Mercurial > dropbear

annotate libtommath/bn_mp_prime_is_prime.c @ 1736:0c31aedc3124

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Added signature for changeset 88f63b8b0f13
author Matt Johnston <matt@ucc.asn.au>
date Fri, 26 Jun 2020 21:57:20 +0800
parents 1051e4eea25a
children
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diff changeset
1 #include "tommath_private.h"
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2 #ifdef BN_MP_PRIME_IS_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
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6 /* portable integer log of two with small footprint */
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7 static unsigned int s_floor_ilog2(int value)
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8 {
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9 unsigned int r = 0;
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10 while ((value >>= 1) != 0) {
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11 r++;
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12 }
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13 return r;
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14 }
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15
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16
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17 mp_err mp_prime_is_prime(const mp_int *a, int t, mp_bool *result)
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18 {
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19 mp_int b;
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20 int ix, p_max = 0, size_a, len;
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21 mp_bool res;
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22 mp_err err;
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23 unsigned int fips_rand, mask;
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24
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25 /* default to no */
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26 *result = MP_NO;
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27
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28 /* Some shortcuts */
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29 /* N > 3 */
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30 if (a->used == 1) {
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31 if ((a->dp[0] == 0u) || (a->dp[0] == 1u)) {
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32 *result = MP_NO;
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33 return MP_OKAY;
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34 }
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35 if (a->dp[0] == 2u) {
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36 *result = MP_YES;
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37 return MP_OKAY;
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38 }
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39 }
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40
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41 /* N must be odd */
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42 if (MP_IS_EVEN(a)) {
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43 return MP_OKAY;
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44 }
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45 /* N is not a perfect square: floor(sqrt(N))^2 != N */
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46 if ((err = mp_is_square(a, &res)) != MP_OKAY) {
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47 return err;
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48 }
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49 if (res != MP_NO) {
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50 return MP_OKAY;
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51 }
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52
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53 /* is the input equal to one of the primes in the table? */
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54 for (ix = 0; ix < PRIVATE_MP_PRIME_TAB_SIZE; ix++) {
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55 if (mp_cmp_d(a, s_mp_prime_tab[ix]) == MP_EQ) {
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56 *result = MP_YES;
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57 return MP_OKAY;
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58 }
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59 }
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60 #ifdef MP_8BIT
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61 /* The search in the loop above was exhaustive in this case */
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62 if ((a->used == 1) && (PRIVATE_MP_PRIME_TAB_SIZE >= 31)) {
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63 return MP_OKAY;
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64 }
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65 #endif
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66
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67 /* first perform trial division */
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68 if ((err = s_mp_prime_is_divisible(a, &res)) != MP_OKAY) {
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69 return err;
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70 }
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71
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72 /* return if it was trivially divisible */
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73 if (res == MP_YES) {
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74 return MP_OKAY;
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75 }
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76
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77 /*
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78 Run the Miller-Rabin test with base 2 for the BPSW test.
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79 */
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80 if ((err = mp_init_set(&b, 2uL)) != MP_OKAY) {
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81 return err;
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82 }
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83
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84 if ((err = mp_prime_miller_rabin(a, &b, &res)) != MP_OKAY) {
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85 goto LBL_B;
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86 }
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87 if (res == MP_NO) {
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88 goto LBL_B;
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89 }
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90 /*
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91 Rumours have it that Mathematica does a second M-R test with base 3.
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92 Other rumours have it that their strong L-S test is slightly different.
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93 It does not hurt, though, beside a bit of extra runtime.
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94 */
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95 b.dp[0]++;
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96 if ((err = mp_prime_miller_rabin(a, &b, &res)) != MP_OKAY) {
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97 goto LBL_B;
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98 }
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99 if (res == MP_NO) {
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100 goto LBL_B;
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101 }
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102
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103 /*
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104 * Both, the Frobenius-Underwood test and the the Lucas-Selfridge test are quite
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diff changeset
105 * slow so if speed is an issue, define LTM_USE_ONLY_MR to use M-R tests with
1655
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1470
diff changeset
106 * bases 2, 3 and t random bases.
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Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1470
diff changeset
107 */
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1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents: 1656
diff changeset
108 #ifndef LTM_USE_ONLY_MR
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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>
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diff changeset
109 if (t >= 0) {
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1470
diff changeset
110 /*
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Steffen Jaeckel <s_jaeckel@gmx.de>
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diff changeset
111 * Use a Frobenius-Underwood test instead of the Lucas-Selfridge test for
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1470
diff changeset
112 * MP_8BIT (It is unknown if the Lucas-Selfridge test works with 16-bit
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1470
diff changeset
113 * integers but the necesssary analysis is on the todo-list).
