annotate libtommath/bn_mp_n_root_ex.c @ 1659:d32bcb5c557d

Add Ed25519 support (#91) * Add support for Ed25519 as a public key type Ed25519 is a elliptic curve signature scheme that offers better security than ECDSA and DSA and good performance. It may be used for both user and host keys. OpenSSH key import and fuzzer are not supported yet. Initially inspired by Peter Szabo. * Add curve25519 and ed25519 fuzzers * Add import and export of Ed25519 keys
author Vladislav Grishenko <themiron@users.noreply.github.com>
date Wed, 11 Mar 2020 21:09:45 +0500
parents f52919ffd3b1
children
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
rev   line source
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1 #include "tommath_private.h"
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2 #ifdef BN_MP_N_ROOT_EX_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 /* find the n'th root of an integer
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16 *
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17 * Result found such that (c)**b <= a and (c+1)**b > a
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18 *
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19 * This algorithm uses Newton's approximation
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20 * x[i+1] = x[i] - f(x[i])/f'(x[i])
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21 * which will find the root in log(N) time where
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22 * each step involves a fair bit. This is not meant to
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23 * find huge roots [square and cube, etc].
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24 */
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25 int mp_n_root_ex(const mp_int *a, mp_digit b, mp_int *c, int fast)
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26 {
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27 mp_int t1, t2, t3, a_;
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28 int res;
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29
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30 /* input must be positive if b is even */
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31 if (((b & 1u) == 0u) && (a->sign == MP_NEG)) {
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32 return MP_VAL;
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33 }
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34
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35 if ((res = mp_init(&t1)) != MP_OKAY) {
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36 return res;
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37 }
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38
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39 if ((res = mp_init(&t2)) != MP_OKAY) {
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40 goto LBL_T1;
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41 }
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42
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43 if ((res = mp_init(&t3)) != MP_OKAY) {
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44 goto LBL_T2;
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45 }
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46
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47 /* if a is negative fudge the sign but keep track */
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48 a_ = *a;
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49 a_.sign = MP_ZPOS;
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50
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51 /* t2 = 2 */
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52 mp_set(&t2, 2uL);
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53
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54 do {
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55 /* t1 = t2 */
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56 if ((res = mp_copy(&t2, &t1)) != MP_OKAY) {
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57 goto LBL_T3;
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58 }
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59
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60 /* t2 = t1 - ((t1**b - a) / (b * t1**(b-1))) */
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61
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62 /* t3 = t1**(b-1) */
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63 if ((res = mp_expt_d_ex(&t1, b - 1u, &t3, fast)) != MP_OKAY) {
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64 goto LBL_T3;
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65 }
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66
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67 /* numerator */
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68 /* t2 = t1**b */
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69 if ((res = mp_mul(&t3, &t1, &t2)) != MP_OKAY) {
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70 goto LBL_T3;
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71 }
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72
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73 /* t2 = t1**b - a */
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74 if ((res = mp_sub(&t2, &a_, &t2)) != MP_OKAY) {
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75 goto LBL_T3;
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76 }
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77
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78 /* denominator */
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79 /* t3 = t1**(b-1) * b */
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80 if ((res = mp_mul_d(&t3, b, &t3)) != MP_OKAY) {
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81 goto LBL_T3;
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82 }
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83
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84 /* t3 = (t1**b - a)/(b * t1**(b-1)) */
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85 if ((res = mp_div(&t2, &t3, &t3, NULL)) != MP_OKAY) {
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86 goto LBL_T3;
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87 }
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88
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89 if ((res = mp_sub(&t1, &t3, &t2)) != MP_OKAY) {
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90 goto LBL_T3;
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91 }
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92 } while (mp_cmp(&t1, &t2) != MP_EQ);
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93
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94 /* result can be off by a few so check */
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95 for (;;) {
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96 if ((res = mp_expt_d_ex(&t1, b, &t2, fast)) != MP_OKAY) {
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97 goto LBL_T3;
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98 }
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99
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100 if (mp_cmp(&t2, &a_) == MP_GT) {
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101 if ((res = mp_sub_d(&t1, 1uL, &t1)) != MP_OKAY) {
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102 goto LBL_T3;
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103 }
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104 } else {
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105 break;
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106 }
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107 }
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108
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109 /* set the result */
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110 mp_exch(&t1, c);
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111
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112 /* set the sign of the result */
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113 c->sign = a->sign;
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114
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115 res = MP_OKAY;
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116
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117 LBL_T3:
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118 mp_clear(&t3);
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119 LBL_T2:
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120 mp_clear(&t2);
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121 LBL_T1:
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122 mp_clear(&t1);
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123 return res;
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124 }
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125 #endif
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126
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127 /* ref: HEAD -> master, tag: v1.1.0 */
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128 /* git commit: 08549ad6bc8b0cede0b357a9c341c5c6473a9c55 */
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129 /* commit time: 2019-01-28 20:32:32 +0100 */