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annotate libtommath/bn_mp_montgomery_reduce.c @ 1843:03dfecca99bd

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author Matt Johnston <matt@ucc.asn.au>
date Mon, 18 Oct 2021 23:25:20 +0800
parents 1051e4eea25a
children
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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 /* SPDX-License-Identifier: Unlicense */
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6 /* computes xR**-1 == x (mod N) via Montgomery Reduction */
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7 mp_err mp_montgomery_reduce(mp_int *x, const mp_int *n, mp_digit rho)
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8 {
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9 int ix, digs;
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10 mp_err err;
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11 mp_digit mu;
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12
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13 /* can the fast reduction [comba] method be used?
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14 *
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15 * Note that unlike in mul you're safely allowed *less*
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16 * than the available columns [255 per default] since carries
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17 * are fixed up in the inner loop.
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18 */
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19 digs = (n->used * 2) + 1;
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20 if ((digs < MP_WARRAY) &&
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21 (x->used <= MP_WARRAY) &&
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22 (n->used < MP_MAXFAST)) {
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23 return s_mp_montgomery_reduce_fast(x, n, rho);
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24 }
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26 /* grow the input as required */
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27 if (x->alloc < digs) {
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28 if ((err = mp_grow(x, digs)) != MP_OKAY) {
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29 return err;
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30 }
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31 }
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32 x->used = digs;
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33
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34 for (ix = 0; ix < n->used; ix++) {
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35 /* mu = ai * rho mod b
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36 *
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37 * The value of rho must be precalculated via
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38 * montgomery_setup() such that
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39 * it equals -1/n0 mod b this allows the
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40 * following inner loop to reduce the
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41 * input one digit at a time
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42 */
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43 mu = (mp_digit)(((mp_word)x->dp[ix] * (mp_word)rho) & MP_MASK);
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44
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45 /* a = a + mu * m * b**i */
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46 {
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47 int iy;
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48 mp_digit *tmpn, *tmpx, u;
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49 mp_word r;
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51 /* alias for digits of the modulus */
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52 tmpn = n->dp;
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53
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54 /* alias for the digits of x [the input] */
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55 tmpx = x->dp + ix;
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56
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57 /* set the carry to zero */
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58 u = 0;
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59
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60 /* Multiply and add in place */
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61 for (iy = 0; iy < n->used; iy++) {
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62 /* compute product and sum */
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63 r = ((mp_word)mu * (mp_word)*tmpn++) +
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64 (mp_word)u + (mp_word)*tmpx;
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65
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66 /* get carry */
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67 u = (mp_digit)(r >> (mp_word)MP_DIGIT_BIT);
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69 /* fix digit */
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70 *tmpx++ = (mp_digit)(r & (mp_word)MP_MASK);
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71 }
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72 /* At this point the ix'th digit of x should be zero */
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73
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75 /* propagate carries upwards as required*/
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76 while (u != 0u) {
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77 *tmpx += u;
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78 u = *tmpx >> MP_DIGIT_BIT;
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79 *tmpx++ &= MP_MASK;
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80 }
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81 }
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82 }
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83
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84 /* at this point the n.used'th least
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85 * significant digits of x are all zero
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86 * which means we can shift x to the
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87 * right by n.used digits and the
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88 * residue is unchanged.
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89 */
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90
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91 /* x = x/b**n.used */
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92 mp_clamp(x);
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93 mp_rshd(x, n->used);
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94
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95 /* if x >= n then x = x - n */
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96 if (mp_cmp_mag(x, n) != MP_LT) {
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97 return s_mp_sub(x, n, x);
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98 }
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99
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100 return MP_OKAY;
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101 }
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102 #endif