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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 the modular inverse via binary extended euclidean algorithm, |
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18 * that is c = 1/a mod b |
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19 * |
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20 * Based on mp_invmod except this is optimized for the case where b is |
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21 * odd as per HAC Note 14.64 on pp. 610 |
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22 */ |
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23 int |
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24 fast_mp_invmod (mp_int * a, mp_int * b, mp_int * c) |
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25 { |
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26 mp_int x, y, u, v, B, D; |
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27 int res, neg; |
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28 |
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29 /* 2. [modified] b must be odd */ |
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30 if (mp_iseven (b) == 1) { |
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31 return MP_VAL; |
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32 } |
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33 |
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34 /* init all our temps */ |
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35 if ((res = mp_init_multi(&x, &y, &u, &v, &B, &D, NULL)) != MP_OKAY) { |
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36 return res; |
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37 } |
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38 |
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39 /* x == modulus, y == value to invert */ |
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40 if ((res = mp_copy (b, &x)) != MP_OKAY) { |
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41 goto __ERR; |
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42 } |
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43 |
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44 /* we need y = |a| */ |
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45 if ((res = mp_abs (a, &y)) != MP_OKAY) { |
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46 goto __ERR; |
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47 } |
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48 |
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49 /* 3. u=x, v=y, A=1, B=0, C=0,D=1 */ |
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50 if ((res = mp_copy (&x, &u)) != MP_OKAY) { |
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51 goto __ERR; |
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52 } |
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53 if ((res = mp_copy (&y, &v)) != MP_OKAY) { |
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54 goto __ERR; |
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55 } |
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56 mp_set (&D, 1); |
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57 |
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58 top: |
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59 /* 4. while u is even do */ |
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60 while (mp_iseven (&u) == 1) { |
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61 /* 4.1 u = u/2 */ |
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62 if ((res = mp_div_2 (&u, &u)) != MP_OKAY) { |
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63 goto __ERR; |
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64 } |
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65 /* 4.2 if B is odd then */ |
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66 if (mp_isodd (&B) == 1) { |
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67 if ((res = mp_sub (&B, &x, &B)) != MP_OKAY) { |
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68 goto __ERR; |
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69 } |
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70 } |
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71 /* B = B/2 */ |
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72 if ((res = mp_div_2 (&B, &B)) != MP_OKAY) { |
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73 goto __ERR; |
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74 } |
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75 } |
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76 |
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77 /* 5. while v is even do */ |
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78 while (mp_iseven (&v) == 1) { |
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79 /* 5.1 v = v/2 */ |
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80 if ((res = mp_div_2 (&v, &v)) != MP_OKAY) { |
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81 goto __ERR; |
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82 } |
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83 /* 5.2 if D is odd then */ |
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84 if (mp_isodd (&D) == 1) { |
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85 /* D = (D-x)/2 */ |
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86 if ((res = mp_sub (&D, &x, &D)) != MP_OKAY) { |
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87 goto __ERR; |
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88 } |
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89 } |
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90 /* D = D/2 */ |
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91 if ((res = mp_div_2 (&D, &D)) != MP_OKAY) { |
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92 goto __ERR; |
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93 } |
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94 } |
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95 |
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96 /* 6. if u >= v then */ |
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97 if (mp_cmp (&u, &v) != MP_LT) { |
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98 /* u = u - v, B = B - D */ |
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99 if ((res = mp_sub (&u, &v, &u)) != MP_OKAY) { |
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100 goto __ERR; |
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101 } |
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102 |
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103 if ((res = mp_sub (&B, &D, &B)) != MP_OKAY) { |
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104 goto __ERR; |
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105 } |
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106 } else { |
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107 /* v - v - u, D = D - B */ |
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108 if ((res = mp_sub (&v, &u, &v)) != MP_OKAY) { |
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109 goto __ERR; |
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110 } |
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111 |
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112 if ((res = mp_sub (&D, &B, &D)) != MP_OKAY) { |
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113 goto __ERR; |
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114 } |
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115 } |
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116 |
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117 /* if not zero goto step 4 */ |
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118 if (mp_iszero (&u) == 0) { |
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119 goto top; |
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120 } |
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121 |
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122 /* now a = C, b = D, gcd == g*v */ |
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123 |
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124 /* if v != 1 then there is no inverse */ |
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125 if (mp_cmp_d (&v, 1) != MP_EQ) { |
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126 res = MP_VAL; |
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127 goto __ERR; |
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128 } |
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129 |
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130 /* b is now the inverse */ |
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131 neg = a->sign; |
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132 while (D.sign == MP_NEG) { |
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133 if ((res = mp_add (&D, b, &D)) != MP_OKAY) { |
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134 goto __ERR; |
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135 } |
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136 } |
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137 mp_exch (&D, c); |
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138 c->sign = neg; |
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139 res = MP_OKAY; |
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140 |
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141 __ERR:mp_clear_multi (&x, &y, &u, &v, &B, &D, NULL); |
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142 return res; |
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143 } |
