Standard curves and curve checking.

[u/mdw/catacomb] / ectab.in

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+# $Id: ectab.in,v 1.1 2004/03/27 17:54:11 mdw Exp $
+#
+# Standard ellipic curves
+
+#----- Curves from SEC2 -----------------------------------------------------
+
+curve secp112r1 prime
+  p 0xdb7c2abf62e35e668076bead208b
+  a 0xdb7c2abf62e35e668076bead2088
+  b 0x659ef8ba043916eede8911702b22
+  r 0xdb7c2abf62e35e7628dfac6561c5
+  h 1
+  gx 0x09487239995a5ee76b55f9c2f098
+  gy 0xa89ce5af8724c0a23e0e0ff77500
+
+curve secp112r2 prime
+  p 0xdb7c2abf62e35e668076bead208b
+  a 0x6127c24c05f38a0aaaf65c0ef02c
+  b 0x51def1815db5ed74fcc34c85d709
+  r 0x36df0aafd8b8d7597ca10520d04b
+  h 4
+  gx 0x4ba30ab5e892b4e1649dd0928643
+  gy 0xadcd46f5882e3747def36e956e97
+
+curve secp128r1 niceprime
+  p 0xfffffffdffffffffffffffffffffffff
+  a 0xfffffffdfffffffffffffffffffffffc
+  b 0xe87579c11079f43dd824993c2cee5ed3
+  r 0xfffffffe0000000075a30d1b9038a115
+  h 1
+  gx 0x161ff7528b899b2d0c28607ca52c5b86
+  gy 0xcf5ac8395bafeb13c02da292dded7a83
+
+curve secp128r2 niceprime
+  p 0xfffffffdffffffffffffffffffffffff
+  a 0xd6031998d1b3bbfebf59cc9bbff9aee1
+  b 0x5eeefca380d02919dc2c6558bb6d8a5d
+  r 0x3fffffff7fffffffbe0024720613b5a3
+  h 4
+  gx 0x7b6aa5d85e572983e6fb32a7cdebc140
+  gy 0x27b6916a894d3aee7106fe805fc34b44
+
+curve secp160k1 niceprime
+  p 0xfffffffffffffffffffffffffffffffeffffac73
+  a 0
+  b 7
+  r 0x0100000000000000000001b8fa16dfab9aca16b6b3
+  h 1
+  gx 0x3b4c382ce37aa192a4019e763036f4f5dd4d7ebb
+  gy 0x938cf935318fdced6bc28286531733c3f03c4fee
+
+curve secp160r1 niceprime
+  p 0xffffffffffffffffffffffffffffffff7fffffff
+  a 0xffffffffffffffffffffffffffffffff7ffffffc
+  b 0x1c97befc54bd7a8b65acf89f81d4d4adc565fa45
+  r 0x0100000000000000000001f4c8f927aed3ca752257
+  h 1
+  gx 0x4a96b5688ef573284664698968c38bb913cbfc82
+  gy 0x23a628553168947d59dcc912042351377ac5fb32
+
+curve secp160r2 niceprime
+  p 0xfffffffffffffffffffffffffffffffeffffac73
+  a 0xfffffffffffffffffffffffffffffffeffffac70
+  b 0xb4e134d3fb59eb8bab57274904664d5af50388ba
+  r 0x0100000000000000000000351ee786a818f3a1a16b
+  h 1
+  gx 0x52dcb034293a117e1f4ff11b30f7199d3144ce6d
+  gy 0xfeaffef2e331f296e071fa0df9982cfea7d43f2e
+
+curve secp192k1 niceprime
+  p 0xfffffffffffffffffffffffffffffffffffffffeffffee37
+  a 0
+  b 3
+  r 0xfffffffffffffffffffffffe26f2fc170f69466a74defd8d
+  h 1
+  gx 0xdb4ff10ec057e9ae26b07d0280b7f4341da5d1b1eae06c7d
+  gy 0x9b2f2f6d9c5628a7844163d015be86344082aa88d95e2f9d
+
+curve secp192r1 niceprime
+  p 0xfffffffffffffffffffffffffffffffeffffffffffffffff
+  a 0xfffffffffffffffffffffffffffffffefffffffffffffffc
+  b 0x64210519e59c80e70fa7e9ab72243049feb8deecc146b9b1
+  r 0xffffffffffffffffffffffff99def836146bc9b1b4d22831
+  h 1
