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list of Certicom curves
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| # Curve25519 | |
| p = 2^255 - 19 | |
| N = 8*(2^252 + 27742317777372353535851937790883648493) | |
| E = EllipticCurve(GF(p),[0,486662,0,1,0]) | |
| G = E.lift_x(9) | |
| assert E.count_points() == N | |
| assert G.order() == N/8 |
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| # To verify some properties: | |
| # E = EllipticCurve(GF(p),[a,b]) | |
| # G = E([Gx,Gy]) | |
| # assert n*G == 0 | |
| # assert n.is_prime() | |
| # assert E.count_points() == n # all these curves have cofactor 1 | |
| # 192k1 | |
| p = 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFEE37 | |
| a = 0x000000000000000000000000000000000000000000000000 | |
| b = 0x000000000000000000000000000000000000000000000003 | |
| Gx= 0xDB4FF10EC057E9AE26B07D0280B7F4341DA5D1B1EAE06C7D | |
| Gy= 0x9B2F2F6D9C5628A7844163D015BE86344082AA88D95E2F9D | |
| n = 0xFFFFFFFFFFFFFFFFFFFFFFFE26F2FC170F69466A74DEFD8D | |
| # 192r1 | |
| S = 0x3045AE6FC8422F64ED579528D38120EAE12196D5 | |
| p = 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFF | |
| a = 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFC | |
| b = 0x64210519E59C80E70FA7E9AB72243049FEB8DEECC146B9B1 | |
| Gx= 0x188DA80EB03090F67CBF20EB43A18800F4FF0AFD82FF1012 | |
| Gy= 0x07192B95FFC8DA78631011ED6B24CDD573F977A11E794811 | |
| n = 0xFFFFFFFFFFFFFFFFFFFFFFFF99DEF836146BC9B1B4D22831 | |
| # 224k1 | |
| p = 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFE56D | |
| a = 0x00000000000000000000000000000000000000000000000000000000 | |
| b = 0x00000000000000000000000000000000000000000000000000000005 | |
| Gx= 0xA1455B334DF099DF30FC28A169A467E9E47075A90F7E650EB6B7A45C | |
| Gy= 0x7E089FED7FBA344282CAFBD6F7E319F7C0B0BD59E2CA4BDB556D61A5 | |
| n = 0x010000000000000000000000000001DCE8D2EC6184CAF0A971769FB1F7 | |
| # 224r1 | |
| S = 0xBD71344799D5C7FCDC45B59FA3B9AB8F6A948BC5 | |
| p = 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF000000000000000000000001 | |
| a = 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFFFFFFFFFE | |
| b = 0xB4050A850C04B3ABF54132565044B0B7D7BFD8BA270B39432355FFB4 | |
| Gx= 0xB70E0CBD6BB4BF7F321390B94A03C1D356C21122343280D6115C1D21 | |
| Gy= 0xBD376388B5F723FB4C22DFE6CD4375A05A07476444D5819985007E34 | |
| n = 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFF16A2E0B8F03E13DD29455C5C2A3D | |
| # 256k1 | |
| p = 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFC2F | |
| a = 0x0000000000000000000000000000000000000000000000000000000000000000 | |
| b = 0x0000000000000000000000000000000000000000000000000000000000000007 | |
| Gx= 0x79BE667EF9DCBBAC55A06295CE870B07029BFCDB2DCE28D959F2815B16F81798 | |
| Gy= 0x483ADA7726A3C4655DA4FBFC0E1108A8FD17B448A68554199C47D08FFB10D4B8 | |
| n = 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD0364141 | |
| # 256r1 | |
| S = 0xC49D360886E704936A6678E1139D26B7819F7E90 | |
| p = 0xFFFFFFFF00000001000000000000000000000000FFFFFFFFFFFFFFFFFFFFFFFF | |
| a = 0xFFFFFFFF00000001000000000000000000000000FFFFFFFFFFFFFFFFFFFFFFFC | |
| b = 0x5AC635D8AA3A93E7B3EBBD55769886BC651D06B0CC53B0F63BCE3C3E27D2604B | |
| Gx= 0x6B17D1F2E12C4247F8BCE6E563A440F277037D812DEB33A0F4A13945D898C296 | |
| Gy= 0x4FE342E2FE1A7F9B8EE7EB4A7C0F9E162BCE33576B315ECECBB6406837BF51F5 | |
| n = 0xFFFFFFFF00000000FFFFFFFFFFFFFFFFBCE6FAADA7179E84F3B9CAC2FC632551 | |
| # 384r1 | |
| S = 0xA335926AA319A27A1D00896A6773A4827ACDAC73 | |
| p = 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFF0000000000000000FFFFFFFF | |
| a = 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFF0000000000000000FFFFFFFC | |
| b = 0xB3312FA7E23EE7E4988E056BE3F82D19181D9C6EFE8141120314088F5013875AC656398D8A2ED19D2A85C8EDD3EC2AEF | |
| Gx= 0xAA87CA22BE8B05378EB1C71EF320AD746E1D3B628BA79B9859F741E082542A385502F25DBF55296C3A545E3872760AB7 | |
| Gy= 0x3617DE4A96262C6F5D9E98BF9292DC29F8F41DBD289A147CE9DA3113B5F0B8C00A60B1CE1D7E819D7A431D7C90EA0E5F | |
| n = 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFC7634D81F4372DDF581A0DB248B0A77AECEC196ACCC52973 | |
| # 521r1 | |
| S = 0xD09E8800291CB85396CC6717393284AAA0DA64BA | |
| p = 0x01FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF | |
| a = 0x01FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFC | |
| b = 0x0051953EB9618E1C9A1F929A21A0B68540EEA2DA725B99B315F3B8B489918EF109E156193951EC7E937B1652C0BD3BB1BF073573DF883D2C34F1EF451FD46B503F00 | |
| Gx= 0x00C6858E06B70404E9CD9E3ECB662395B4429C648139053FB521F828AF606B4D3DBAA14B5E77EFE75928FE1DC127A2FFA8DE3348B3C1856A429BF97E7E31C2E5BD66 | |
| Gy= 0x011839296A789A3BC0045C8A5FB42C7D1BD998F54449579B446817AFBD17273E662C97EE72995EF42640C550B9013FAD0761353C7086A272C24088BE94769FD16650 | |
| n = 0x01FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFA51868783BF2F966B7FCC0148F709A5D03BB5C9B8899C47AEBB6FB71E91386409 |
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