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/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is library that provides for multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library is designed directly after the MPI library by
* 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, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
#include <tommath.h>
/* setups the montgomery reduction stuff */
int
mp_montgomery_setup (mp_int * n, mp_digit * rho)
{
mp_digit x, b;
/* fast inversion mod 2**k
*
* Based on the fact that
*
* 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
*/
b = n->dp[0];
if ((b & 1) == 0) {
return MP_VAL;
}
x = (((b + 2) & 4) << 1) + b; /* here x*a==1 mod 2**4 */
x *= 2 - b * x; /* here x*a==1 mod 2**8 */
#if !defined(MP_8BIT)
x *= 2 - b * x; /* here x*a==1 mod 2**16 */
#endif
#if defined(MP_64BIT) || !(defined(MP_8BIT) || defined(MP_16BIT))
x *= 2 - b * x; /* here x*a==1 mod 2**32 */
#endif
#ifdef MP_64BIT
x *= 2 - b * x; /* here x*a==1 mod 2**64 */
#endif
/* rho = -1/m mod b */
*rho = (((mp_digit) 1 << ((mp_digit) DIGIT_BIT)) - x) & MP_MASK;
return MP_OKAY;
}
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