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annotate libtommath/bn_s_mp_montgomery_reduce_fast.c @ 1843:03dfecca99bd

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author Matt Johnston <matt@ucc.asn.au>
date Mon, 18 Oct 2021 23:25:20 +0800
parents 1051e4eea25a
children
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1692
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1 #include "tommath_private.h"
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2 #ifdef BN_S_MP_MONTGOMERY_REDUCE_FAST_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 /* computes xR**-1 == x (mod N) via Montgomery Reduction
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7 *
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8 * This is an optimized implementation of montgomery_reduce
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9 * which uses the comba method to quickly calculate the columns of the
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10 * reduction.
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11 *
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12 * Based on Algorithm 14.32 on pp.601 of HAC.
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13 */
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14 mp_err s_mp_montgomery_reduce_fast(mp_int *x, const mp_int *n, mp_digit rho)
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15 {
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16 int ix, olduse;
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17 mp_err err;
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18 mp_word W[MP_WARRAY];
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19
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20 if (x->used > MP_WARRAY) {
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21 return MP_VAL;
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22 }
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23
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24 /* get old used count */
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25 olduse = x->used;
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26
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27 /* grow a as required */
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28 if (x->alloc < (n->used + 1)) {
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29 if ((err = mp_grow(x, n->used + 1)) != MP_OKAY) {
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30 return err;
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31 }
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32 }
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33
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34 /* first we have to get the digits of the input into
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35 * an array of double precision words W[...]
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36 */
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37 {
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38 mp_word *_W;
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39 mp_digit *tmpx;
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40
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41 /* alias for the W[] array */
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42 _W = W;
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43
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44 /* alias for the digits of x*/
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45 tmpx = x->dp;
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46
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47 /* copy the digits of a into W[0..a->used-1] */
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48 for (ix = 0; ix < x->used; ix++) {
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49 *_W++ = *tmpx++;
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50 }
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51
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52 /* zero the high words of W[a->used..m->used*2] */
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53 if (ix < ((n->used * 2) + 1)) {
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54 MP_ZERO_BUFFER(_W, sizeof(mp_word) * (size_t)(((n->used * 2) + 1) - ix));
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55 }
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56 }
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57
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58 /* now we proceed to zero successive digits
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59 * from the least significant upwards
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60 */
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61 for (ix = 0; ix < n->used; ix++) {
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62 /* mu = ai * m' mod b
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63 *
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64 * We avoid a double precision multiplication (which isn't required)
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65 * by casting the value down to a mp_digit. Note this requires
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66 * that W[ix-1] have the carry cleared (see after the inner loop)
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67 */
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68 mp_digit mu;
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69 mu = ((W[ix] & MP_MASK) * rho) & MP_MASK;
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70
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71 /* a = a + mu * m * b**i
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72 *
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73 * This is computed in place and on the fly. The multiplication
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74 * by b**i is handled by offseting which columns the results
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75 * are added to.
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76 *
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77 * Note the comba method normally doesn't handle carries in the
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78 * inner loop In this case we fix the carry from the previous
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79 * column since the Montgomery reduction requires digits of the
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80 * result (so far) [see above] to work. This is
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81 * handled by fixing up one carry after the inner loop. The
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82 * carry fixups are done in order so after these loops the
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83 * first m->used words of W[] have the carries fixed
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84 */
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85 {
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86 int iy;
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87 mp_digit *tmpn;
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88 mp_word *_W;
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89
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90 /* alias for the digits of the modulus */
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91 tmpn = n->dp;
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92
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93 /* Alias for the columns set by an offset of ix */
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94 _W = W + ix;
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95
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96 /* inner loop */
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97 for (iy = 0; iy < n->used; iy++) {
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98 *_W++ += (mp_word)mu * (mp_word)*tmpn++;
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99 }
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100 }
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101
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102 /* now fix carry for next digit, W[ix+1] */
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103 W[ix + 1] += W[ix] >> (mp_word)MP_DIGIT_BIT;
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104 }
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105
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106 /* now we have to propagate the carries and
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107 * shift the words downward [all those least
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108 * significant digits we zeroed].
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109 */
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110 {
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111 mp_digit *tmpx;
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112 mp_word *_W, *_W1;
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113
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114 /* nox fix rest of carries */
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115
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116 /* alias for current word */
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117 _W1 = W + ix;
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118
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119 /* alias for next word, where the carry goes */
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120 _W = W + ++ix;
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121
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122 for (; ix < ((n->used * 2) + 1); ix++) {
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123 *_W++ += *_W1++ >> (mp_word)MP_DIGIT_BIT;
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124 }
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125
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126 /* copy out, A = A/b**n
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127 *
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128 * The result is A/b**n but instead of converting from an
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129 * array of mp_word to mp_digit than calling mp_rshd
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130 * we just copy them in the right order
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131 */
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132
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133 /* alias for destination word */
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134 tmpx = x->dp;
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135
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136 /* alias for shifted double precision result */
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137 _W = W + n->used;
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138
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139 for (ix = 0; ix < (n->used + 1); ix++) {
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140 *tmpx++ = *_W++ & (mp_word)MP_MASK;
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141 }
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142
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143 /* zero oldused digits, if the input a was larger than
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144 * m->used+1 we'll have to clear the digits
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145 */
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146 MP_ZERO_DIGITS(tmpx, olduse - ix);
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147 }
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148
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149 /* set the max used and clamp */
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150 x->used = n->used + 1;
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151 mp_clamp(x);
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152
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153 /* if A >= m then A = A - m */
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154 if (mp_cmp_mag(x, n) != MP_LT) {
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155 return s_mp_sub(x, n, x);
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156 }
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157 return MP_OKAY;
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158 }
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159 #endif