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1470
diff changeset
114 */
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Steffen Jaeckel <s_jaeckel@gmx.de>
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diff changeset
115 #if defined (MP_8BIT) || defined (LTM_USE_FROBENIUS_TEST)
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
116 err = mp_prime_frobenius_underwood(a, &res);
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diff changeset
117 if ((err != MP_OKAY) && (err != MP_ITER)) {
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
118 goto LBL_B;
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Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1470
diff changeset
119 }
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Steffen Jaeckel <s_jaeckel@gmx.de>
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diff changeset
120 if (res == MP_NO) {
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Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1470
diff changeset
121 goto LBL_B;
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1470
diff changeset
122 }
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Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1470
diff changeset
123 #else
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Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1470
diff changeset
124 if ((err = mp_prime_strong_lucas_selfridge(a, &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: 1470
diff changeset
125 goto LBL_B;
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1470
diff changeset
126 }
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Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1470
diff changeset
127 if (res == MP_NO) {
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Steffen Jaeckel <s_jaeckel@gmx.de>
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diff changeset
128 goto LBL_B;
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1470
diff changeset
129 }
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Steffen Jaeckel <s_jaeckel@gmx.de>
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diff changeset
130 #endif
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Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1470
diff changeset
131 }
284
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583)
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
132 #endif
389
5ff8218bcee9 propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 2af95f00ebd5bb7a28b3817db1218442c935388e)
Matt Johnston <matt@ucc.asn.au>
parents: 284
diff changeset
133
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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diff changeset
134 /* run at least one Miller-Rabin test with a random base */
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Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1470
diff changeset
135 if (t == 0) {
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
136 t = 1;
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Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1470
diff changeset
137 }
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1470
diff changeset
138
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1470
diff changeset
139 /*
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
140 Only recommended if the input range is known to be < 3317044064679887385961981
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1470
diff changeset
141
1692
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents: 1656
diff changeset
142 It uses the bases necessary for a deterministic M-R test if the input is
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents: 1656
diff changeset
143 smaller than 3317044064679887385961981
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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diff changeset
144 The caller has to check the size.
1692
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents: 1656
diff changeset
145 TODO: can be made a bit finer grained but comparing is not free.
1655
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Steffen Jaeckel <s_jaeckel@gmx.de>
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diff changeset
146 */
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1470
diff changeset
147 if (t < 0) {
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Steffen Jaeckel <s_jaeckel@gmx.de>
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diff changeset
148 /*
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Steffen Jaeckel <s_jaeckel@gmx.de>
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diff changeset
149 Sorenson, Jonathan; Webster, Jonathan (2015).
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diff changeset
150 "Strong Pseudoprimes to Twelve Prime Bases".
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Steffen Jaeckel <s_jaeckel@gmx.de>
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diff changeset
151 */
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Steffen Jaeckel <s_jaeckel@gmx.de>
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diff changeset
152 /* 0x437ae92817f9fc85b7e5 = 318665857834031151167461 */
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1470
diff changeset
153 if ((err = mp_read_radix(&b, "437ae92817f9fc85b7e5", 16)) != 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: 1470
diff changeset
154 goto LBL_B;
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1470
diff changeset
155 }
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Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1470
diff changeset
156
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1470
diff changeset
157 if (mp_cmp(a, &b) == MP_LT) {
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1470
diff changeset
158 p_max = 12;
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Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1470
diff changeset
159 } else {
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Steffen Jaeckel <s_jaeckel@gmx.de>
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diff changeset
160 /* 0x2be6951adc5b22410a5fd = 3317044064679887385961981 */
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Steffen Jaeckel <s_jaeckel@gmx.de>
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diff changeset
161 if ((err = mp_read_radix(&b, "2be6951adc5b22410a5fd", 16)) != 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: 1470
diff changeset
162 goto LBL_B;
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1470
diff changeset
163 }
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1470
diff changeset
164
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1470
diff changeset
165 if (mp_cmp(a, &b) == MP_LT) {
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1470
diff changeset
166 p_max = 13;
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Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1470
diff changeset
167 } else {
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1470
diff changeset
168 err = MP_VAL;
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1470
diff changeset
169 goto LBL_B;
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1470
diff changeset
170 }
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1470
diff changeset
171 }
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1470
diff changeset
172
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1470
diff changeset
173 /* we did bases 2 and 3 already, skip them */
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Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1470
diff changeset
174 for (ix = 2; ix < p_max; ix++) {
1692
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
Steffen Jaeckel <s@jaeckel.eu>
parents: 1656
diff changeset
175 mp_set(&b, s_mp_prime_tab[ix]);
1655
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1470
diff changeset
176 if ((err = mp_prime_miller_rabin(a, &b, &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: 1470
diff changeset
177 goto LBL_B;
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1470
diff changeset
178 }
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1470
diff changeset
179 if (res == 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: 1470
diff changeset
180 goto LBL_B;
