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annotate libtommath/bn_mp_sqrtmod_prime.c @ 1820:e9854650d45b

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Clarify help text for dropbear -e environment option
author Matt Johnston <matt@ucc.asn.au>
date Thu, 19 Aug 2021 23:17:34 +0800
parents 1051e4eea25a
children
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rev   line source
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f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
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diff changeset
1 #include "tommath_private.h"
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2 #ifdef BN_MP_SQRTMOD_PRIME_C
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3 /* LibTomMath, multiple-precision integer library -- Tom St Denis */
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4 /* SPDX-License-Identifier: Unlicense */
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5
60fc6476e044 Update to libtommath v1.0
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6 /* Tonelli-Shanks algorithm
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7 * https://en.wikipedia.org/wiki/Tonelli%E2%80%93Shanks_algorithm
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8 * https://gmplib.org/list-archives/gmp-discuss/2013-April/005300.html
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9 *
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10 */
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11
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12 mp_err mp_sqrtmod_prime(const mp_int *n, const mp_int *prime, mp_int *ret)
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13 {
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14 mp_err err;
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
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15 int legendre;
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f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1436
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16 mp_int t1, C, Q, S, Z, M, T, R, two;
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
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17 mp_digit i;
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18
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f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
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diff changeset
19 /* first handle the simple cases */
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
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20 if (mp_cmp_d(n, 0uL) == MP_EQ) {
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
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21 mp_zero(ret);
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22 return MP_OKAY;
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
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parents: 1436
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23 }
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
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24 if (mp_cmp_d(prime, 2uL) == MP_EQ) return MP_VAL; /* prime must be odd */
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25 if ((err = mp_kronecker(n, prime, &legendre)) != MP_OKAY) return err;
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Steffen Jaeckel <s_jaeckel@gmx.de>
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26 if (legendre == -1) return MP_VAL; /* quadratic non-residue mod prime */
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27
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28 if ((err = mp_init_multi(&t1, &C, &Q, &S, &Z, &M, &T, &R, &two, NULL)) != MP_OKAY) {
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
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29 return err;
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30 }
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31
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32 /* SPECIAL CASE: if prime mod 4 == 3
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33 * compute directly: err = n^(prime+1)/4 mod prime
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34 * Handbook of Applied Cryptography algorithm 3.36
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35 */
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36 if ((err = mp_mod_d(prime, 4uL, &i)) != MP_OKAY) goto cleanup;
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f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
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37 if (i == 3u) {
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parents: 1655
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38 if ((err = mp_add_d(prime, 1uL, &t1)) != MP_OKAY) goto cleanup;
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
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39 if ((err = mp_div_2(&t1, &t1)) != MP_OKAY) goto cleanup;
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
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40 if ((err = mp_div_2(&t1, &t1)) != MP_OKAY) goto cleanup;
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
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parents: 1655
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41 if ((err = mp_exptmod(n, &t1, prime, ret)) != MP_OKAY) goto cleanup;
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
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42 err = MP_OKAY;
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60fc6476e044 Update to libtommath v1.0
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43 goto cleanup;
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f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
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44 }
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Steffen Jaeckel <s_jaeckel@gmx.de>
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45
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
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46 /* NOW: Tonelli-Shanks algorithm */
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
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47
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
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48 /* factor out powers of 2 from prime-1, defining Q and S as: prime-1 = Q*2^S */
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49 if ((err = mp_copy(prime, &Q)) != MP_OKAY) goto cleanup;
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
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parents: 1655
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50 if ((err = mp_sub_d(&Q, 1uL, &Q)) != MP_OKAY) goto cleanup;
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f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
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51 /* Q = prime - 1 */
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
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52 mp_zero(&S);
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53 /* S = 0 */
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54 while (MP_IS_EVEN(&Q)) {
