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annotate libtommath/bn_fast_mp_montgomery_reduce.c @ 1686:83d48276885b

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fix typo
author Matt Johnston <matt@ucc.asn.au>
date Tue, 26 May 2020 20:15:00 +0800
parents f52919ffd3b1
children
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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 */