| /* LibTomMath, multiple-precision integer library -- Tom St Denis |
| * |
| * LibTomMath is a library that provides multiple-precision |
| * integer arithmetic as well as number theoretic functionality. |
| * |
| * The library was 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> |
| |
| /* calculates a = B^n mod b for Montgomery reduction |
| * Where B is the base [e.g. 2^DIGIT_BIT]. |
| * B^n mod b is computed by first computing |
| * A = B^(n-1) which doesn't require a reduction but a simple OR. |
| * then C = A * B = B^n is computed by performing upto DIGIT_BIT |
| * shifts with subtractions when the result is greater than b. |
| * |
| * The method is slightly modified to shift B unconditionally upto just under |
| * the leading bit of b. This saves alot of multiple precision shifting. |
| */ |
| int |
| mp_montgomery_calc_normalization (mp_int * a, mp_int * b) |
| { |
| int x, bits, res; |
| |
| /* how many bits of last digit does b use */ |
| bits = mp_count_bits (b) % DIGIT_BIT; |
| |
| /* compute A = B^(n-1) * 2^(bits-1) */ |
| if ((res = mp_2expt (a, (b->used - 1) * DIGIT_BIT + bits - 1)) != MP_OKAY) { |
| return res; |
| } |
| |
| /* now compute C = A * B mod b */ |
| for (x = bits - 1; x < (int)DIGIT_BIT; x++) { |
| if ((res = mp_mul_2 (a, a)) != MP_OKAY) { |
| return res; |
| } |
| if (mp_cmp_mag (a, b) != MP_LT) { |
| if ((res = s_mp_sub (a, b, a)) != MP_OKAY) { |
| return res; |
| } |
| } |
| } |
| |
| return MP_OKAY; |
| } |