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annotate libtommath/bn_mp_prime_is_prime.c @ 1680:5e763ad6e2e0

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author Matt Johnston <matt@ucc.asn.au>
date Sun, 24 May 2020 13:34:19 +0800
parents a36e545fb43d
children 1051e4eea25a
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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 *
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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
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15 /* portable integer log of two with small footprint */
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16 static unsigned int s_floor_ilog2(int value)
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17 {
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18 unsigned int r = 0;
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19 while ((value >>= 1) != 0) {
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20 r++;
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21 }
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22 return r;
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23 }
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24
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25
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26 int mp_prime_is_prime(const mp_int *a, int t, int *result)
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27 {
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28 mp_int b;
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29 int ix, err, res, p_max = 0, size_a, len;
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30 unsigned int fips_rand, mask;
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31
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32 /* default to no */
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33 *result = MP_NO;
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34
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35 /* valid value of t? */
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36 if (t > PRIME_SIZE) {
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37 return MP_VAL;
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38 }
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39
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40 /* Some shortcuts */
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41 /* N > 3 */
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42 if (a->used == 1) {
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43 if ((a->dp[0] == 0u) || (a->dp[0] == 1u)) {
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44 *result = 0;
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45 return MP_OKAY;
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46 }
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47 if (a->dp[0] == 2u) {
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48 *result = 1;
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49 return MP_OKAY;
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50 }
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51 }
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52
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53 /* N must be odd */
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54 if (mp_iseven(a) == MP_YES) {
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55 return MP_OKAY;
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56 }
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57 /* N is not a perfect square: floor(sqrt(N))^2 != N */
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58 if ((err = mp_is_square(a, &res)) != MP_OKAY) {
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59 return err;
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60 }
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61 if (res != 0) {
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62 return MP_OKAY;
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63 }
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64
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65 /* is the input equal to one of the primes in the table? */
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66 for (ix = 0; ix < PRIME_SIZE; ix++) {
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67 if (mp_cmp_d(a, ltm_prime_tab[ix]) == MP_EQ) {
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68 *result = MP_YES;
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69 return MP_OKAY;
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70 }
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71 }
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72 #ifdef MP_8BIT
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73 /* The search in the loop above was exhaustive in this case */
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74 if ((a->used == 1) && (PRIME_SIZE >= 31)) {
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75 return MP_OKAY;
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76 }
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77 #endif
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78
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79 /* first perform trial division */
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80 if ((err = mp_prime_is_divisible(a, &res)) != MP_OKAY) {
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81 return err;
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82 }
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83
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84 /* return if it was trivially divisible */
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85 if (res == MP_YES) {
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86 return MP_OKAY;
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87 }
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88
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89 /*
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90 Run the Miller-Rabin test with base 2 for the BPSW test.
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91 */
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92 if ((err = mp_init_set(&b, 2uL)) != MP_OKAY) {
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93 return err;
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94 }
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95
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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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parents: 1470
diff changeset
103 Rumours have it that Mathematica does a second M-R test with base 3.
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
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parents: 1470
diff changeset
104 Other rumours have it that their strong L-S test is slightly different.
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
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parents: 1470
diff changeset
105 It does not hurt, though, beside a bit of extra runtime.
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
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parents: 1470
diff changeset
106 */
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
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parents: 1470
diff changeset
107 b.dp[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
108 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)
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parents: 1470
diff changeset
109 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
110 }
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
111 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
112 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
113 }
284
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583)
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
114
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
115 /*
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
116 * Both, the Frobenius-Underwood test and the the Lucas-Selfridge test are quite
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1470
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117 * slow so if speed is an issue, define LTM_USE_FIPS_ONLY to use M-R tests with
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
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diff changeset
118 * bases 2, 3 and t random bases.
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parents: 1470
diff changeset
119 */
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120 #ifndef LTM_USE_FIPS_ONLY
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diff changeset
121 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
122 /*
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
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parents: 1470
diff changeset
123 * 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)
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124 * 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)
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diff changeset
125 * integers but the necesssary analysis is on the todo-list).
