131 lines
4.0 KiB
C
131 lines
4.0 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://math.libtomcrypt.org
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*/
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#include <tommath.h>
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/* Fast (comba) multiplier
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*
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* This is the fast column-array [comba] multiplier. It is
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* designed to compute the columns of the product first
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* then handle the carries afterwards. This has the effect
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* of making the nested loops that compute the columns very
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* simple and schedulable on super-scalar processors.
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*
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* This has been modified to produce a variable number of
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* digits of output so if say only a half-product is required
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* you don't have to compute the upper half (a feature
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* required for fast Barrett reduction).
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*
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* Based on Algorithm 14.12 on pp.595 of HAC.
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*
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*/
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int
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fast_s_mp_mul_digs (mp_int * a, mp_int * b, mp_int * c, int digs)
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{
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int olduse, res, pa, ix;
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mp_word W[MP_WARRAY];
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/* grow the destination as required */
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if (c->alloc < digs) {
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if ((res = mp_grow (c, digs)) != MP_OKAY) {
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return res;
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}
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}
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/* clear temp buf (the columns) */
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memset (W, 0, sizeof (mp_word) * digs);
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/* calculate the columns */
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pa = a->used;
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for (ix = 0; ix < pa; ix++) {
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/* this multiplier has been modified to allow you to
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* control how many digits of output are produced.
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* So at most we want to make upto "digs" digits of output.
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*
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* this adds products to distinct columns (at ix+iy) of W
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* note that each step through the loop is not dependent on
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* the previous which means the compiler can easily unroll
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* the loop without scheduling problems
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*/
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{
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register mp_digit tmpx, *tmpy;
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register mp_word *_W;
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register int iy, pb;
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/* alias for the the word on the left e.g. A[ix] * A[iy] */
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tmpx = a->dp[ix];
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/* alias for the right side */
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tmpy = b->dp;
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/* alias for the columns, each step through the loop adds a new
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term to each column
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*/
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_W = W + ix;
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/* the number of digits is limited by their placement. E.g.
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we avoid multiplying digits that will end up above the # of
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digits of precision requested
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*/
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pb = MIN (b->used, digs - ix);
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for (iy = 0; iy < pb; iy++) {
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*_W++ += ((mp_word)tmpx) * ((mp_word)*tmpy++);
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}
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}
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}
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/* setup dest */
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olduse = c->used;
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c->used = digs;
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{
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register mp_digit *tmpc;
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/* At this point W[] contains the sums of each column. To get the
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* correct result we must take the extra bits from each column and
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* carry them down
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*
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* Note that while this adds extra code to the multiplier it
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* saves time since the carry propagation is removed from the
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* above nested loop.This has the effect of reducing the work
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* from N*(N+N*c)==N**2 + c*N**2 to N**2 + N*c where c is the
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* cost of the shifting. On very small numbers this is slower
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* but on most cryptographic size numbers it is faster.
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*
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* In this particular implementation we feed the carries from
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* behind which means when the loop terminates we still have one
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* last digit to copy
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*/
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tmpc = c->dp;
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for (ix = 1; ix < digs; ix++) {
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/* forward the carry from the previous temp */
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W[ix] += (W[ix - 1] >> ((mp_word) DIGIT_BIT));
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/* now extract the previous digit [below the carry] */
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*tmpc++ = (mp_digit) (W[ix - 1] & ((mp_word) MP_MASK));
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}
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/* fetch the last digit */
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*tmpc++ = (mp_digit) (W[digs - 1] & ((mp_word) MP_MASK));
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/* clear unused digits [that existed in the old copy of c] */
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for (; ix < olduse; ix++) {
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*tmpc++ = 0;
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}
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}
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mp_clamp (c);
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return MP_OKAY;
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}
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