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| 1 # ======================= |
| 2 # From the pyECC package |
| 3 # ======================= |
| 4 # |
| 5 # Predefined Elliptic Curves |
| 6 # for use in signing and key exchange |
| 7 # |
| 8 """ |
| 9 Predefined elliptic curves for use in signing and key exchange. |
| 10 This Module implements FIPS approved standard curves P-192, P-224, P-256, |
| 11 P-384 and P-521 along with two weak non-standard curves of field size 128 |
| 12 and 160 bits. |
| 13 |
| 14 The weak curves cannot be used for signing but provide a faster way to |
| 15 obfuscate non-critical transmissions. |
| 16 """ |
| 17 |
| 18 # FIPS approved elliptic curves over prime fields |
| 19 # (see FIPS 186-3, Appendix D.1.2) |
| 20 DOMAINS = { |
| 21 # Bits : (p, order of E(GF(P)), parameter b, base point x, base point y) |
| 22 192: (0xfffffffffffffffffffffffffffffffeffffffffffffffff, |
| 23 0xffffffffffffffffffffffff99def836146bc9b1b4d22831, |
| 24 0x64210519e59c80e70fa7e9ab72243049feb8deecc146b9b1, |
| 25 0x188da80eb03090f67cbf20eb43a18800f4ff0afd82ff1012, |
| 26 0x07192b95ffc8da78631011ed6b24cdd573f977a11e794811), |
| 27 |
| 28 224: (0xffffffffffffffffffffffffffffffff000000000000000000000001, |
| 29 0xffffffffffffffffffffffffffff16a2e0b8f03e13dd29455c5c2a3d, |
| 30 0xb4050a850c04b3abf54132565044b0b7d7bfd8ba270b39432355ffb4, |
| 31 0xb70e0cbd6bb4bf7f321390b94a03c1d356c21122343280d6115c1d21, |
| 32 0xbd376388b5f723fb4c22dfe6cd4375a05a07476444d5819985007e34), |
| 33 |
| 34 256: (0xffffffff00000001000000000000000000000000ffffffffffffffffffffffff, |
| 35 0xffffffff00000000ffffffffffffffffbce6faada7179e84f3b9cac2fc632551, |
| 36 0x5ac635d8aa3a93e7b3ebbd55769886bc651d06b0cc53b0f63bce3c3e27d2604b, |
| 37 0x6b17d1f2e12c4247f8bce6e563a440f277037d812deb33a0f4a13945d898c296, |
| 38 0x4fe342e2fe1a7f9b8ee7eb4a7c0f9e162bce33576b315ececbb6406837bf51f5), |
| 39 |
| 40 384: ( |
| 41 0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffeffffffff00
00000000000000ffffffff, |
| 42 0xffffffffffffffffffffffffffffffffffffffffffffffffc7634d81f4372ddf581a0db248
b0a77aecec196accc52973, |
| 43 0xb3312fa7e23ee7e4988e056be3f82d19181d9c6efe8141120314088f5013875ac656398d8a
2ed19d2a85c8edd3ec2aef, |
| 44 0xaa87ca22be8b05378eb1c71ef320ad746e1d3b628ba79b9859f741e082542a385502f25dbf
55296c3a545e3872760ab7, |
| 45 0x3617de4a96262c6f5d9e98bf9292dc29f8f41dbd289a147ce9da3113b5f0b8c00a60b1ce1d
7e819d7a431d7c90ea0e5f), |
| 46 |
| 47 521: ( |
| 48 0x1fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
fffffffffffffffffffffffffffffffffffffffffffffffffffffffff, |
| 49 0x1fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffa5186878
3bf2f966b7fcc0148f709a5d03bb5c9b8899c47aebb6fb71e91386409, |
| 50 0x051953eb9618e1c9a1f929a21a0b68540eea2da725b99b315f3b8b489918ef109e15619395
1ec7e937b1652c0bd3bb1bf073573df883d2c34f1ef451fd46b503f00, |
| 51 0x0c6858e06b70404e9cd9e3ecb662395b4429c648139053fb521f828af606b4d3dbaa14b5e7
7efe75928fe1dc127a2ffa8de3348b3c1856a429bf97e7e31c2e5bd66, |
| 52 0x11839296a789a3bc0045c8a5fb42c7d1bd998f54449579b446817afbd17273e662c97ee729
95ef42640c550b9013fad0761353c7086a272c24088be94769fd16650) |
| 53 } |
| 54 |
| 55 |
| 56 # Additional non-standard curves for low security but high performance |
| 57 # (not intended for use in signing, hence the missing group order) |
| 58 |
| 59 DOMAINS.update({ |
| 60 128: (0xffffffffffffffffffffffffffffff61, |
| 61 None, |
| 62 0xd83d3eb8266a89927d73d5fe263d5f23, |
| 63 0xa94d2d8531f7af8bde367def12b98ead, |
| 64 0x9f44e1d671beb68fd2df7f877ab13fa6), |
| 65 |
| 66 160: (0xffffffffffffffffffffffffffffffffffffffd1, |
| 67 None, |
| 68 0x94bfe70deef7b94742c089ca4db3ca27fbe1f754, |
| 69 0xcc6562c2969ac57524b8d0f300d1f598c908c121, |
| 70 0x952ddde80a252683dd7ba90fb5919899b5af69f5) |
| 71 }) |
| 72 |
| 73 CURVE_P = 3 # global parameter of all curves (for efficiency reasons) |
| 74 |
| 75 |
| 76 def get_curve(bits): |
| 77 """Get a known curve of the given size => (bits, prime, order, p, q, point). |
| 78 Order may be None if unknown.""" |
| 79 if bits in DOMAINS: |
| 80 p, n, b, x, y = DOMAINS[bits] |
| 81 return bits, p, n, CURVE_P, p - b, (x, y) |
| 82 else: |
| 83 raise KeyError("Key size not implemented: %s" % bits) |
| 84 |
| 85 |
| 86 def implemented_keys(must_sign=False): |
| 87 return [k for k in DOMAINS if not must_sign or DOMAINS[k][1]] |
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