59 lines
1.6 KiB
C
59 lines
1.6 KiB
C
#include <tommath_private.h>
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#ifdef BN_MP_MONTGOMERY_SETUP_C
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/* LibTomMath, multiple-precision integer library -- Tom St Denis
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*
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* LibTomMath is a library that provides multiple-precision
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* integer arithmetic as well as number theoretic functionality.
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*
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* The library was designed directly after the MPI library by
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* Michael Fromberger but has been written from scratch with
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* additional optimizations in place.
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*
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* The library is free for all purposes without any express
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* guarantee it works.
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*
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* Tom St Denis, tstdenis82@gmail.com, http://libtom.org
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*/
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/* setups the montgomery reduction stuff */
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int 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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#if !defined(MP_8BIT)
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x *= 2u - (b * x); /* here x*a==1 mod 2**16 */
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#endif
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#if defined(MP_64BIT) || !(defined(MP_8BIT) || 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)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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/* ref: $Format:%D$ */
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/* git commit: $Format:%H$ */
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/* commit time: $Format:%ai$ */
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