+  gx 0x188da80eb03090f67cbf20eb43a18800f4ff0afd82ff1012
+  gy 0x07192b95ffc8da78631011ed6b24cdd573f977a11e794811
+
+curve secp224k1 niceprime
+  p 0xfffffffffffffffffffffffffffffffffffffffffffffffeffffe56d
+  a 0
+  b 5
+  r 0x010000000000000000000000000001dce8d2ec6184caf0a971769fb1f7
+  h 1
+  gx 0xa1455b334df099df30fc28a169a467e9e47075a90f7e650eb6b7a45c
+  gy 0x7e089fed7fba344282cafbd6f7e319f7c0b0bd59e2ca4bdb556d61a5
+
+curve secp224r1 niceprime
+  p 0xffffffffffffffffffffffffffffffff000000000000000000000001
+  a 0xfffffffffffffffffffffffffffffffefffffffffffffffffffffffe
+  b 0xb4050a850c04b3abf54132565044b0b7d7bfd8ba270b39432355ffb4
+  r 0xffffffffffffffffffffffffffff16a2e0b8f03e13dd29455c5c2a3d
+  h 1
+  gx 0xb70e0cbd6bb4bf7f321390b94a03c1d356c21122343280d6115c1d21
+  gy 0xbd376388b5f723fb4c22dfe6cd4375a05a07476444d5819985007e34
+
+curve secp256k1 niceprime
+  p 0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f
+  a 0
+  b 7
+  r 0xfffffffffffffffffffffffffffffffebaaedce6af48a03bbfd25e8cd0364141
+  h 1
+  gx 0x79be667ef9dcbbac55a06295ce870b07029bfcdb2dce28d959f2815b16f81798
+  gy 0x483ada7726a3c4655da4fbfc0e1108a8fd17b448a68554199c47d08ffb10d4b8
+
+curve secp256r1 niceprime
+  p 0xffffffff00000001000000000000000000000000ffffffffffffffffffffffff
+  a 0xffffffff00000001000000000000000000000000fffffffffffffffffffffffc
+  b 0x5ac635d8aa3a93e7b3ebbd55769886bc651d06b0cc53b0f63bce3c3e27d2604b
+  r 0xffffffff00000000ffffffffffffffffbce6faada7179e84f3b9cac2fc632551
+  h 1
+  gx 0x6b17d1f2e12c4247f8bce6e563a440f277037d812deb33a0f4a13945d898c296
+  gy 0x4fe342e2fe1a7f9b8ee7eb4a7c0f9e162bce33576b315ececbb6406837bf51f5
+
+curve secp384r1 niceprime
+  p 0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffeffffffff0000000000000000ffffffff
+  a 0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffeffffffff0000000000000000fffffffc
+  b 0xb3312fa7e23ee7e4988e056be3f82d19181d9c6efe8141120314088f5013875ac656398d8a2ed19d2a85c8edd3ec2aef
+  r 0xffffffffffffffffffffffffffffffffffffffffffffffffc7634d81f4372ddf581a0db248b0a77aecec196accc52973
+  h 1
+  gx 0xaa87ca22be8b05378eb1c71ef320ad746e1d3b628ba79b9859f741e082542a385502f25dbf55296c3a545e3872760ab7
+  gy 0x3617de4a96262c6f5d9e98bf9292dc29f8f41dbd289a147ce9da3113b5f0b8c00a60b1ce1d7e819d7a431d7c90ea0e5f
+
+curve secp521r1 niceprime
+  p 0x01ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
+  a 0x01fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffc
+  b 0x0051953eb9618e1c9a1f929a21a0b68540eea2da725b99b315f3b8b489918ef109e156193951ec7e937b1652c0bd3bb1bf073573df883d2c34f1ef451fd46b503f00
+  r 0x01fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffa51868783bf2f966b7fcc0148f709a5d03bb5c9b8899c47aebb6fb71e91386409
+  h 1