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1470
diff changeset
181 }
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1470
diff changeset
182 }
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1470
diff changeset
183 }
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1470
diff changeset
184 /*
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1470
diff changeset
185 Do "t" M-R tests with random bases between 3 and "a".
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1470
diff changeset
186 See Fips 186.4 p. 126ff
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1470
diff changeset
187 */
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1470
diff changeset
188 else if (t > 0) {
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1470
diff changeset
189 /*
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1470
diff changeset
190 * The mp_digit's have a defined bit-size but the size of the
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1470
diff changeset
191 * array a.dp is a simple 'int' and this library can not assume full
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1470
diff changeset
192 * compliance to the current C-standard (ISO/IEC 9899:2011) because
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1470
diff changeset
193 * it gets used for small embeded processors, too. Some of those MCUs
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1470
diff changeset
194 * have compilers that one cannot call standard compliant by any means.
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1470
diff changeset
195 * Hence the ugly type-fiddling in the following code.
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1470
diff changeset
196 */
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1470
diff changeset
197 size_a = mp_count_bits(a);
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1470
diff changeset
198 mask = (1u << s_floor_ilog2(size_a)) - 1u;
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1470
diff changeset
199 /*
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1470
diff changeset
200 Assuming the General Rieman hypothesis (never thought to write that in a
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1470
diff changeset
201 comment) the upper bound can be lowered to 2*(log a)^2.
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1470
diff changeset
202 E. Bach, "Explicit bounds for primality testing and related problems,"
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1470
diff changeset
203 Math. Comp. 55 (1990), 355-380.
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
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parents: 1470
diff changeset
204
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1470
diff changeset
205 size_a = (size_a/10) * 7;
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1470
diff changeset
206 len = 2 * (size_a * size_a);
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1470
diff changeset
207
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1470
diff changeset
208 E.g.: a number of size 2^2048 would be reduced to the upper limit
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1470
diff changeset
209
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1470
diff changeset
210 floor(2048/10)*7 = 1428
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Steffen Jaeckel <s_jaeckel@gmx.de>
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diff changeset
211 2 * 1428^2 = 4078368
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diff changeset
212
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diff changeset
213 (would have been ~4030331.9962 with floats and natural log instead)
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
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diff changeset
214 That number is smaller than 2^28, the default bit-size of mp_digit.
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diff changeset
215 */
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diff changeset
216
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
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diff changeset
217 /*
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diff changeset
218 How many tests, you might ask? Dana Jacobsen of Math::Prime::Util fame
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diff changeset
219 does exactly 1. In words: one. Look at the end of _GMP_is_prime() in
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
220 Math-Prime-Util-GMP-0.50/primality.c if you do not believe it.
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diff changeset
221
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diff changeset
222 The function mp_rand() goes to some length to use a cryptographically
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Steffen Jaeckel <s_jaeckel@gmx.de>
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diff changeset
223 good PRNG. That also means that the chance to always get the same base
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Steffen Jaeckel <s_jaeckel@gmx.de>
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diff changeset
224 in the loop is non-zero, although very low.
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
225 If the BPSW test and/or the addtional Frobenious test have been
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Steffen Jaeckel <s_jaeckel@gmx.de>
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diff changeset
226 performed instead of just the Miller-Rabin test with the bases 2 and 3,
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
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227 a single extra test should suffice, so such a very unlikely event
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diff changeset
228 will not do much harm.
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229
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230 To preemptivly answer the dangling question: no, a witness does not
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diff changeset
231 need to be prime.
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232 */
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diff changeset
233 for (ix = 0; ix < t; ix++) {
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234 /* mp_rand() guarantees the first digit to be non-zero */
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235 if ((err = mp_rand(&b, 1)) != MP_OKAY) {
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236 goto LBL_B;
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Steffen Jaeckel <s_jaeckel@gmx.de>
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237 }
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Steffen Jaeckel <s_jaeckel@gmx.de>
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diff changeset
238 /*
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239 * Reduce digit before casting because mp_digit might be bigger than
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240 * an unsigned int and "mask" on the other side is most probably not.
