ECC support for curve y^2 = x^3 + a*x + b (`a` used to be fixed to -3)
Karel Miko
10 years ago
139 | 139 | if (self->key.idx>=0) { |
140 | 140 | not_used = hv_store(rv_hash, "curve_name", 10, newSVpv(self->key.dp->name, strlen(self->key.dp->name)), 0); |
141 | 141 | not_used = hv_store(rv_hash, "curve_prime", 11, newSVpv(self->key.dp->prime, strlen(self->key.dp->prime)), 0); |
142 | not_used = hv_store(rv_hash, "curve_A", 7, newSVpv(self->key.dp->A, strlen(self->key.dp->A)), 0); | |
142 | 143 | not_used = hv_store(rv_hash, "curve_B", 7, newSVpv(self->key.dp->B, strlen(self->key.dp->B)), 0); |
143 | 144 | not_used = hv_store(rv_hash, "curve_order", 11, newSVpv(self->key.dp->order, strlen(self->key.dp->order)), 0); |
144 | 145 | not_used = hv_store(rv_hash, "curve_Gx", 8, newSVpv(self->key.dp->Gx, strlen(self->key.dp->Gx)), 0); |
218 | 218 | /** The prime that defines the field the curve is in (encoded in hex) */ |
219 | 219 | char *prime; |
220 | 220 | |
221 | /** The fields A param (hex) */ | |
222 | char *A; | |
223 | ||
221 | 224 | /** The fields B param (hex) */ |
222 | 225 | char *B; |
223 | 226 |
8 | 8 | * Tom St Denis, tomstdenis@gmail.com, http://libtom.org |
9 | 9 | */ |
10 | 10 | |
11 | /* Implements ECC over Z/pZ for curve y^2 = x^3 - 3x + b | |
11 | /* Implements ECC over Z/pZ for curve y^2 = x^3 + a*x + b | |
12 | 12 | * |
13 | 13 | * All curves taken from NIST recommendation paper of July 1999 |
14 | 14 | * Available at http://csrc.nist.gov/cryptval/dss.htm |
29 | 29 | 14, |
30 | 30 | "SECP112R1", |
31 | 31 | "DB7C2ABF62E35E668076BEAD208B", |
32 | "DB7C2ABF62E35E668076BEAD2088", | |
32 | 33 | "659EF8BA043916EEDE8911702B22", |
33 | 34 | "DB7C2ABF62E35E7628DFAC6561C5", |
34 | 35 | "09487239995A5EE76B55F9C2F098", |
40 | 41 | 16, |
41 | 42 | "SECP128R1", |
42 | 43 | "FFFFFFFDFFFFFFFFFFFFFFFFFFFFFFFF", |
44 | "FFFFFFFDFFFFFFFFFFFFFFFFFFFFFFFC", | |
43 | 45 | "E87579C11079F43DD824993C2CEE5ED3", |
44 | 46 | "FFFFFFFE0000000075A30D1B9038A115", |
45 | 47 | "161FF7528B899B2D0C28607CA52C5B86", |
51 | 53 | 20, |
52 | 54 | "SECP160R1", |
53 | 55 | "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF7FFFFFFF", |
56 | "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF7FFFFFFC", | |
54 | 57 | "1C97BEFC54BD7A8B65ACF89F81D4D4ADC565FA45", |
55 | 58 | "0100000000000000000001F4C8F927AED3CA752257", |
56 | 59 | "4A96B5688EF573284664698968C38BB913CBFC82", |
62 | 65 | 24, |
63 | 66 | "ECC-192", |
64 | 67 | "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFF", |
68 | "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFC", | |
65 | 69 | "64210519E59C80E70FA7E9AB72243049FEB8DEECC146B9B1", |
66 | 70 | "FFFFFFFFFFFFFFFFFFFFFFFF99DEF836146BC9B1B4D22831", |
67 | 71 | "188DA80EB03090F67CBF20EB43A18800F4FF0AFD82FF1012", |
73 | 77 | 28, |
74 | 78 | "ECC-224", |
75 | 79 | "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF000000000000000000000001", |
80 | "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFFFFFFFFFE", | |
76 | 81 | "B4050A850C04B3ABF54132565044B0B7D7BFD8BA270B39432355FFB4", |
77 | 82 | "FFFFFFFFFFFFFFFFFFFFFFFFFFFF16A2E0B8F03E13DD29455C5C2A3D", |
78 | 83 | "B70E0CBD6BB4BF7F321390B94A03C1D356C21122343280D6115C1D21", |
84 | 89 | 32, |
