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annotate libtommath/bn_mp_montgomery_setup.c @ 1899:ab9c5467970d

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Merge pull request #152 from HansH111/tracelevel2
author Matt Johnston <matt@ucc.asn.au>
date Wed, 23 Mar 2022 21:55:33 +0800
parents 1051e4eea25a
children
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1 #include "tommath_private.h"
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2 #ifdef BN_MP_MONTGOMERY_SETUP_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 /* setups the montgomery reduction stuff */
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7 mp_err mp_montgomery_setup(const mp_int *n, mp_digit *rho)
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8 {
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9 mp_digit x, b;
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10
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11 /* fast inversion mod 2**k
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12 *
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13 * Based on the fact that
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14 *
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15 * XA = 1 (mod 2**n) => (X(2-XA)) A = 1 (mod 2**2n)
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16 * => 2*X*A - X*X*A*A = 1
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17 * => 2*(1) - (1) = 1
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18 */
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19 b = n->dp[0];
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20
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21 if ((b & 1u) == 0u) {
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22 return MP_VAL;
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23 }
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25 x = (((b + 2u) & 4u) << 1) + b; /* here x*a==1 mod 2**4 */
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26 x *= 2u - (b * x); /* here x*a==1 mod 2**8 */
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27 #if !defined(MP_8BIT)
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28 x *= 2u - (b * x); /* here x*a==1 mod 2**16 */
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29 #endif
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30 #if defined(MP_64BIT) || !(defined(MP_8BIT) || defined(MP_16BIT))
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31 x *= 2u - (b * x); /* here x*a==1 mod 2**32 */
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32 #endif
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33 #ifdef MP_64BIT
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34 x *= 2u - (b * x); /* here x*a==1 mod 2**64 */
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35 #endif
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37 /* rho = -1/m mod b */
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38 *rho = (mp_digit)(((mp_word)1 << (mp_word)MP_DIGIT_BIT) - x) & MP_MASK;
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39
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40 return MP_OKAY;
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41 }
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42 #endif