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diff changeset
126 */
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127 #if defined (MP_8BIT) || defined (LTM_USE_FROBENIUS_TEST)
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diff changeset
128 err = mp_prime_frobenius_underwood(a, &res);
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
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diff changeset
129 if ((err != MP_OKAY) && (err != MP_ITER)) {
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
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parents: 1470
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130 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
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131 }
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
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parents: 1470
diff changeset
132 if (res == MP_NO) {
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
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133 goto LBL_B;
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parents: 1470
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134 }
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
135 #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
136 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
137 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
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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 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
140 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
141 }
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diff changeset
142 #endif
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
143 }
284
eed26cff980b propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 6c790cad5a7fa866ad062cb3a0c279f7ba788583)
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
144 #endif
389
5ff8218bcee9 propagate from branch 'au.asn.ucc.matt.ltm.dropbear' (head 2af95f00ebd5bb7a28b3817db1218442c935388e)
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parents: 284
diff changeset
145
1655
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parents: 1470
diff changeset
146 /* run at least one Miller-Rabin test with a random base */
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diff changeset
147 if (t == 0) {
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diff changeset
148 t = 1;
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149 }
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diff changeset
150
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
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parents: 1470
diff changeset
151 /*
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diff changeset
152 abs(t) extra rounds of M-R to extend the range of primes it can find if t < 0.
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diff changeset
153 Only recommended if the input range is known to be < 3317044064679887385961981
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diff changeset
154
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diff changeset
155 It uses the bases for a deterministic M-R test if input < 3317044064679887385961981
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diff changeset
156 The caller has to check the size.
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parents: 1470
diff changeset
157
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
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diff changeset
158 Not for cryptographic use because with known bases strong M-R pseudoprimes can
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
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parents: 1470
diff changeset
159 be constructed. Use at least one M-R test with a random base (t >= 1).
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
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parents: 1470
diff changeset
160
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
161 The 1119 bit large number
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
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parents: 1470
diff changeset
162
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
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parents: 1470
diff changeset
163 80383745745363949125707961434194210813883768828755814583748891752229742737653\
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 33652186502336163960045457915042023603208766569966760987284043965408232928738\
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 79185086916685732826776177102938969773947016708230428687109997439976544144845\
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 34115587245063340927902227529622941498423068816854043264575340183297861112989\
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
167 60644845216191652872597534901
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
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 has been constructed by F. Arnault (F. Arnault, "Rabin-Miller primality test:
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 composite numbers which pass it.", Mathematics of Computation, 1995, 64. Jg.,
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 Nr. 209, S. 355-361), is a semiprime with the two factors
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 40095821663949960541830645208454685300518816604113250877450620473800321707011\
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
174 96242716223191597219733582163165085358166969145233813917169287527980445796800\
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
175 452592031836601
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
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 20047910831974980270915322604227342650259408302056625438725310236900160853505\
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 98121358111595798609866791081582542679083484572616906958584643763990222898400\
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 226296015918301
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
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 and it is a strong pseudoprime to all forty-six prime M-R bases up to 200
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
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Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1470
diff changeset
183 It does not fail the strong Bailley-PSP test as implemented here, it is just
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 given as an example, if not the reason to use the BPSW-test instead of M-R-tests
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 with a sequence of primes 2...n.
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
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 if (t < 0) {
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
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parents: 1470
diff changeset
189 t = -t;
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Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1470
diff changeset
190 /*
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
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parents: 1470
diff changeset
191 Sorenson, Jonathan; Webster, Jonathan (2015).
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
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parents: 1470
diff changeset
192 "Strong Pseudoprimes to Twelve Prime Bases".