85 | 90 | "ECC-256", |
86 | 91 | "FFFFFFFF00000001000000000000000000000000FFFFFFFFFFFFFFFFFFFFFFFF", |
92 | "FFFFFFFF00000001000000000000000000000000FFFFFFFFFFFFFFFFFFFFFFFC", | |
87 | 93 | "5AC635D8AA3A93E7B3EBBD55769886BC651D06B0CC53B0F63BCE3C3E27D2604B", |
88 | 94 | "FFFFFFFF00000000FFFFFFFFFFFFFFFFBCE6FAADA7179E84F3B9CAC2FC632551", |
89 | 95 | "6B17D1F2E12C4247F8BCE6E563A440F277037D812DEB33A0F4A13945D898C296", |
95 | 101 | 48, |
96 | 102 | "ECC-384", |
97 | 103 | "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFF0000000000000000FFFFFFFF", |
104 | "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFF0000000000000000FFFFFFFC", | |
98 | 105 | "B3312FA7E23EE7E4988E056BE3F82D19181D9C6EFE8141120314088F5013875AC656398D8A2ED19D2A85C8EDD3EC2AEF", |
99 | 106 | "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFC7634D81F4372DDF581A0DB248B0A77AECEC196ACCC52973", |
100 | 107 | "AA87CA22BE8B05378EB1C71EF320AD746E1D3B628BA79B9859F741E082542A385502F25DBF55296C3A545E3872760AB7", |
106 | 113 | 66, |
107 | 114 | "ECC-521", |
108 | 115 | "1FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF", |
116 | "1FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFC", | |
109 | 117 | "51953EB9618E1C9A1F929A21A0B68540EEA2DA725B99B315F3B8B489918EF109E156193951EC7E937B1652C0BD3BB1BF073573DF883D2C34F1EF451FD46B503F00", |
110 | 118 | "1FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFA51868783BF2F966B7FCC0148F709A5D03BB5C9B8899C47AEBB6FB71E91386409", |
111 | 119 | "C6858E06B70404E9CD9E3ECB662395B4429C648139053FB521F828AF606B4D3DBAA14B5E77EFE75928FE1DC127A2FFA8DE3348B3C1856A429BF97E7E31C2E5BD66", |
8 | 8 | * Tom St Denis, tomstdenis@gmail.com, http://libtom.org |
9 | 9 | */ |
10 | 10 | |
11 | /* Implements ECC over Z/pZ for curve y^2 = x^3 - 3x + b | |
11 | /* Implements ECC over Z/pZ for curve y^2 = x^3 + a*x + b | |
12 | 12 | * |
13 | 13 | * All curves taken from NIST recommendation paper of July 1999 |
14 | 14 | * Available at http://csrc.nist.gov/cryptval/dss.htm |
8 | 8 | * Tom St Denis, tomstdenis@gmail.com, http://libtom.org |
9 | 9 | */ |
10 | 10 | |
11 | /* Implements ECC over Z/pZ for curve y^2 = x^3 - 3x + b | |
11 | /* Implements ECC over Z/pZ for curve y^2 = x^3 + a*x + b | |
12 | 12 | * |
13 | 13 | * All curves taken from NIST recommendation paper of July 1999 |
14 | 14 | * Available at http://csrc.nist.gov/cryptval/dss.htm |
8 | 8 | * Tom St Denis, tomstdenis@gmail.com, http://libtom.org |
9 | 9 | */ |
10 | 10 | |
11 | /* Implements ECC over Z/pZ for curve y^2 = x^3 - 3x + b | |
11 | /* Implements ECC over Z/pZ for curve y^2 = x^3 + a*x + b | |
12 | 12 | * |
13 | 13 | * All curves taken from NIST recommendation paper of July 1999 |
14 | 14 | * Available at http://csrc.nist.gov/cryptval/dss.htm |
8 | 8 | * Tom St Denis, tomstdenis@gmail.com, http://libtom.org |
9 | 9 | */ |
10 | 10 | |
11 | /* Implements ECC over Z/pZ for curve y^2 = x^3 - 3x + b | |
11 | /* Implements ECC over Z/pZ for curve y^2 = x^3 + a*x + b | |
12 | 12 | * |
13 | 13 | * All curves taken from NIST recommendation paper of July 1999 |
14 | 14 | * Available at http://csrc.nist.gov/cryptval/dss.htm |
8 | 8 | * Tom St Denis, tomstdenis@gmail.com, http://libtom.org |
9 | 9 | */ |
