tommath/bn_mp_montgomery_setup.c

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#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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* LibTomMath is a library that provides multiple-precision
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* integer arithmetic as well as number theoretic functionality.
*
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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
* additional optimizations in place.
*
* The library is free for all purposes without any express
* guarantee it works.
*
* Tom St Denis, tstdenis82@gmail.com, http://libtom.org
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*/
/* setups the montgomery reduction stuff */
int
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mp_montgomery_setup (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)
* => 2*X*A - X*X*A*A = 1
* => 2*(1) - (1) = 1
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*/
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b = n->dp[0];
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if ((b & 1) == 0) {
return MP_VAL;
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}
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x = (((b + 2) & 4) << 1) + b; /* here x*a==1 mod 2**4 */
x *= 2 - (b * x); /* here x*a==1 mod 2**8 */
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#if !defined(MP_8BIT)
x *= 2 - (b * x); /* here x*a==1 mod 2**16 */
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#endif
#if defined(MP_64BIT) || !(defined(MP_8BIT) || defined(MP_16BIT))
x *= 2 - (b * x); /* here x*a==1 mod 2**32 */
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#endif
#ifdef MP_64BIT
x *= 2 - (b * x); /* here x*a==1 mod 2**64 */
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#endif
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/* rho = -1/m mod b */
*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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