Mercurial > dropbear
annotate libtommath/bn_s_mp_montgomery_reduce_fast.c @ 1873:2c9d635a1c04
Avoid unused argument warning when reexec is unused
author | Matt Johnston <matt@ucc.asn.au> |
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date | Thu, 03 Feb 2022 22:12:11 +0800 |
parents | 1051e4eea25a |
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rev | line source |
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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 |