10 | 10 | |
11 | /* Implements ECC over Z/pZ for curve y^2 = x^3 - 3x + b | |
11 | /* Implements ECC over Z/pZ for curve y^2 = x^3 + a*x + b | |
12 | 12 | * |
13 | 13 | * All curves taken from NIST recommendation paper of July 1999 |
14 | 14 | * Available at http://csrc.nist.gov/cryptval/dss.htm |
8 | 8 | * Tom St Denis, tomstdenis@gmail.com, http://libtom.org |
9 | 9 | */ |
10 | 10 | |
11 | /* Implements ECC over Z/pZ for curve y^2 = x^3 - 3x + b | |
11 | /* Implements ECC over Z/pZ for curve y^2 = x^3 + a*x + b | |
12 | 12 | * |
13 | 13 | * All curves taken from NIST recommendation paper of July 1999 |
14 | 14 | * Available at http://csrc.nist.gov/cryptval/dss.htm |
8 | 8 | * Tom St Denis, tomstdenis@gmail.com, http://libtom.org |
9 | 9 | */ |
10 | 10 | |
11 | /* Implements ECC over Z/pZ for curve y^2 = x^3 - 3x + b | |
11 | /* Implements ECC over Z/pZ for curve y^2 = x^3 + a*x + b | |
12 | 12 | * |
13 | 13 | * All curves taken from NIST recommendation paper of July 1999 |
14 | 14 | * Available at http://csrc.nist.gov/cryptval/dss.htm |
8 | 8 | * Tom St Denis, tomstdenis@gmail.com, http://libtom.org |
9 | 9 | */ |
10 | 10 | |
11 | /* Implements ECC over Z/pZ for curve y^2 = x^3 - 3x + b | |
11 | /* Implements ECC over Z/pZ for curve y^2 = x^3 + a*x + b | |
12 | 12 | * |
13 | 13 | * All curves taken from NIST recommendation paper of July 1999 |
14 | 14 | * Available at http://csrc.nist.gov/cryptval/dss.htm |
18 | 18 | /** |
19 | 19 | @file ecc_import.c |
20 | 20 | ECC Crypto, Tom St Denis |
21 | */ | |
21 | */ | |
22 | 22 | |
23 | 23 | #ifdef LTC_MECC |
24 | 24 | |
25 | 25 | static int is_point(ecc_key *key) |
26 | 26 | { |
27 | void *prime, *b, *t1, *t2; | |
27 | void *prime, *a, *b, *t1, *t2; | |
28 | 28 | int err; |
29 | ||
30 | if ((err = mp_init_multi(&prime, &b, &t1, &t2, NULL)) != CRYPT_OK) { | |
29 | ||
30 | if ((err = mp_init_multi(&prime, &a, &b, &t1, &t2, NULL)) != CRYPT_OK) { | |
31 | 31 | return err; |
32 | 32 | } |
33 | ||
34 | /* load prime and b */ | |
33 | ||
34 | /* load prime, a and b */ | |
35 | 35 | if ((err = mp_read_radix(prime, key->dp->prime, 16)) != CRYPT_OK) { goto error; } |
36 | 36 | if ((err = mp_read_radix(b, key->dp->B, 16)) != CRYPT_OK) { goto error; } |
37 | ||
37 | if ((err = mp_read_radix(a, key->dp->A, 16)) != CRYPT_OK) { goto error; } | |
38 | ||
38 | 39 | /* compute y^2 */ |
39 | 40 | if ((err = mp_sqr(key->pubkey.y, t1)) != CRYPT_OK) { goto error; } |
40 | ||
41 | ||
41 | 42 | /* compute x^3 */ |
42 | 43 | if ((err = mp_sqr(key->pubkey.x, t2)) != CRYPT_OK) { goto error; } |
43 | 44 | if ((err = mp_mod(t2, prime, t2)) != CRYPT_OK) { goto error; } |
44 | 45 | if ((err = mp_mul(key->pubkey.x, t2, t2)) != CRYPT_OK) { goto error; } |
45 | ||
46 | ||
46 | 47 | /* compute y^2 - x^3 */ |
47 | 48 | if ((err = mp_sub(t1, t2, t1)) != CRYPT_OK) { goto error; } |
48 | ||
49 | /* compute y^2 - x^3 + 3x */ | |
50 | if ((err = mp_add(t1, key->pubkey.x, t1)) != CRYPT_OK) { goto error; } | |
51 | if ((err = mp_add(t1, key->pubkey.x, t1)) != CRYPT_OK) { goto error; } | |
52 | if ((err = mp_add(t1, key->pubkey.x, t1)) != CRYPT_OK) { goto error; } | |
53 | if ((err = mp_mod(t1, prime, t1)) != CRYPT_OK) { goto error; } | |
49 | ||