+  gx 0x00c6858e06b70404e9cd9e3ecb662395b4429c648139053fb521f828af606b4d3dbaa14b5e77efe75928fe1dc127a2ffa8de3348b3c1856a429bf97e7e31c2e5bd66
+  gy 0x011839296a789a3bc0045c8a5fb42c7d1bd998f54449579b446817afbd17273e662c97ee72995ef42640c550b9013fad0761353c7086a272c24088be94769fd16650
+
+curve sect113r1 binpoly
+  p 0x20000000000000000000000000201
+  a 0x003088250ca6e7c7fe649ce85820f7
+  b 0x00e8bee4d3e2260744188be0e9c723
+  r 0x0100000000000000d9ccec8a39e56f
+  h 2
+  gx 0x009d73616f35f4ab1407d73562c10f
+  gy 0x00a52830277958ee84d1315ed31886
+
+curve sect113r2 binpoly
+  p 0x20000000000000000000000000201
+  a 0x00689918dbec7e5a0dd6dfc0aa55c7
+  b 0x0095e9a9ec9b297bd4bf36e059184f
+  r 0x010000000000000108789b2496af93
+  h 2
+  gx 0x01a57a6a7b26ca5ef52fcdb8164797
+  gy 0x00b3adc94ed1fe674c06e695baba1d
+
+curve sect131r1 binpoly
+  p 0x80000000000000000000000000000010d
+  a 0x07a11b09a76b562144418ff3ff8c2570b8
+  b 0x0217c05610884b63b9c6c7291678f9d341
+  r 0x0400000000000000023123953a9464b54d
+  h 2
+  gx 0x0081baf91fdf9833c40f9c181343638399
+  gy 0x078c6e7ea38c001f73c8134b1b4ef9e150
+
+curve sect131r2 binpoly
+  p 0x80000000000000000000000000000010d
+  a 0x03e5a88919d7cafcbf415f07c2176573b2
+  b 0x04b8266a46c55657ac734ce38f018f2192
+  r 0x0400000000000000016954a233049ba98f
+  h 2
+  gx 0x0356dcd8f2f95031ad652d23951bb366a8
+  gy 0x0648f06d867940a5366d9e265de9eb240f
+
+curve sect163k1 binpoly
+  p 0x800000000000000000000000000000000000000c9
+  a 1
+  b 1
+  r 0x04000000000000000000020108a2e0cc0d99f8a5ef
+  h 2
+  gx 0x02fe13c0537bbc11acaa07d793de4e6d5e5c94eee8
+  gy 0x0289070fb05d38ff58321f2e800536d538ccdaa3d9
+
+curve sect163r1 binpoly
+  p 0x800000000000000000000000000000000000000c9
+  a 0x07b6882caaefa84f9554ff8428bd88e246d2782ae2
+  b 0x0713612dcddcb40aab946bda29ca91f73af958afd9
+  r 0x03ffffffffffffffffffff48aab689c29ca710279b
+  h 2
+  gx 0x0369979697ab43897789566789567f787a7876a654
+  gy 0x00435edb42efafb2989d51fefce3c80988f41ff883
+
+curve sect163r2 binpoly
+  p 0x800000000000000000000000000000000000000c9
+  a 1
+  b 0x020a601907b8c953ca1481eb10512f78744a3205fd
+  r 0x040000000000000000000292fe77e70c12a4234c33
+  h 2
+  gx 0x03f0eba16286a2d57ea0991168d4994637e8343e36
+  gy 0x00d51fbc6c71a0094fa2cdd545b11c5c0c797324f1
+
+curve sect193r1 binpoly
+  p 0x2000000000000000000000000000000000000000000008001
+  a 0x0017858feb7a98975169e171f77b4087de098ac8a911df7b01
+  b 0x00fdfb49bfe6c3a89facadaa7a1e5bbc7cc1c2e5d831478814
+  r 0x01000000000000000000000000c7f34a778f443acc920eba49
+  h 2
+  gx 0x01f481bc5f0ff84a74ad6cdf6fdef4bf6179625372d8c0c5e1
+  gy 0x0025e399f2903712ccf3ea9e3a1ad17fb0b3201b6af7ce1b05
+
+curve sect193r2 binpoly
+  p 0x2000000000000000000000000000000000000000000008001
+  a 0x0163f35a5137c2ce3ea6ed8667190b0bc43ecd69977702709b
+  b 0x00c9bb9e8927d4d64c377e2ab2856a5b16e3efb7f61d4316ae
