})
getCurveByName SEC_t193r1 = CurveF2M \$ CurveBinary
0x02000000000000000000000000000000000000000000008001
(CurveCommon
{ ecc_a = 0x0017858feb7a98975169e171f77b4087de098ac8a911df7b01
, ecc_g = Point { point_x = 0x01f481bc5f0ff84a74ad6cdf6fdef4bf6179625372d8c0c5e1
}
, ecc_n = 0x01000000000000000000000000c7f34a778f443acc920eba49
, ecc_h = 2
})
getCurveByName SEC_t193r2 = CurveF2M \$ CurveBinary
0x02000000000000000000000000000000000000000000008001
(CurveCommon
{ ecc_a = 0x0163f35a5137c2ce3ea6ed8667190b0bc43ecd69977702709b
, ecc_b = 0x00c9bb9e8927d4d64c377e2ab2856a5b16e3efb7f61d4316ae
, ecc_g = Point { point_x = 0x00d9b67d192e0367c803f39e1a7e82ca14a651350aae617e8f
, point_y = 0x01ce94335607c304ac29e7defbd9ca01f596f927224cdecf6c
}
, ecc_n = 0x010000000000000000000000015aab561b005413ccd4ee99d5
, ecc_h = 2
})
getCurveByName SEC_t233k1 = CurveF2M \$ CurveBinary
0x020000000000000000000000000000000000000004000000000000000001
(CurveCommon
{ ecc_a = 0x000000000000000000000000000000000000000000000000000000000000
, ecc_b = 0x000000000000000000000000000000000000000000000000000000000001
, ecc_g = Point { point_x = 0x017232ba853a7e731af129f22ff4149563a419c26bf50a4c9d6eefad6126
, point_y = 0x01db537dece819b7f70f555a67c427a8cd9bf18aeb9b56e0c11056fae6a3
}
, ecc_h = 4
})
getCurveByName SEC_t233r1 = CurveF2M \$ CurveBinary
0x020000000000000000000000000000000000000004000000000000000001
(CurveCommon
{ ecc_a = 0x000000000000000000000000000000000000000000000000000000000001
, ecc_g = Point { point_x = 0x00fac9dfcbac8313bb2139f1bb755fef65bc391f8b36f8f8eb7371fd558b
, point_y = 0x01006a08a41903350678e58528bebf8a0beff867a7ca36716f7e01f81052
}
, ecc_n = 0x01000000000000000000000000000013e974e72f8a6922031d2603cfe0d7
, ecc_h = 2
})
getCurveByName SEC_t239k1 = CurveF2M \$ CurveBinary
0x800000000000000000004000000000000000000000000000000000000001
(CurveCommon
{ ecc_a = 0x000000000000000000000000000000000000000000000000000000000000
, ecc_b = 0x000000000000000000000000000000000000000000000000000000000001
, ecc_g = Point { point_x = 0x29a0b6a887a983e9730988a68727a8b2d126c44cc2cc7b2a6555193035dc
, point_y = 0x76310804f12e549bdb011c103089e73510acb275fc312a5dc6b76553f0ca
}
, ecc_n = 0x2000000000000000000000000000005a79fec67cb6e91f1c1da800e478a5
, ecc_h = 4
})
getCurveByName SEC_t283k1 = CurveF2M \$ CurveBinary
0x0800000000000000000000000000000000000000000000000000000000000000000010a1
(CurveCommon
{ ecc_a = 0x000000000000000000000000000000000000000000000000000000000000000000000000
, ecc_b = 0x000000000000000000000000000000000000000000000000000000000000000000000001
, ecc_g = Point { point_x = 0x0503213f78ca44883f1a3b8162f188e553cd265f23c1567a16876913b0c2ac2458492836
, point_y = 0x01ccda380f1c9e318d90f95d07e5426fe87e45c0e8184698e45962364e34116177dd2259
}
, ecc_n = 0x01ffffffffffffffffffffffffffffffffffe9ae2ed07577265dff7f94451e061e163c61
, ecc_h = 4
})
getCurveByName SEC_t283r1 = CurveF2M \$ CurveBinary
0x0800000000000000000000000000000000000000000000000000000000000000000010a1
(CurveCommon
{ ecc_a = 0x000000000000000000000000000000000000000000000000000000000000000000000001
, ecc_b = 0x027b680ac8b8596da5a4af8a19a0303fca97fd7645309fa2a581485af6263e313b79a2f5
, ecc_g = Point { point_x = 0x05f939258db7dd90e1934f8c70b0dfec2eed25b8557eac9c80e2e198f8cdbecd86b12053
, point_y = 0x03676854fe24141cb98fe6d4b20d02b4516ff702350eddb0826779c813f0df45be8112f4
}
, ecc_h = 2
})
getCurveByName SEC_t409k1 = CurveF2M \$ CurveBinary
0x02000000000000000000000000000000000000000000000000000000000000000000000000000000008000000000000000000001
(CurveCommon
{ ecc_a = 0x00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
, ecc_b = 0x00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001
, ecc_g = Point { point_x = 0x0060f05f658f49c1ad3ab1890f7184210efd0987e307c84c27accfb8f9f67cc2c460189eb5aaaa62ee222eb1b35540cfe9023746
, point_y = 0x01e369050b7c4e42acba1dacbf04299c3460782f918ea427e6325165e9ea10e3da5f6c42e9c55215aa9ca27a5863ec48d8e0286b
}
, ecc_n = 0x007ffffffffffffffffffffffffffffffffffffffffffffffffffe5f83b2d4ea20400ec4557d5ed3e3e7ca5b4b5c83b8e01e5fcf
, ecc_h = 4
})
getCurveByName SEC_t409r1 = CurveF2M \$ CurveBinary
0x02000000000000000000000000000000000000000000000000000000000000000000000000000000008000000000000000000001
(CurveCommon
{ ecc_a = 0x00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001
, ecc_b = 0x0021a5c2c8ee9feb5c4b9a753b7b476b7fd6422ef1f3dd674761fa99d6ac27c8a9a197b272822f6cd57a55aa4f50ae317b13545f
, ecc_g = Point { point_x = 0x015d4860d088ddb3496b0c6064756260441cde4af1771d4db01ffe5b34e59703dc255a868a1180515603aeab60794e54bb7996a7
, point_y = 0x0061b1cfab6be5f32bbfa78324ed106a7636b9c5a7bd198d0158aa4f5488d08f38514f1fdf4b4f40d2181b3681c364ba0273c706
}
, ecc_h = 2
})
getCurveByName SEC_t571k1 = CurveF2M \$ CurveBinary
0x080000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000425
(CurveCommon
{ ecc_a = 0x000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
, ecc_b = 0x000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001
, ecc_g = Point { point_x = 0x026eb7a859923fbc82189631f8103fe4ac9ca2970012d5d46024804801841ca44370958493b205e647da304db4ceb08cbbd1ba39494776fb988b47174dca88c7e2945283a01c8972
}
, ecc_n = 0x020000000000000000000000000000000000000000000000000000000000000000000000131850e1f19a63e4b391a8db917f4138b630d84be5d639381e91deb45cfe778f637c1001
, ecc_h = 4
})
getCurveByName SEC_t571r1 = CurveF2M \$ CurveBinary
0x080000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000425
(CurveCommon
{ ecc_a = 0x000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001