50 | /* compute y^2 - x^3 - a*x */ | |
51 | if ((err = mp_submod(prime, a, prime, t2)) != CRYPT_OK) { goto error; } | |
52 | if ((err = mp_mulmod(t2, key->pubkey.x, prime, t2)) != CRYPT_OK) { goto error; } | |
53 | if ((err = mp_addmod(t1, t2, prime, t1)) != CRYPT_OK) { goto error; } | |
54 | ||
55 | /* adjust range (0, prime) */ | |
54 | 56 | while (mp_cmp_d(t1, 0) == LTC_MP_LT) { |
55 | 57 | if ((err = mp_add(t1, prime, t1)) != CRYPT_OK) { goto error; } |
56 | 58 | } |
57 | 59 | while (mp_cmp(t1, prime) != LTC_MP_LT) { |
58 | 60 | if ((err = mp_sub(t1, prime, t1)) != CRYPT_OK) { goto error; } |
59 | 61 | } |
60 | ||
62 | ||
61 | 63 | /* compare to b */ |
62 | 64 | if (mp_cmp(t1, b) != LTC_MP_EQ) { |
63 | 65 | err = CRYPT_INVALID_PACKET; |
64 | 66 | } else { |
65 | 67 | err = CRYPT_OK; |
66 | 68 | } |
67 | ||
69 | ||
68 | 70 | error: |
69 | 71 | mp_clear_multi(prime, b, t1, t2, NULL); |
70 | 72 | return err; |
106 | 108 | } |
107 | 109 | |
108 | 110 | /* find out what type of key it is */ |
109 | if ((err = der_decode_sequence_multi(in, inlen, | |
111 | if ((err = der_decode_sequence_multi(in, inlen, | |
110 | 112 | LTC_ASN1_BIT_STRING, 1UL, &flags, |
111 | 113 | LTC_ASN1_EOL, 0UL, NULL)) != CRYPT_OK) { |
112 | 114 | goto done; |
152 | 154 | } |
153 | 155 | /* set z */ |
154 | 156 | if ((err = mp_set(key->pubkey.z, 1)) != CRYPT_OK) { goto done; } |
155 | ||
157 | ||
156 | 158 | /* is it a point on the curve? */ |
157 | 159 | if ((err = is_point(key)) != CRYPT_OK) { |
158 | 160 | goto done; |
8 | 8 | * Tom St Denis, tomstdenis@gmail.com, http://libtom.org |
9 | 9 | */ |
10 | 10 | |
11 | /* Implements ECC over Z/pZ for curve y^2 = x^3 - 3x + b | |
11 | /* Implements ECC over Z/pZ for curve y^2 = x^3 + a*x + b | |
12 | 12 | * |
13 | 13 | * All curves taken from NIST recommendation paper of July 1999 |
14 | 14 | * Available at http://csrc.nist.gov/cryptval/dss.htm |
8 | 8 | * Tom St Denis, tomstdenis@gmail.com, http://libtom.org |
9 | 9 | */ |
10 | 10 | |
11 | /* Implements ECC over Z/pZ for curve y^2 = x^3 - 3x + b | |
11 | /* Implements ECC over Z/pZ for curve y^2 = x^3 + a*x + b | |
12 | 12 | * |
13 | 13 | * All curves taken from NIST recommendation paper of July 1999 |
14 | 14 | * Available at http://csrc.nist.gov/cryptval/dss.htm |
8 | 8 | * Tom St Denis, tomstdenis@gmail.com, http://libtom.org |
9 | 9 | */ |
10 | 10 | |
11 | /* Implements ECC over Z/pZ for curve y^2 = x^3 - 3x + b | |
11 | /* Implements ECC over Z/pZ for curve y^2 = x^3 + a*x + b | |
12 | 12 | * |
13 | 13 | * All curves taken from NIST recommendation paper of July 1999 |
14 | 14 | * Available at http://csrc.nist.gov/cryptval/dss.htm |
8 | 8 | * Tom St Denis, tomstdenis@gmail.com, http://libtom.org |
9 | 9 | */ |
10 | 10 | |
11 | /* Implements ECC over Z/pZ for curve y^2 = x^3 - 3x + b | |
11 | /* Implements ECC over Z/pZ for curve y^2 = x^3 + a*x + b | |
12 | 12 | * |
13 | 13 | * All curves taken from NIST recommendation paper of July 1999 |
14 | 14 | * Available at http://csrc.nist.gov/cryptval/dss.htm |
8 | 8 | * Tom St Denis, tomstdenis@gmail.com, http://libtom.org |
9 | 9 | */ |
10 | 10 | |
11 | /* Implements ECC over Z/pZ for curve y^2 = x^3 - 3x + b | |