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
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55 if ((err = mp_div_2(&Q, &Q)) != MP_OKAY) goto cleanup;
1655
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1436
diff changeset
56 /* Q = Q / 2 */
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57 if ((err = mp_add_d(&S, 1uL, &S)) != MP_OKAY) goto cleanup;
1655
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
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58 /* S = S + 1 */
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
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59 }
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
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parents: 1436
diff changeset
60
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
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diff changeset
61 /* find a Z such that the Legendre symbol (Z|prime) == -1 */
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62 mp_set_u32(&Z, 2u);
1655
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
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63 /* Z = 2 */
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64 for (;;) {
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
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65 if ((err = mp_kronecker(&Z, prime, &legendre)) != MP_OKAY) goto cleanup;
1655
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1436
diff changeset
66 if (legendre == -1) break;
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Steffen Jaeckel <s@jaeckel.eu>
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diff changeset
67 if ((err = mp_add_d(&Z, 1uL, &Z)) != MP_OKAY) goto cleanup;
1655
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1436
diff changeset
68 /* Z = Z + 1 */
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1436
diff changeset
69 }
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1436
diff changeset
70
1692
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents: 1655
diff changeset
71 if ((err = mp_exptmod(&Z, &Q, prime, &C)) != MP_OKAY) goto cleanup;
1655
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1436
diff changeset
72 /* C = Z ^ Q mod prime */
1692
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents: 1655
diff changeset
73 if ((err = mp_add_d(&Q, 1uL, &t1)) != MP_OKAY) goto cleanup;
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents: 1655
diff changeset
74 if ((err = mp_div_2(&t1, &t1)) != MP_OKAY) goto cleanup;
1655
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1436
diff changeset
75 /* t1 = (Q + 1) / 2 */
1692
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents: 1655
diff changeset
76 if ((err = mp_exptmod(n, &t1, prime, &R)) != MP_OKAY) goto cleanup;
1655
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1436
diff changeset
77 /* R = n ^ ((Q + 1) / 2) mod prime */
1692
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents: 1655
diff changeset
78 if ((err = mp_exptmod(n, &Q, prime, &T)) != MP_OKAY) goto cleanup;
1655
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1436
diff changeset
79 /* T = n ^ Q mod prime */
1692
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents: 1655
diff changeset
80 if ((err = mp_copy(&S, &M)) != MP_OKAY) goto cleanup;
1655
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1436
diff changeset
81 /* M = S */
1692
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents: 1655
diff changeset
82 mp_set_u32(&two, 2u);
1655
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1436
diff changeset
83
1692
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents: 1655
diff changeset
84 for (;;) {
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents: 1655
diff changeset
85 if ((err = mp_copy(&T, &t1)) != MP_OKAY) goto cleanup;
1655
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1436
diff changeset
86 i = 0;
1692
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents: 1655
diff changeset
87 for (;;) {
1655
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1436
diff changeset
88 if (mp_cmp_d(&t1, 1uL) == MP_EQ) break;
1692
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents: 1655
diff changeset
89 if ((err = mp_exptmod(&t1, &two, prime, &t1)) != MP_OKAY) goto cleanup;
1655
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1436
diff changeset
90 i++;
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1436
diff changeset
91 }
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1436
diff changeset
92 if (i == 0u) {
1692
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents: 1655
diff changeset
93 if ((err = mp_copy(&R, ret)) != MP_OKAY) goto cleanup;
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents: 1655
diff changeset
94 err = MP_OKAY;
1655
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1436
diff changeset
95 goto cleanup;
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1436
diff changeset
96 }
1692
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents: 1655
diff changeset
97 if ((err = mp_sub_d(&M, i, &t1)) != MP_OKAY) goto cleanup;
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents: 1655
diff changeset
98 if ((err = mp_sub_d(&t1, 1uL, &t1)) != MP_OKAY) goto cleanup;
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents: 1655
diff changeset
99 if ((err = mp_exptmod(&two, &t1, prime, &t1)) != MP_OKAY) goto cleanup;
1655
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1436
diff changeset
100 /* t1 = 2 ^ (M - i - 1) */
1692
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents: 1655
diff changeset
101 if ((err = mp_exptmod(&C, &t1, prime, &t1)) != MP_OKAY) goto cleanup;
1655
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1436
diff changeset
102 /* t1 = C ^ (2 ^ (M - i - 1)) mod prime */
1692
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents: 1655
diff changeset
103 if ((err = mp_sqrmod(&t1, prime, &C)) != MP_OKAY) goto cleanup;
1655
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1436
diff changeset
104 /* C = (t1 * t1) mod prime */
1692
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents: 1655
diff changeset
105 if ((err = mp_mulmod(&R, &t1, prime, &R)) != MP_OKAY) goto cleanup;
1655
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1436
diff changeset
106 /* R = (R * t1) mod prime */
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107 if ((err = mp_mulmod(&T, &C, prime, &T)) != MP_OKAY) goto cleanup;
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108 /* T = (T * C) mod prime */
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109 mp_set(&M, i);
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110 /* M = i */
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111 }
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112
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113 cleanup:
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114 mp_clear_multi(&t1, &C, &Q, &S, &Z, &M, &T, &R, &two, NULL);
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115 return err;
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116 }
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117
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118 #endif