+  r 0x010000000000000000000000015aab561b005413ccd4ee99d5
+  h 2
+  gx 0x00d9b67d192e0367c803f39e1a7e82ca14a651350aae617e8f
+  gy 0x01ce94335607c304ac29e7defbd9ca01f596f927224cdecf6c
+
+curve sect233k1 binpoly
+  p 0x20000000000000000000000000000000000000004000000000000000001
+  a 0
+  b 1
+  r 0x8000000000000000000000000000069d5bb915bcd46efb1ad5f173abdf
+  h 4
+  gx 0x017232ba853a7e731af129f22ff4149563a419c26bf50a4c9d6eefad6126
+  gy 0x01db537dece819b7f70f555a67c427a8cd9bf18aeb9b56e0c11056fae6a3
+
+curve sect233r1 binpoly
+  p 0x20000000000000000000000000000000000000004000000000000000001
+  a 1
+  b 0x0066647ede6c332c7f8c0923bb58213b333b20e9ce4281fe115f7d8f90ad
+  r 0x01000000000000000000000000000013e974e72f8a6922031d2603cfe0d7
+  h 2
+  gx 0x00fac9dfcbac8313bb2139f1bb755fef65bc391f8b36f8f8eb7371fd558b
+  gy 0x01006a08a41903350678e58528bebf8a0beff867a7ca36716f7e01f81052
+
+curve sect239k1 binpoly
+  p 0x800000000000000000004000000000000000000000000000000000000001
+  a 0
+  b 1
+  r 0x2000000000000000000000000000005a79fec67cb6e91f1c1da800e478a5
+  h 4
+  gx 0x29a0b6a887a983e9730988a68727a8b2d126c44cc2cc7b2a6555193035dc
+  gy 0x76310804f12e549bdb011c103089e73510acb275fc312a5dc6b76553f0ca
+
+curve sect283k1 binpoly
+  p 0x800000000000000000000000000000000000000000000000000000000000000000010a1
+  a 0
+  b 1
+  r 0x01ffffffffffffffffffffffffffffffffffe9ae2ed07577265dff7f94451e061e163c61
+  h 4
+  gx 0x0503213f78ca44883f1a3b8162f188e553cd265f23c1567a16876913b0c2ac2458492836
+  gy 0x01ccda380f1c9e318d90f95d07e5426fe87e45c0e8184698e45962364e34116177dd2259
+
+curve sect283r1 binpoly
+  p 0x800000000000000000000000000000000000000000000000000000000000000000010a1
+  a 1
+  b 0x027b680ac8b8596da5a4af8a19a0303fca97fd7645309fa2a581485af6263e313b79a2f5
+  r 0x03ffffffffffffffffffffffffffffffffffef90399660fc938a90165b042a7cefadb307
+  h 2
+  gx 0x05f939258db7dd90e1934f8c70b0dfec2eed25b8557eac9c80e2e198f8cdbecd86b12053
+  gy 0x03676854fe24141cb98fe6d4b20d02b4516ff702350eddb0826779c813f0df45be8112f4
+
+curve sect409k1 binpoly
+  p 0x2000000000000000000000000000000000000000000000000000000000000000000000000000000008000000000000000000001
+  a 0
+  b 1
+  r 0x7ffffffffffffffffffffffffffffffffffffffffffffffffffe5f83b2d4ea20400ec4557d5ed3e3e7ca5b4b5c83b8e01e5fcf
+  h 4
+  gx 0x0060f05f658f49c1ad3ab1890f7184210efd0987e307c84c27accfb8f9f67cc2c460189eb5aaaa62ee222eb1b35540cfe9023746
+  gy 0x01e369050b7c4e42acba1dacbf04299c3460782f918ea427e6325165e9ea10e3da5f6c42e9c55215aa9ca27a5863ec48d8e0286b
+
+curve sect409r1 binpoly
+  p 0x2000000000000000000000000000000000000000000000000000000000000000000000000000000008000000000000000000001
+  a 1
+  b 0x0021a5c2c8ee9feb5c4b9a753b7b476b7fd6422ef1f3dd674761fa99d6ac27c8a9a197b272822f6cd57a55aa4f50ae317b13545f
