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annotate libtommath/bn_mp_montgomery_reduce.c @ 1684:d5d25ce2a2ed

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cast to fix warning
author Matt Johnston <matt@ucc.asn.au>
date Tue, 26 May 2020 19:57:28 +0800
parents f52919ffd3b1
children 1051e4eea25a
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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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parents: 1470
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115 /* commit time: 2019-01-28 20:32:32 +0100 */