2 #ifdef BN_MP_MONTGOMERY_SETUP_C
3 /* LibTomMath, multiple-precision integer library -- Tom St Denis
5 * LibTomMath is a library that provides multiple-precision
6 * integer arithmetic as well as number theoretic functionality.
8 * The library was designed directly after the MPI library by
9 * Michael Fromberger but has been written from scratch with
10 * additional optimizations in place.
12 * The library is free for all purposes without any express
15 * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
18 /* setups the montgomery reduction stuff */
20 mp_montgomery_setup (mp_int * n, mp_digit * rho)
24 /* fast inversion mod 2**k
26 * Based on the fact that
28 * XA = 1 (mod 2**n) => (X(2-XA)) A = 1 (mod 2**2n)
29 * => 2*X*A - X*X*A*A = 1
38 x = (((b + 2) & 4) << 1) + b; /* here x*a==1 mod 2**4 */
39 x *= 2 - b * x; /* here x*a==1 mod 2**8 */
41 x *= 2 - b * x; /* here x*a==1 mod 2**16 */
43 #if defined(MP_64BIT) || !(defined(MP_8BIT) || defined(MP_16BIT))
44 x *= 2 - b * x; /* here x*a==1 mod 2**32 */
47 x *= 2 - b * x; /* here x*a==1 mod 2**64 */
50 /* rho = -1/m mod b */
51 *rho = (((mp_word)1 << ((mp_word) DIGIT_BIT)) - x) & MP_MASK;