Mercurial > dropbear
annotate libtommath/bn_mp_root_u32.c @ 1707:41a0ff8d5a89
void return types for curve25519
author | Matt Johnston <matt@ucc.asn.au> |
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date | Sat, 30 May 2020 00:05:49 +0800 |
parents | 1051e4eea25a |
children |
rev | line source |
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1692
1051e4eea25a
Update LibTomMath to 1.2.0 (#84)
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1 #include "tommath_private.h" |
1051e4eea25a
Update LibTomMath to 1.2.0 (#84)
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2 #ifdef BN_MP_ROOT_U32_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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Update LibTomMath to 1.2.0 (#84)
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5 |
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6 /* find the n'th root of an integer |
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7 * |
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8 * Result found such that (c)**b <= a and (c+1)**b > a |
1051e4eea25a
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9 * |
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10 * This algorithm uses Newton's approximation |
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11 * x[i+1] = x[i] - f(x[i])/f'(x[i]) |
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12 * which will find the root in log(N) time where |
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13 * each step involves a fair bit. |
1051e4eea25a
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14 */ |
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15 mp_err mp_root_u32(const mp_int *a, uint32_t b, mp_int *c) |
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16 { |
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17 mp_int t1, t2, t3, a_; |
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18 mp_ord cmp; |
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19 int ilog2; |
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20 mp_err err; |
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21 |
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22 /* input must be positive if b is even */ |
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23 if (((b & 1u) == 0u) && (a->sign == MP_NEG)) { |
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24 return MP_VAL; |
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25 } |
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26 |
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27 if ((err = mp_init_multi(&t1, &t2, &t3, NULL)) != MP_OKAY) { |
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28 return err; |
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29 } |
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30 |
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31 /* if a is negative fudge the sign but keep track */ |
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32 a_ = *a; |
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33 a_.sign = MP_ZPOS; |
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34 |
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35 /* Compute seed: 2^(log_2(n)/b + 2)*/ |
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36 ilog2 = mp_count_bits(a); |
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37 |
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38 /* |
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39 If "b" is larger than INT_MAX it is also larger than |
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40 log_2(n) because the bit-length of the "n" is measured |
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41 with an int and hence the root is always < 2 (two). |
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42 */ |
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43 if (b > (uint32_t)(INT_MAX/2)) { |
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44 mp_set(c, 1uL); |
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45 c->sign = a->sign; |
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46 err = MP_OKAY; |
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47 goto LBL_ERR; |
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48 } |
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49 |
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50 /* "b" is smaller than INT_MAX, we can cast safely */ |
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51 if (ilog2 < (int)b) { |
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52 mp_set(c, 1uL); |
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53 c->sign = a->sign; |
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54 err = MP_OKAY; |
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55 goto LBL_ERR; |
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56 } |
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57 ilog2 = ilog2 / ((int)b); |
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58 if (ilog2 == 0) { |
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59 mp_set(c, 1uL); |
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60 c->sign = a->sign; |
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61 err = MP_OKAY; |
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62 goto LBL_ERR; |
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63 } |
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64 /* Start value must be larger than root */ |
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65 ilog2 += 2; |
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66 if ((err = mp_2expt(&t2,ilog2)) != MP_OKAY) goto LBL_ERR; |
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67 do { |
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68 /* t1 = t2 */ |
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69 if ((err = mp_copy(&t2, &t1)) != MP_OKAY) goto LBL_ERR; |
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70 |
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71 /* t2 = t1 - ((t1**b - a) / (b * t1**(b-1))) */ |
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72 |
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73 /* t3 = t1**(b-1) */ |
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74 if ((err = mp_expt_u32(&t1, b - 1u, &t3)) != MP_OKAY) goto LBL_ERR; |
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75 |
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76 /* numerator */ |
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77 /* t2 = t1**b */ |
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78 if ((err = mp_mul(&t3, &t1, &t2)) != MP_OKAY) goto LBL_ERR; |
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79 |
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80 /* t2 = t1**b - a */ |
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81 if ((err = mp_sub(&t2, &a_, &t2)) != MP_OKAY) goto LBL_ERR; |
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82 |
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83 /* denominator */ |
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84 /* t3 = t1**(b-1) * b */ |
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85 if ((err = mp_mul_d(&t3, b, &t3)) != MP_OKAY) goto LBL_ERR; |
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86 |
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87 /* t3 = (t1**b - a)/(b * t1**(b-1)) */ |
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88 if ((err = mp_div(&t2, &t3, &t3, NULL)) != MP_OKAY) goto LBL_ERR; |
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89 |
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90 if ((err = mp_sub(&t1, &t3, &t2)) != MP_OKAY) goto LBL_ERR; |
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91 |
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92 /* |
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93 Number of rounds is at most log_2(root). If it is more it |
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94 got stuck, so break out of the loop and do the rest manually. |
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95 */ |
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96 if (ilog2-- == 0) { |
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97 break; |
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98 } |
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99 } while (mp_cmp(&t1, &t2) != MP_EQ); |
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100 |
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101 /* result can be off by a few so check */ |
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102 /* Loop beneath can overshoot by one if found root is smaller than actual root */ |
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103 for (;;) { |
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104 if ((err = mp_expt_u32(&t1, b, &t2)) != MP_OKAY) goto LBL_ERR; |
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105 cmp = mp_cmp(&t2, &a_); |
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106 if (cmp == MP_EQ) { |
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107 err = MP_OKAY; |
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108 goto LBL_ERR; |
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109 } |
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110 if (cmp == MP_LT) { |
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111 if ((err = mp_add_d(&t1, 1uL, &t1)) != MP_OKAY) goto LBL_ERR; |
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112 } else { |
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113 break; |
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114 } |
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115 } |
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116 /* correct overshoot from above or from recurrence */ |
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117 for (;;) { |
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118 if ((err = mp_expt_u32(&t1, b, &t2)) != MP_OKAY) goto LBL_ERR; |
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119 if (mp_cmp(&t2, &a_) == MP_GT) { |
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120 if ((err = mp_sub_d(&t1, 1uL, &t1)) != MP_OKAY) goto LBL_ERR; |
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121 } else { |
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122 break; |
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123 } |
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124 } |
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125 |
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126 /* set the result */ |
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127 mp_exch(&t1, c); |
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128 |
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129 /* set the sign of the result */ |
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130 c->sign = a->sign; |
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131 |
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132 err = MP_OKAY; |
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133 |
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134 LBL_ERR: |
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135 mp_clear_multi(&t1, &t2, &t3, NULL); |
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136 return err; |
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137 } |
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138 |
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139 #endif |