41 lines
1.1 KiB
C
41 lines
1.1 KiB
C
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#include "tommath_private.h"
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#ifdef MP_MONTGOMERY_SETUP_C
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/* LibTomMath, multiple-precision integer library -- Tom St Denis */
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/* SPDX-License-Identifier: Unlicense */
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/* setups the montgomery reduction stuff */
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mp_err mp_montgomery_setup(const mp_int *n, mp_digit *rho)
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{
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mp_digit x, b;
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/* fast inversion mod 2**k
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*
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* Based on the fact that
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*
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* XA = 1 (mod 2**n) => (X(2-XA)) A = 1 (mod 2**2n)
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* => 2*X*A - X*X*A*A = 1
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* => 2*(1) - (1) = 1
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*/
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b = n->dp[0];
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if ((b & 1u) == 0u) {
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return MP_VAL;
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}
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x = (((b + 2u) & 4u) << 1) + b; /* here x*a==1 mod 2**4 */
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x *= 2u - (b * x); /* here x*a==1 mod 2**8 */
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x *= 2u - (b * x); /* here x*a==1 mod 2**16 */
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#if defined(MP_64BIT) || !(defined(MP_16BIT))
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x *= 2u - (b * x); /* here x*a==1 mod 2**32 */
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#endif
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#ifdef MP_64BIT
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x *= 2u - (b * x); /* here x*a==1 mod 2**64 */
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#endif
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/* rho = -1/m mod b */
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*rho = (mp_digit)(((mp_word)1 << (mp_word)MP_DIGIT_BIT) - x) & MP_MASK;
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return MP_OKAY;
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}
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#endif
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