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annotate libtommath/bn_mp_sqrtmod_prime.c @ 1674:ba6fc7afe1c5

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author Matt Johnston <matt@ucc.asn.au>
date Mon, 06 Apr 2020 23:18:26 +0800
parents f52919ffd3b1
children 1051e4eea25a
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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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parents: 1436
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 *
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5 * LibTomMath is a library that provides multiple-precision
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6 * integer arithmetic as well as number theoretic functionality.
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7 *
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8 * The library was designed directly after the MPI library by
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9 * Michael Fromberger but has been written from scratch with
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10 * additional optimizations in place.
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11 *
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12 * SPDX-License-Identifier: Unlicense
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13 */
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14
60fc6476e044 Update to libtommath v1.0
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15 /* Tonelli-Shanks algorithm
60fc6476e044 Update to libtommath v1.0
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16 * https://en.wikipedia.org/wiki/Tonelli%E2%80%93Shanks_algorithm
60fc6476e044 Update to libtommath v1.0
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17 * https://gmplib.org/list-archives/gmp-discuss/2013-April/005300.html
60fc6476e044 Update to libtommath v1.0
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18 *
60fc6476e044 Update to libtommath v1.0
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19 */
60fc6476e044 Update to libtommath v1.0
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20
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f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
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21 int mp_sqrtmod_prime(const mp_int *n, const mp_int *prime, mp_int *ret)
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22 {
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f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
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23 int res, legendre;
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24 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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25 mp_digit i;
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26
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27 /* 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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28 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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29 mp_zero(ret);
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30 return MP_OKAY;
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
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31 }
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32 if (mp_cmp_d(prime, 2uL) == MP_EQ) return MP_VAL; /* prime must be odd */
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
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33 if ((res = mp_jacobi(n, prime, &legendre)) != MP_OKAY) return res;
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34 if (legendre == -1) return MP_VAL; /* quadratic non-residue mod prime */
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35
1655
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36 if ((res = mp_init_multi(&t1, &C, &Q, &S, &Z, &M, &T, &R, &two, NULL)) != MP_OKAY) {
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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37 return res;
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
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38 }
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60fc6476e044 Update to libtommath v1.0
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39
1655
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40 /* SPECIAL CASE: if prime mod 4 == 3
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41 * compute directly: res = n^(prime+1)/4 mod prime
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42 * Handbook of Applied Cryptography algorithm 3.36
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43 */
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Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1436
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44 if ((res = mp_mod_d(prime, 4uL, &i)) != MP_OKAY) goto cleanup;
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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45 if (i == 3u) {
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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46 if ((res = mp_add_d(prime, 1uL, &t1)) != MP_OKAY) goto cleanup;
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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47 if ((res = mp_div_2(&t1, &t1)) != MP_OKAY) 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
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48 if ((res = mp_div_2(&t1, &t1)) != MP_OKAY) 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
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49 if ((res = mp_exptmod(n, &t1, prime, ret)) != MP_OKAY) goto cleanup;
1436
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50 res = MP_OKAY;
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51 goto cleanup;
1655
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
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52 }
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53
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
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54 /* NOW: Tonelli-Shanks algorithm */
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55
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
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56 /* factor out powers of 2 from prime-1, defining Q and S as: prime-1 = Q*2^S */
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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57 if ((res = mp_copy(prime, &Q)) != MP_OKAY) goto cleanup;
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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58 if ((res = mp_sub_d(&Q, 1uL, &Q)) != MP_OKAY) goto cleanup;
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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59 /* Q = prime - 1 */
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60 mp_zero(&S);
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
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61 /* S = 0 */
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
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62 while (mp_iseven(&Q) != MP_NO) {
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
63 if ((res = mp_div_2(&Q, &Q)) != MP_OKAY) 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
64 /* Q = Q / 2 */
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
65 if ((res = mp_add_d(&S, 1uL, &S)) != MP_OKAY) 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
66 /* S = S + 1 */
