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1 /* LibTomMath, multiple-precision integer library -- Tom St Denis |
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2 * |
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3 * LibTomMath is a library that provides multiple-precision |
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4 * integer arithmetic as well as number theoretic functionality. |
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5 * |
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6 * The library was designed directly after the MPI library by |
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7 * Michael Fromberger but has been written from scratch with |
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8 * additional optimizations in place. |
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9 * |
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10 * The library is free for all purposes without any express |
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11 * guarantee it works. |
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12 * |
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13 * Tom St Denis, [email protected], http://math.libtomcrypt.org |
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14 */ |
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15 #include <tommath.h> |
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16 |
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17 /* computes xR**-1 == x (mod N) via Montgomery Reduction |
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18 * |
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19 * This is an optimized implementation of mp_montgomery_reduce |
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20 * which uses the comba method to quickly calculate the columns of the |
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21 * reduction. |
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22 * |
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23 * Based on Algorithm 14.32 on pp.601 of HAC. |
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24 */ |
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25 int |
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26 fast_mp_montgomery_reduce (mp_int * x, mp_int * n, mp_digit rho) |
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27 { |
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28 int ix, res, olduse; |
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29 mp_word W[MP_WARRAY]; |
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30 |
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31 /* get old used count */ |
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32 olduse = x->used; |
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33 |
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34 /* grow a as required */ |
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35 if (x->alloc < n->used + 1) { |
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36 if ((res = mp_grow (x, n->used + 1)) != MP_OKAY) { |
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37 return res; |
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38 } |
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39 } |
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40 |
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41 /* first we have to get the digits of the input into |
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42 * an array of double precision words W[...] |
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43 */ |
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44 { |
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45 register mp_word *_W; |
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46 register mp_digit *tmpx; |
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47 |
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48 /* alias for the W[] array */ |
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49 _W = W; |
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50 |
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51 /* alias for the digits of x*/ |
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52 tmpx = x->dp; |
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53 |
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54 /* copy the digits of a into W[0..a->used-1] */ |
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55 for (ix = 0; ix < x->used; ix++) { |
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56 *_W++ = *tmpx++; |
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57 } |
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58 |
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59 /* zero the high words of W[a->used..m->used*2] */ |
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60 for (; ix < n->used * 2 + 1; ix++) { |
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61 *_W++ = 0; |
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62 } |
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63 } |
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64 |
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65 /* now we proceed to zero successive digits |
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66 * from the least significant upwards |
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67 */ |
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68 for (ix = 0; ix < n->used; ix++) { |
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69 /* mu = ai * m' mod b |
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70 * |
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71 * We avoid a double precision multiplication (which isn't required) |
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72 * by casting the value down to a mp_digit. Note this requires |
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73 * that W[ix-1] have the carry cleared (see after the inner loop) |
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74 */ |
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75 register mp_digit mu; |
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76 mu = (mp_digit) (((W[ix] & MP_MASK) * rho) & MP_MASK); |
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77 |
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78 /* a = a + mu * m * b**i |
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79 * |
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80 * This is computed in place and on the fly. The multiplication |
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81 * by b**i is handled by offseting which columns the results |
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82 * are added to. |
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83 * |
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84 * Note the comba method normally doesn't handle carries in the |
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85 * inner loop In this case we fix the carry from the previous |
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86 * column since the Montgomery reduction requires digits of the |
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87 * result (so far) [see above] to work. This is |
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88 * handled by fixing up one carry after the inner loop. The |
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89 * carry fixups are done in order so after these loops the |
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90 * first m->used words of W[] have the carries fixed |
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91 */ |
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92 { |
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93 register int iy; |
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94 register mp_digit *tmpn; |
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95 register mp_word *_W; |
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96 |
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97 /* alias for the digits of the modulus */ |
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98 tmpn = n->dp; |
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99 |
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100 /* Alias for the columns set by an offset of ix */ |
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101 _W = W + ix; |
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102 |
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103 /* inner loop */ |
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104 for (iy = 0; iy < n->used; iy++) { |
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105 *_W++ += ((mp_word)mu) * ((mp_word)*tmpn++); |
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106 } |
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107 } |
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108 |
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109 /* now fix carry for next digit, W[ix+1] */ |
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110 W[ix + 1] += W[ix] >> ((mp_word) DIGIT_BIT); |
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111 } |
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112 |
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113 /* now we have to propagate the carries and |
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114 * shift the words downward [all those least |
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115 * significant digits we zeroed]. |
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116 */ |
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117 { |
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118 register mp_digit *tmpx; |
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119 register mp_word *_W, *_W1; |
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120 |
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121 /* nox fix rest of carries */ |
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122 |
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123 /* alias for current word */ |
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124 _W1 = W + ix; |
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125 |
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126 /* alias for next word, where the carry goes */ |
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127 _W = W + ++ix; |
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128 |
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129 for (; ix <= n->used * 2 + 1; ix++) { |
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130 *_W++ += *_W1++ >> ((mp_word) DIGIT_BIT); |
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131 } |
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132 |
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133 /* copy out, A = A/b**n |
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134 * |
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135 * The result is A/b**n but instead of converting from an |
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136 * array of mp_word to mp_digit than calling mp_rshd |
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137 * we just copy them in the right order |
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138 */ |
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139 |
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140 /* alias for destination word */ |
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141 tmpx = x->dp; |
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142 |
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143 /* alias for shifted double precision result */ |
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144 _W = W + n->used; |
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145 |
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146 for (ix = 0; ix < n->used + 1; ix++) { |
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147 *tmpx++ = (mp_digit)(*_W++ & ((mp_word) MP_MASK)); |
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148 } |
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149 |
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150 /* zero oldused digits, if the input a was larger than |
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151 * m->used+1 we'll have to clear the digits |
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152 */ |
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153 for (; ix < olduse; ix++) { |
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154 *tmpx++ = 0; |
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155 } |
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156 } |
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157 |
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158 /* set the max used and clamp */ |
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159 x->used = n->used + 1; |
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160 mp_clamp (x); |
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161 |
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162 /* if A >= m then A = A - m */ |
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163 if (mp_cmp_mag (x, n) != MP_LT) { |
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164 return s_mp_sub (x, n, x); |
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165 } |
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166 return MP_OKAY; |
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167 } |