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Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1470
diff changeset
193 */
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Steffen Jaeckel <s_jaeckel@gmx.de>
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diff changeset
194 /* 0x437ae92817f9fc85b7e5 = 318665857834031151167461 */
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
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parents: 1470
diff changeset
195 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
196 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
197 }
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
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 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
200 p_max = 12;
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 } 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
202 /* 0x2be6951adc5b22410a5fd = 3317044064679887385961981 */
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
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parents: 1470
diff changeset
203 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
204 goto LBL_B;
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Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1470
diff changeset
205 }
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Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1470
diff changeset
206
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diff changeset
207 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>
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diff changeset
208 p_max = 13;
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Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1470
diff changeset
209 } else {
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
210 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>
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diff changeset
211 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
212 }
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Steffen Jaeckel <s_jaeckel@gmx.de>
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diff changeset
213 }
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Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1470
diff changeset
214
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
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diff changeset
215 /* for compatibility with the current API (well, compatible within a sign's width) */
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diff changeset
216 if (p_max < t) {
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diff changeset
217 p_max = t;
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diff changeset
218 }
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diff changeset
219
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 if (p_max > PRIME_SIZE) {
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Steffen Jaeckel <s_jaeckel@gmx.de>
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diff changeset
221 err = MP_VAL;
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
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222 goto LBL_B;
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Steffen Jaeckel <s_jaeckel@gmx.de>
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diff changeset
223 }
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diff changeset
224 /* we did bases 2 and 3 already, skip them */
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diff changeset
225 for (ix = 2; ix < p_max; ix++) {
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diff changeset
226 mp_set(&b, ltm_prime_tab[ix]);
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diff changeset
227 if ((err = mp_prime_miller_rabin(a, &b, &res)) != MP_OKAY) {
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228 goto LBL_B;
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diff changeset
229 }
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Steffen Jaeckel <s_jaeckel@gmx.de>
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diff changeset
230 if (res == MP_NO) {
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diff changeset
231 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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232 }
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diff changeset
233 }
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234 }
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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235 /*
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236 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)
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237 See Fips 186.4 p. 126ff
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diff changeset
238 */
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diff changeset
239 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>
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diff changeset
240 /*
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
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diff changeset
241 * 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>
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242 * 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)
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diff changeset
243 * compliance to the current C-standard (ISO/IEC 9899:2011) because
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Steffen Jaeckel <s_jaeckel@gmx.de>
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244 * it gets used for small embeded processors, too. Some of those MCUs
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245 * have compilers that one cannot call standard compliant by any means.
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Steffen Jaeckel <s_jaeckel@gmx.de>
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diff changeset
246 * Hence the ugly type-fiddling in the following code.
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Steffen Jaeckel <s_jaeckel@gmx.de>
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diff changeset
247 */
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Steffen Jaeckel <s_jaeckel@gmx.de>
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diff changeset
248 size_a = mp_count_bits(a);
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diff changeset
249 mask = (1u << s_floor_ilog2(size_a)) - 1u;
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250 /*
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diff changeset
251 Assuming the General Rieman hypothesis (never thought to write that in a
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diff changeset
252 comment) the upper bound can be lowered to 2*(log a)^2.
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diff changeset
253 E. Bach, "Explicit bounds for primality testing and related problems,"
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diff changeset
254 Math. Comp. 55 (1990), 355-380.
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diff changeset
255
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
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diff changeset
256 size_a = (size_a/10) * 7;
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
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diff changeset
257 len = 2 * (size_a * size_a);
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diff changeset
258
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diff changeset
259 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>
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diff changeset
260
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
261 floor(2048/10)*7 = 1428
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
262 2 * 1428^2 = 4078368
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
263
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
264 (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)
Steffen Jaeckel <s_jaeckel@gmx.de>
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diff changeset
265 That number is smaller than 2^28, the default bit-size of mp_digit.
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
266 */
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Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1470
diff changeset
267
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
268 /*
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Steffen Jaeckel <s_jaeckel@gmx.de>
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diff changeset
269 How many tests, you might ask? Dana Jacobsen of Math::Prime::Util fame
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
270 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
271 Math-Prime-Util-GMP-0.50/primality.c if you do not believe it.
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
272
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
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diff changeset
273 The function mp_rand() goes to some length to use a cryptographically
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
274 good PRNG. That also means that the chance to always get the same base
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Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1470
diff changeset
275 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
276 If the BPSW test and/or the addtional Frobenious test have been
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
277 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)
Steffen Jaeckel <s_jaeckel@gmx.de>
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diff changeset
278 a single extra test should suffice, so such a very unlikely event
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 will not do much harm.
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
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 To preemptivly answer the dangling question: no, a witness does not
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Steffen Jaeckel <s_jaeckel@gmx.de>
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diff changeset
282 need to be 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
283 */
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
284 for (ix = 0; ix < t; ix++) {
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
285 /* mp_rand() guarantees the first digit to be non-zero */
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Steffen Jaeckel <s_jaeckel@gmx.de>
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diff changeset
286 if ((err = mp_rand(&b, 1)) != 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
287 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
288 }
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
289 /*
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 * Reduce digit before casting because mp_digit might be bigger than
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Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1470
diff changeset
291 * an unsigned int and "mask" on the other side is most probably not.