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
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67 }
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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68
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
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diff changeset
69 /* find a Z such that the Legendre symbol (Z|prime) == -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
70 if ((res = mp_set_int(&Z, 2uL)) != MP_OKAY) goto cleanup;
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
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parents: 1436
diff changeset
71 /* Z = 2 */
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parents: 1436
diff changeset
72 while (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
73 if ((res = mp_jacobi(&Z, prime, &legendre)) != MP_OKAY) 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
74 if (legendre == -1) break;
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 if ((res = mp_add_d(&Z, 1uL, &Z)) != MP_OKAY) goto cleanup;
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
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parents: 1436
diff changeset
76 /* 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>
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77 }
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
78
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 if ((res = mp_exptmod(&Z, &Q, prime, &C)) != MP_OKAY) 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
80 /* C = Z ^ Q mod prime */
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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diff changeset
81 if ((res = mp_add_d(&Q, 1uL, &t1)) != MP_OKAY) 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
82 if ((res = mp_div_2(&t1, &t1)) != MP_OKAY) 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
83 /* t1 = (Q + 1) / 2 */
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
84 if ((res = mp_exptmod(n, &t1, prime, &R)) != MP_OKAY) 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
85 /* R = n ^ ((Q + 1) / 2) mod prime */
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 if ((res = mp_exptmod(n, &Q, prime, &T)) != MP_OKAY) 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
87 /* T = n ^ Q mod prime */
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 ((res = mp_copy(&S, &M)) != MP_OKAY) 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
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89 /* M = S */
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 if ((res = mp_set_int(&two, 2uL)) != MP_OKAY) 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
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 res = MP_VAL;
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Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1436
diff changeset
93 while (1) {
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Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1436
diff changeset
94 if ((res = mp_copy(&T, &t1)) != MP_OKAY) 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
95 i = 0;
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Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1436
diff changeset
96 while (1) {
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Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1436
diff changeset
97 if (mp_cmp_d(&t1, 1uL) == MP_EQ) break;
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
98 if ((res = mp_exptmod(&t1, &two, prime, &t1)) != MP_OKAY) 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
99 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
100 }
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
101 if (i == 0u) {
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 if ((res = mp_copy(&R, ret)) != MP_OKAY) 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
103 res = MP_OKAY;
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 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
105 }
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
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106 if ((res = mp_sub_d(&M, i, &t1)) != MP_OKAY) goto cleanup;
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107 if ((res = mp_sub_d(&t1, 1uL, &t1)) != MP_OKAY) goto cleanup;
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108 if ((res = mp_exptmod(&two, &t1, prime, &t1)) != MP_OKAY) goto cleanup;
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diff changeset
109 /* t1 = 2 ^ (M - i - 1) */
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110 if ((res = mp_exptmod(&C, &t1, prime, &t1)) != MP_OKAY) goto cleanup;
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
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parents: 1436
diff changeset
111 /* t1 = C ^ (2 ^ (M - i - 1)) mod prime */
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
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parents: 1436
diff changeset
112 if ((res = mp_sqrmod(&t1, prime, &C)) != MP_OKAY) goto cleanup;
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
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parents: 1436
diff changeset
113 /* C = (t1 * t1) mod prime */
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parents: 1436
diff changeset
114 if ((res = mp_mulmod(&R, &t1, prime, &R)) != MP_OKAY) goto cleanup;
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
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parents: 1436
diff changeset
115 /* R = (R * t1) mod prime */
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parents: 1436
diff changeset
116 if ((res = mp_mulmod(&T, &C, prime, &T)) != MP_OKAY) goto cleanup;
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
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parents: 1436
diff changeset
117 /* T = (T * C) mod prime */
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
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parents: 1436
diff changeset
118 mp_set(&M, i);
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diff changeset
119 /* M = i */
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parents: 1436
diff changeset
120 }
1436
60fc6476e044 Update to libtommath v1.0
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
121
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parents:
diff changeset
122 cleanup:
1655
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
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parents: 1436
diff changeset
123 mp_clear_multi(&t1, &C, &Q, &S, &Z, &M, &T, &R, &two, NULL);
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
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parents: 1436
diff changeset
124 return res;
1436
60fc6476e044 Update to libtommath v1.0
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
125 }
60fc6476e044 Update to libtommath v1.0
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
126
60fc6476e044 Update to libtommath v1.0
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parents:
diff changeset
127 #endif
1655
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parents: 1436
diff changeset
128
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
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parents: 1436
diff changeset
129 /* ref: HEAD -> master, tag: v1.1.0 */
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
130 /* git commit: 08549ad6bc8b0cede0b357a9c341c5c6473a9c55 */
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
131 /* commit time: 2019-01-28 20:32:32 +0100 */