11 | /* Implements ECC over Z/pZ for curve y^2 = x^3 + a*x + b | |
12 | 12 | * |
13 | 13 | * All curves taken from NIST recommendation paper of July 1999 |
14 | 14 | * Available at http://csrc.nist.gov/cryptval/dss.htm |
8 | 8 | * Tom St Denis, tomstdenis@gmail.com, http://libtom.org |
9 | 9 | */ |
10 | 10 | |
11 | /* Implements ECC over Z/pZ for curve y^2 = x^3 - 3x + b | |
11 | /* Implements ECC over Z/pZ for curve y^2 = x^3 + a*x + b | |
12 | 12 | * |
13 | 13 | * All curves taken from NIST recommendation paper of July 1999 |
14 | 14 | * Available at http://csrc.nist.gov/cryptval/dss.htm |
8 | 8 | * Tom St Denis, tomstdenis@gmail.com, http://libtom.org |
9 | 9 | */ |
10 | 10 | |
11 | /* Implements ECC over Z/pZ for curve y^2 = x^3 - 3x + b | |
11 | /* Implements ECC over Z/pZ for curve y^2 = x^3 + a*x + b | |
12 | 12 | * |
13 | 13 | * All curves taken from NIST recommendation paper of July 1999 |
14 | 14 | * Available at http://csrc.nist.gov/cryptval/dss.htm |
8 | 8 | * Tom St Denis, tomstdenis@gmail.com, http://libtom.org |
9 | 9 | */ |
10 | 10 | |
11 | /* Implements ECC over Z/pZ for curve y^2 = x^3 - 3x + b | |
11 | /* Implements ECC over Z/pZ for curve y^2 = x^3 + a*x + b | |
12 | 12 | * |
13 | 13 | * All curves taken from NIST recommendation paper of July 1999 |
14 | 14 | * Available at http://csrc.nist.gov/cryptval/dss.htm |
8 | 8 | * Tom St Denis, tomstdenis@gmail.com, http://libtom.org |
9 | 9 | */ |
10 | 10 | |
11 | /* Implements ECC over Z/pZ for curve y^2 = x^3 - 3x + b | |
11 | /* Implements ECC over Z/pZ for curve y^2 = x^3 + a*x + b | |
12 | 12 | * |
13 | 13 | * All curves taken from NIST recommendation paper of July 1999 |
14 | 14 | * Available at http://csrc.nist.gov/cryptval/dss.htm |
8 | 8 | * Tom St Denis, tomstdenis@gmail.com, http://libtom.org |
9 | 9 | */ |
10 | 10 | |
11 | /* Implements ECC over Z/pZ for curve y^2 = x^3 - 3x + b | |
11 | /* Implements ECC over Z/pZ for curve y^2 = x^3 + a*x + b | |
12 | 12 | * |
13 | 13 | * All curves taken from NIST recommendation paper of July 1999 |
14 | 14 | * Available at http://csrc.nist.gov/cryptval/dss.htm |
8 | 8 | * Tom St Denis, tomstdenis@gmail.com, http://libtom.org |
9 | 9 | */ |
10 | 10 | |
11 | /* Implements ECC over Z/pZ for curve y^2 = x^3 - 3x + b | |
11 | /* Implements ECC over Z/pZ for curve y^2 = x^3 + a*x + b | |
12 | 12 | * |
13 | 13 | * All curves taken from NIST recommendation paper of July 1999 |
14 | 14 | * Available at http://csrc.nist.gov/cryptval/dss.htm |
8 | 8 | * Tom St Denis, tomstdenis@gmail.com, http://libtom.org |
9 | 9 | */ |
10 | 10 | |
11 | /* Implements ECC over Z/pZ for curve y^2 = x^3 - 3x + b | |
11 | /* Implements ECC over Z/pZ for curve y^2 = x^3 + a*x + b | |
12 | 12 | * |
13 | 13 | * All curves taken from NIST recommendation paper of July 1999 |
14 | 14 | * Available at http://csrc.nist.gov/cryptval/dss.htm |
8 | 8 | * Tom St Denis, tomstdenis@gmail.com, http://libtom.org |
9 | 9 | */ |
10 | 10 | |
11 | /* Implements ECC over Z/pZ for curve y^2 = x^3 - 3x + b | |
11 | /* Implements ECC over Z/pZ for curve y^2 = x^3 + a*x + b | |
12 | 12 | * |
13 | 13 | * All curves taken from NIST recommendation paper of July 1999 |
14 | 14 | * Available at http://csrc.nist.gov/cryptval/dss.htm |