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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 * a, mp_digit * mp)
{
unsigned long x, b;
/* fast inversion mod 2^32
*
* 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 = a->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 */
x *= 2 - b * x; /* here x*a==1 mod 2^16; each step doubles the nb of bits */
x *= 2 - b * x; /* here x*a==1 mod 2^32 */
/* t = -1/m mod b */
*mp = ((mp_digit) 1 << ((mp_digit) DIGIT_BIT)) - (x & MP_MASK);
return MP_OKAY;
}
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