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annotate libtommath/bn_mp_montgomery_reduce.c @ 1663:c795520269f9

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Fallback for key gen without hard link support (#89) Add a non-atomic fallback for key generation on platforms where link() is not permitted (such as most stock Android installs) or on filesystems without hard link support (such as FAT).
author Matt Robinson <git@nerdoftheherd.com>
date Sat, 14 Mar 2020 14:37:35 +0000
parents f52919ffd3b1
children 1051e4eea25a
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
rev   line source
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1 #include "tommath_private.h"
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2 #ifdef BN_MP_MONTGOMERY_REDUCE_C
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3 /* LibTomMath, multiple-precision integer library -- Tom St Denis
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4 *
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5 * LibTomMath is a library that provides multiple-precision
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6 * integer arithmetic as well as number theoretic functionality.
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7 *
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8 * The library was designed directly after the MPI library by
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9 * Michael Fromberger but has been written from scratch with
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10 * additional optimizations in place.
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11 *
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12 * SPDX-License-Identifier: Unlicense
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13 */
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14
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15 /* computes xR**-1 == x (mod N) via Montgomery Reduction */
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16 int mp_montgomery_reduce(mp_int *x, const mp_int *n, mp_digit rho)
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17 {
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18 int ix, res, digs;
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19 mp_digit mu;
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20
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21 /* can the fast reduction [comba] method be used?
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22 *
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23 * Note that unlike in mul you're safely allowed *less*
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24 * than the available columns [255 per default] since carries
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25 * are fixed up in the inner loop.
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26 */
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27 digs = (n->used * 2) + 1;
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28 if ((digs < (int)MP_WARRAY) &&
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29 (x->used <= (int)MP_WARRAY) &&
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30 (n->used <
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31 (int)(1u << (((size_t)CHAR_BIT * sizeof(mp_word)) - (2u * (size_t)DIGIT_BIT))))) {
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32 return fast_mp_montgomery_reduce(x, n, rho);
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33 }
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34
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35 /* grow the input as required */
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36 if (x->alloc < digs) {
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37 if ((res = mp_grow(x, digs)) != MP_OKAY) {
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38 return res;
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39 }
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40 }
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41 x->used = digs;
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42
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43 for (ix = 0; ix < n->used; ix++) {
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44 /* mu = ai * rho mod b
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45 *
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46 * The value of rho must be precalculated via
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47 * montgomery_setup() such that
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48 * it equals -1/n0 mod b this allows the
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49 * following inner loop to reduce the
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50 * input one digit at a time
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51 */
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52 mu = (mp_digit)(((mp_word)x->dp[ix] * (mp_word)rho) & MP_MASK);
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53
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54 /* a = a + mu * m * b**i */
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55 {
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56 int iy;
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57 mp_digit *tmpn, *tmpx, u;
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58 mp_word r;
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59
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60 /* alias for digits of the modulus */
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61 tmpn = n->dp;
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62
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63 /* alias for the digits of x [the input] */
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64 tmpx = x->dp + ix;
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65
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66 /* set the carry to zero */
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67 u = 0;
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68
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69 /* Multiply and add in place */
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70 for (iy = 0; iy < n->used; iy++) {
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71 /* compute product and sum */
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72 r = ((mp_word)mu * (mp_word)*tmpn++) +
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73 (mp_word)u + (mp_word)*tmpx;
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74
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75 /* get carry */
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76 u = (mp_digit)(r >> (mp_word)DIGIT_BIT);
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77
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78 /* fix digit */
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79 *tmpx++ = (mp_digit)(r & (mp_word)MP_MASK);
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80 }
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81 /* At this point the ix'th digit of x should be zero */
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82
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83
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84 /* propagate carries upwards as required*/
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85 while (u != 0u) {
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86 *tmpx += u;
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87 u = *tmpx >> DIGIT_BIT;
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88 *tmpx++ &= MP_MASK;
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89 }
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90 }
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91 }
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92
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93 /* at this point the n.used'th least
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94 * significant digits of x are all zero
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95 * which means we can shift x to the
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96 * right by n.used digits and the
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97 * residue is unchanged.
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98 */
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99
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100 /* x = x/b**n.used */
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101 mp_clamp(x);
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102 mp_rshd(x, n->used);
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103
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104 /* if x >= n then x = x - n */
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105 if (mp_cmp_mag(x, n) != MP_LT) {
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106 return s_mp_sub(x, n, x);
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107 }
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108
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109 return MP_OKAY;
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110 }
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111 #endif
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112
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113 /* ref: HEAD -> master, tag: v1.1.0 */
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114 /* git commit: 08549ad6bc8b0cede0b357a9c341c5c6473a9c55 */
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115 /* commit time: 2019-01-28 20:32:32 +0100 */