+  r 0x010000000000000000000000000000000000000000000000000001e2aad6a612f33307be5fa47c3c9e052f838164cd37d9a21173
+  h 2
+  gx 0x015d4860d088ddb3496b0c6064756260441cde4af1771d4db01ffe5b34e59703dc255a868a1180515603aeab60794e54bb7996a7
+  gy 0x0061b1cfab6be5f32bbfa78324ed106a7636b9c5a7bd198d0158aa4f5488d08f38514f1fdf4b4f40d2181b3681c364ba0273c706
+
+curve sect571k1 binpoly
+  p 0x80000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000425
+  a 0
+  b 1
+  r 0x020000000000000000000000000000000000000000000000000000000000000000000000131850e1f19a63e4b391a8db917f4138b630d84be5d639381e91deb45cfe778f637c1001
+  h 4
+  gx 0x026eb7a859923fbc82189631f8103fe4ac9ca2970012d5d46024804801841ca44370958493b205e647da304db4ceb08cbbd1ba39494776fb988b47174dca88c7e2945283a01c8972
+  gy 0x0349dc807f4fbf374f4aeade3bca95314dd58cec9f307a54ffc61efc006d8a2c9d4979c0ac44aea74fbebbb9f772aedcb620b01a7ba7af1b320430c8591984f601cd4c143ef1c7a3
+
+curve sect571r1 binpoly
+  p 0x80000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000425
+  a 1
+  b 0x02f40e7e2221f295de297117b7f3d62f5c6a97ffcb8ceff1cd6ba8ce4a9a18ad84ffabbd8efa59332be7ad6756a66e294afd185a78ff12aa520e4de739baca0c7ffeff7f2955727a
+  r 0x03ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffe661ce18ff55987308059b186823851ec7dd9ca1161de93d5174d66e8382e9bb2fe84e47
+  h 2
+  gx 0x0303001d34b856296c16c0d40d3cd7750a93d1d2955fa80aa5f40fc8db7b2abdbde53950f4c0d293cdd711a35b67fb1499ae60038614f1394abfa3b4c850d927e1e7769c8eec2d19
+  gy 0x037bf27342da639b6dccfffeb73d69d78c6c27a6009cbbca1980f8533921e8a684423e43bab08a576291af8f461bb2a8b3531d2f0485c19b16e2f1516e23dd3c1a4827af1b8ac15b
+
+#----- Curves from RFC2414 (Oakley) -----------------------------------------
+#
+# oakley155 has too large a cofactor
+# oakley185's group has composite order; we double the generator to
+#   produce a group of composite order
+
+curve oakley185 binpoly
+  p 0x020000000000000000000000000000200000000000000001
+  a 0
+  b 0x1ee9
+  r 0x007ffffffffffffffffffffff6fcbe226dcf92105d7e53af
+  h 4
+  gx 0x1bd555555555555555555555555554e8000000000000158
+  gy 0x14e999999999999999999999999998d7000000000001fe6
+
+#----- NIST curves from FIPS186-2 -------------------------------------------
+#
+# Most of these are duplicates of SEC2 curves.
+
+alias nist-p192 secp192r1
+alias nist-p224 secp224r1
+alias nist-p256 secp256r1
+alias nist-p384 secp384r1
+alias nist-p521 secp521r1
+
+alias nist-k163 sect163k1
+alias nist-k233 sect233k1
+alias nist-k283 sect283k1
+alias nist-k409 sect409k1
+alias nist-k571 sect571k1
+
+alias nist-b163 sect163r2
+alias nist-b233 sect233r1
+alias nist-b283 sect283r1
+alias nist-b409 sect409r1
+alias nist-b571 sect571r1
+
+#----- That's all, folks ----------------------------------------------------