# libtom/libtommath

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 #include #ifdef BN_FAST_MP_MONTGOMERY_REDUCE_C /* 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 */ /* computes xR**-1 == x (mod N) via Montgomery Reduction * * This is an optimized implementation of montgomery_reduce * which uses the comba method to quickly calculate the columns of the * reduction. * * Based on Algorithm 14.32 on pp.601 of HAC. */ int fast_mp_montgomery_reduce (mp_int * x, mp_int * n, mp_digit rho) { int ix, res, olduse; mp_word W[MP_WARRAY]; /* get old used count */ olduse = x->used; /* grow a as required */ if (x->alloc < n->used + 1) { if ((res = mp_grow (x, n->used + 1)) != MP_OKAY) { return res; } } /* first we have to get the digits of the input into * an array of double precision words W[...] */ { register mp_word *_W; register mp_digit *tmpx; /* alias for the W[] array */ _W = W; /* alias for the digits of x*/ tmpx = x->dp; /* copy the digits of a into W[0..a->used-1] */ for (ix = 0; ix < x->used; ix++) { *_W++ = *tmpx++; } /* zero the high words of W[a->used..m->used*2] */ for (; ix < n->used * 2 + 1; ix++) { *_W++ = 0; } } /* now we proceed to zero successive digits * from the least significant upwards */ for (ix = 0; ix < n->used; ix++) { /* mu = ai * m' mod b * * We avoid a double precision multiplication (which isn't required) * by casting the value down to a mp_digit. Note this requires * that W[ix-1] have the carry cleared (see after the inner loop) */ register mp_digit mu; mu = (mp_digit) (((W[ix] & MP_MASK) * rho) & MP_MASK); /* a = a + mu * m * b**i * * This is computed in place and on the fly. The multiplication * by b**i is handled by offseting which columns the results * are added to. * * Note the comba method normally doesn't handle carries in the * inner loop In this case we fix the carry from the previous * column since the Montgomery reduction requires digits of the * result (so far) [see above] to work. This is * handled by fixing up one carry after the inner loop. The * carry fixups are done in order so after these loops the * first m->used words of W[] have the carries fixed */ { register int iy; register mp_digit *tmpn; register mp_word *_W; /* alias for the digits of the modulus */ tmpn = n->dp; /* Alias for the columns set by an offset of ix */ _W = W + ix; /* inner loop */ for (iy = 0; iy < n->used; iy++) { *_W++ += ((mp_word)mu) * ((mp_word)*tmpn++); } } /* now fix carry for next digit, W[ix+1] */ W[ix + 1] += W[ix] >> ((mp_word) DIGIT_BIT); } /* now we have to propagate the carries and * shift the words downward [all those least * significant digits we zeroed]. */ { register mp_digit *tmpx; register mp_word *_W, *_W1; /* nox fix rest of carries */ /* alias for current word */ _W1 = W + ix; /* alias for next word, where the carry goes */ _W = W + ++ix; for (; ix <= n->used * 2 + 1; ix++) { *_W++ += *_W1++ >> ((mp_word) DIGIT_BIT); } /* copy out, A = A/b**n * * The result is A/b**n but instead of converting from an * array of mp_word to mp_digit than calling mp_rshd * we just copy them in the right order */ /* alias for destination word */ tmpx = x->dp; /* alias for shifted double precision result */ _W = W + n->used; for (ix = 0; ix < n->used + 1; ix++) { *tmpx++ = (mp_digit)(*_W++ & ((mp_word) MP_MASK)); } /* zero oldused digits, if the input a was larger than * m->used+1 we'll have to clear the digits */ for (; ix < olduse; ix++) { *tmpx++ = 0; } } /* set the max used and clamp */ x->used = n->used + 1; mp_clamp (x); /* if A >= m then A = A - m */ if (mp_cmp_mag (x, n) != MP_LT) { return s_mp_sub (x, n, x); } return MP_OKAY; } #endif
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