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Steffen Jaeckel <s_jaeckel@gmx.de>
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diff changeset
292 */
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
293 fips_rand = (unsigned int)(b.dp[0] & (mp_digit) mask);
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diff changeset
294 #ifdef MP_8BIT
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diff changeset
295 /*
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diff changeset
296 * 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)
Steffen Jaeckel <s_jaeckel@gmx.de>
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diff changeset
297 * unsigned int allows for it.
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Steffen Jaeckel <s_jaeckel@gmx.de>
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diff changeset
298 */
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
299 if (((sizeof(unsigned int) * CHAR_BIT)/2) >= (sizeof(mp_digit) * CHAR_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
300 if ((err = mp_rand(&b, 1)) != 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
301 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
302 }
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
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diff changeset
303 fips_rand <<= sizeof(mp_digit) * CHAR_BIT;
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
304 fips_rand |= (unsigned int) b.dp[0];
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
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diff changeset
305 fips_rand &= mask;
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diff changeset
306 }
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
307 #endif
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
308 if (fips_rand > (unsigned int)(INT_MAX - DIGIT_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
309 len = INT_MAX / DIGIT_BIT;
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310 } else {
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311 len = (((int)fips_rand + DIGIT_BIT) / DIGIT_BIT);
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312 }
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313 /* Unlikely. */
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314 if (len < 0) {
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315 ix--;
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316 continue;
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317 }
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318 /*
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319 * As mentioned above, one 8-bit digit is too small and
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320 * although it can only happen in the unlikely case that
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321 * an "unsigned int" is smaller than 16 bit a simple test
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322 * is cheap and the correction even cheaper.
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323 */
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324 #ifdef MP_8BIT
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325 /* All "a" < 2^8 have been caught before */
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326 if (len == 1) {
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327 len++;
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328 }
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diff changeset
329 #endif
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330 if ((err = mp_rand(&b, len)) != MP_OKAY) {
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
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parents: 1470
diff changeset
331 goto LBL_B;
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parents: 1470
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332 }
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parents: 1470
diff changeset
333 /*
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diff changeset
334 * That number might got too big and the witness has to be
1656
a36e545fb43d Prime-related bugfixes (#81)
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parents: 1655
diff changeset
335 * smaller than "a"
1655
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diff changeset
336 */
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diff changeset
337 len = mp_count_bits(&b);
1656
a36e545fb43d Prime-related bugfixes (#81)
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diff changeset
338 if (len >= size_a) {
a36e545fb43d Prime-related bugfixes (#81)
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diff changeset
339 len = (len - size_a) + 1;
1655
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parents: 1470
diff changeset
340 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)
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parents: 1470
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341 goto LBL_B;
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342 }
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diff changeset
343 }
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
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344 /* Although the chance for b <= 3 is miniscule, try again. */
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diff changeset
345 if (mp_cmp_d(&b, 3uL) != MP_GT) {
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diff changeset
346 ix--;
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Steffen Jaeckel <s_jaeckel@gmx.de>
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diff changeset
347 continue;
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Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1470
diff changeset
348 }
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Steffen Jaeckel <s_jaeckel@gmx.de>
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diff changeset
349 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
350 goto LBL_B;
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parents: 1470
diff changeset
351 }
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Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1470
diff changeset
352 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
353 goto LBL_B;
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Steffen Jaeckel <s_jaeckel@gmx.de>
parents: 1470
diff changeset
354 }
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
355 }
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
356 }
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
357
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
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diff changeset
358 /* passed the test */
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359 *result = MP_YES;
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diff changeset
360 LBL_B:
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diff changeset
361 mp_clear(&b);
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diff changeset
362 return err;
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79)
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parents: 1470
diff changeset
363 }
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
364
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
365 #endif
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
366
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
367 /* 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: 1470
diff changeset
368 /* 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: 1470
diff changeset
369 /* commit time: 2019-01-28 20:32:32 +0100 */