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annotate libtommath/bn_fast_mp_montgomery_reduce.c @ 1663:c795520269f9

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Fallback for key gen without hard link support (#89) Add a non-atomic fallback for key generation on platforms where link() is not permitted (such as most stock Android installs) or on filesystems without hard link support (such as FAT).
author Matt Robinson <git@nerdoftheherd.com>
date Sat, 14 Mar 2020 14:37:35 +0000
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_FAST_MP_MONTGOMERY_REDUCE_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 /* computes xR**-1 == x (mod N) via Montgomery Reduction
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16 *
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17 * This is an optimized implementation of montgomery_reduce
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18 * which uses the comba method to quickly calculate the columns of the
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19 * reduction.
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20 *
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21 * Based on Algorithm 14.32 on pp.601 of HAC.
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22 */
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23 int fast_mp_montgomery_reduce(mp_int *x, const mp_int *n, mp_digit rho)
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24 {
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25 int ix, res, olduse;
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26 mp_word W[MP_WARRAY];
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27
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28 if (x->used > (int)MP_WARRAY) {
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29 return MP_VAL;
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30 }
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31
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32 /* get old used count */
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33 olduse = x->used;
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34
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35 /* grow a as required */
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36 if (x->alloc < (n->used + 1)) {
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37 if ((res = mp_grow(x, n->used + 1)) != MP_OKAY) {
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38 return res;
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39 }
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40 }
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41
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42 /* first we have to get the digits of the input into
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43 * an array of double precision words W[...]
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44 */
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45 {
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46 mp_word *_W;
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47 mp_digit *tmpx;
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48
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49 /* alias for the W[] array */
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50 _W = W;
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51
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52 /* alias for the digits of x*/
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53 tmpx = x->dp;
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54
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55 /* copy the digits of a into W[0..a->used-1] */
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56 for (ix = 0; ix < x->used; ix++) {
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57 *_W++ = *tmpx++;
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58 }
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59
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60 /* zero the high words of W[a->used..m->used*2] */
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61 for (; ix < ((n->used * 2) + 1); ix++) {
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62 *_W++ = 0;
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63 }
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64 }
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65
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66 /* now we proceed to zero successive digits
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67 * from the least significant upwards
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68 */
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69 for (ix = 0; ix < n->used; ix++) {
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70 /* mu = ai * m' mod b
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71 *
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72 * We avoid a double precision multiplication (which isn't required)
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73 * by casting the value down to a mp_digit. Note this requires
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74 * that W[ix-1] have the carry cleared (see after the inner loop)
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75 */
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76 mp_digit mu;
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77 mu = ((W[ix] & MP_MASK) * rho) & MP_MASK;
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78
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79 /* a = a + mu * m * b**i
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80 *
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81 * This is computed in place and on the fly. The multiplication
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82 * by b**i is handled by offseting which columns the results
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83 * are added to.
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84 *
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85 * Note the comba method normally doesn't handle carries in the
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86 * inner loop In this case we fix the carry from the previous
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87 * column since the Montgomery reduction requires digits of the
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88 * result (so far) [see above] to work. This is
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89 * handled by fixing up one carry after the inner loop. The
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90 * carry fixups are done in order so after these loops the
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91 * first m->used words of W[] have the carries fixed
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92 */
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93 {
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94 int iy;
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95 mp_digit *tmpn;
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96 mp_word *_W;
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97
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98 /* alias for the digits of the modulus */
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99 tmpn = n->dp;
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100
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101 /* Alias for the columns set by an offset of ix */
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102 _W = W + ix;
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103
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104 /* inner loop */
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105 for (iy = 0; iy < n->used; iy++) {
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106 *_W++ += (mp_word)mu * (mp_word)*tmpn++;
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107 }
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108 }
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109
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110 /* now fix carry for next digit, W[ix+1] */
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111 W[ix + 1] += W[ix] >> (mp_word)DIGIT_BIT;
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112 }
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113
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114 /* now we have to propagate the carries and
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115 * shift the words downward [all those least
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116 * significant digits we zeroed].
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117 */
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118 {
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119 mp_digit *tmpx;
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120 mp_word *_W, *_W1;
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121
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122 /* nox fix rest of carries */
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123
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124 /* alias for current word */
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125 _W1 = W + ix;
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126
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127 /* alias for next word, where the carry goes */
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128 _W = W + ++ix;
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129
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130 for (; ix <= ((n->used * 2) + 1); ix++) {
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131 *_W++ += *_W1++ >> (mp_word)DIGIT_BIT;
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132 }
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133
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134 /* copy out, A = A/b**n
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135 *
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136 * The result is A/b**n but instead of converting from an
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137 * array of mp_word to mp_digit than calling mp_rshd
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138 * we just copy them in the right order
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139 */
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140
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141 /* alias for destination word */
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142 tmpx = x->dp;
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143
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144 /* alias for shifted double precision result */
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145 _W = W + n->used;
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146
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147 for (ix = 0; ix < (n->used + 1); ix++) {
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148 *tmpx++ = *_W++ & (mp_word)MP_MASK;
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149 }
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150
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151 /* zero oldused digits, if the input a was larger than
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152 * m->used+1 we'll have to clear the digits
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153 */
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154 for (; ix < olduse; ix++) {
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155 *tmpx++ = 0;
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156 }
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157 }
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158
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159 /* set the max used and clamp */
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160 x->used = n->used + 1;
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161 mp_clamp(x);
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162
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163 /* if A >= m then A = A - m */
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164 if (mp_cmp_mag(x, n) != MP_LT) {
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165 return s_mp_sub(x, n, x);
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166 }
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167 return MP_OKAY;
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168 }
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169 #endif
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170
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171 /* ref: HEAD -> master, tag: v1.1.0 */
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172 /* git commit: 08549ad6bc8b0cede0b357a9c341c5c6473a9c55 */
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173 /* commit time: 2019-01-28 20:32:32 +0100 */