54 lines
1.6 KiB
C
54 lines
1.6 KiB
C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
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*
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* LibTomMath is library that provides for multiple-precision
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* integer arithmetic as well as number theoretic functionality.
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*
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* The library is designed directly after the MPI library by
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* Michael Fromberger but has been written from scratch with
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* additional optimizations in place.
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*
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* The library is free for all purposes without any express
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* guarantee it works.
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*
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* Tom St Denis, tomstdenis@iahu.ca, http://libtommath.iahu.ca
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*/
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#include <tommath.h>
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/* calculates a = B^n mod b for Montgomery reduction
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* Where B is the base [e.g. 2^DIGIT_BIT].
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* B^n mod b is computed by first computing
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* A = B^(n-1) which doesn't require a reduction but a simple OR.
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* then C = A * B = B^n is computed by performing upto DIGIT_BIT
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* shifts with subtractions when the result is greater than b.
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*
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* The method is slightly modified to shift B unconditionally upto just under
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* the leading bit of b. This saves alot of multiple precision shifting.
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*/
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int
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mp_montgomery_calc_normalization (mp_int * a, mp_int * b)
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{
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int x, bits, res;
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/* how many bits of last digit does b use */
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bits = mp_count_bits (b) % DIGIT_BIT;
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/* compute A = B^(n-1) * 2^(bits-1) */
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if ((res = mp_2expt (a, (b->used - 1) * DIGIT_BIT + bits - 1)) != MP_OKAY) {
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return res;
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}
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/* now compute C = A * B mod b */
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for (x = bits - 1; x < DIGIT_BIT; x++) {
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if ((res = mp_mul_2 (a, a)) != MP_OKAY) {
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return res;
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}
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if (mp_cmp_mag (a, b) != MP_LT) {
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if ((res = s_mp_sub (a, b, a)) != MP_OKAY) {
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return res;
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}
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}
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}
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return MP_OKAY;
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}
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