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diff changeset
241 */
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diff changeset
242 fips_rand = (unsigned int)(b.dp[0] & (mp_digit) mask);
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243 #ifdef MP_8BIT
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244 /*
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245 * One 8-bit digit is too small, so concatenate two if the size of
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
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246 * unsigned int allows for it.
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247 */
1692
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
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diff changeset
248 if ((MP_SIZEOF_BITS(unsigned int)/2) >= MP_SIZEOF_BITS(mp_digit)) {
1655
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
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diff changeset
249 if ((err = mp_rand(&b, 1)) != MP_OKAY) {
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250 goto LBL_B;
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251 }
1692
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
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252 fips_rand <<= MP_SIZEOF_BITS(mp_digit);
1655
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253 fips_rand |= (unsigned int) b.dp[0];
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254 fips_rand &= mask;
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255 }
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diff changeset
256 #endif
1692
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
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diff changeset
257 if (fips_rand > (unsigned int)(INT_MAX - MP_DIGIT_BIT)) {
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
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diff changeset
258 len = INT_MAX / MP_DIGIT_BIT;
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259 } else {
1692
1051e4eea25a Update LibTomMath to 1.2.0 (#84)
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260 len = (((int)fips_rand + MP_DIGIT_BIT) / MP_DIGIT_BIT);
1655
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
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261 }
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
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diff changeset
262 /* Unlikely. */
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diff changeset
263 if (len < 0) {
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diff changeset
264 ix--;
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
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diff changeset
265 continue;
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266 }
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Steffen Jaeckel <s_jaeckel@gmx.de>
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diff changeset
267 /*
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268 * As mentioned above, one 8-bit digit is too small and
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diff changeset
269 * although it can only happen in the unlikely case that
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diff changeset
270 * an "unsigned int" is smaller than 16 bit a simple test
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Steffen Jaeckel <s_jaeckel@gmx.de>
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diff changeset
271 * is cheap and the correction even cheaper.
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diff changeset
272 */
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Steffen Jaeckel <s_jaeckel@gmx.de>
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diff changeset
273 #ifdef MP_8BIT
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Steffen Jaeckel <s_jaeckel@gmx.de>
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diff changeset
274 /* All "a" < 2^8 have been caught before */
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Steffen Jaeckel <s_jaeckel@gmx.de>
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diff changeset
275 if (len == 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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diff changeset
276 len++;
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
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diff changeset
277 }
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Steffen Jaeckel <s_jaeckel@gmx.de>
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diff changeset
278 #endif
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
279 if ((err = mp_rand(&b, len)) != 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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diff changeset
280 goto LBL_B;
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
281 }
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
282 /*
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
283 * That number might got too big and the witness has to be
1656
a36e545fb43d Prime-related bugfixes (#81)
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diff changeset
284 * smaller than "a"
1655
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
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diff changeset
285 */
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
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diff changeset
286 len = mp_count_bits(&b);
1656
a36e545fb43d Prime-related bugfixes (#81)
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diff changeset
287 if (len >= size_a) {
a36e545fb43d Prime-related bugfixes (#81)
Steffen Jaeckel <s@jaeckel.eu>
parents: 1655
diff changeset
288 len = (len - size_a) + 1;
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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diff changeset
289 if ((err = mp_div_2d(&b, len, &b, 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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diff changeset
290 goto LBL_B;
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1470
diff changeset
291 }
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
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diff changeset
292 }
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
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diff changeset
293 /* Although the chance for b <= 3 is miniscule, try again. */
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diff changeset
294 if (mp_cmp_d(&b, 3uL) != MP_GT) {
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diff changeset
295 ix--;
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diff changeset
296 continue;
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
297 }
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
298 if ((err = mp_prime_miller_rabin(a, &b, &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>
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diff changeset
299 goto LBL_B;
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1470
diff changeset
300 }
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Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1470
diff changeset
301 if (res == MP_NO) {
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
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parents: 1470
diff changeset
302 goto LBL_B;
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
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parents: 1470
diff changeset
303 }
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1470
diff changeset
304 }
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1470
diff changeset
305 }
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1470
diff changeset
306
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
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parents: 1470
diff changeset
307 /* passed the test */
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Steffen Jaeckel <s_jaeckel@gmx.de>
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diff changeset
308 *result = MP_YES;
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
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diff changeset
309 LBL_B:
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Steffen Jaeckel <s_jaeckel@gmx.de>
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diff changeset
310 mp_clear(&b);
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Steffen Jaeckel <s_jaeckel@gmx.de>
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diff changeset
311 return err;
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
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diff changeset
312 }
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
313
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1470
diff changeset
314 #endif