1 #include <tommath.h> 2 #ifdef BN_MP_MONTGOMERY_SETUP_C 3 /* LibTomMath, multiple-precision integer library -- Tom St Denis 4 * 5 * LibTomMath is a library that provides multiple-precision 6 * integer arithmetic as well as number theoretic functionality. 7 * 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. 11 * 12 * The library is free for all purposes without any express 13 * guarantee it works. 14 * 15 * Tom St Denis, tomstdenis (at) gmail.com, http://math.libtomcrypt.com 16 */ 17 18 /* setups the montgomery reduction stuff */ 19 int 20 mp_montgomery_setup (mp_int * n, mp_digit * rho) 21 { 22 mp_digit x, b; 23 24 /* fast inversion mod 2**k 25 * 26 * Based on the fact that 27 * 28 * XA = 1 (mod 2**n) => (X(2-XA)) A = 1 (mod 2**2n) 29 * => 2*X*A - X*X*A*A = 1 30 * => 2*(1) - (1) = 1 31 */ 32 b = n->dp[0]; 33 34 if ((b & 1) == 0) { 35 return MP_VAL; 36 } 37 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 */ 40 #if !defined(MP_8BIT) 41 x *= 2 - b * x; /* here x*a==1 mod 2**16 */ 42 #endif 43 #if defined(MP_64BIT) || !(defined(MP_8BIT) || defined(MP_16BIT)) 44 x *= 2 - b * x; /* here x*a==1 mod 2**32 */ 45 #endif 46 #ifdef MP_64BIT 47 x *= 2 - b * x; /* here x*a==1 mod 2**64 */ 48 #endif 49 50 /* rho = -1/m mod b */ 51 *rho = (unsigned long)(((mp_word)1 << ((mp_word) DIGIT_BIT)) - x) & MP_MASK; 52 53 return MP_OKAY; 54 } 55 #endif 56 57 /* $Source: /cvs/libtom/libtommath/bn_mp_montgomery_setup.c,v $ */ 58 /* $Revision: 1.4 $ */ 59 /* $Date: 2006/12/04 21:34:03 $ */ 60
