/* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is library that provides for multiple-precision * integer arithmetic as well as number theoretic functionality. * * The library is 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 /* computes xR**-1 == x (mod N) via Montgomery Reduction */ int mp_montgomery_reduce (mp_int * x, mp_int * n, mp_digit rho) { int ix, res, digs; mp_digit mu; /* can the fast reduction [comba] method be used? * * Note that unlike in mp_mul you're safely allowed *less* * than the available columns [255 per default] since carries * are fixed up in the inner loop. */ digs = n->used * 2 + 1; if ((digs < MP_WARRAY) && n->used < (1 << ((CHAR_BIT * sizeof (mp_word)) - (2 * DIGIT_BIT)))) { return fast_mp_montgomery_reduce (x, n, rho); } /* grow the input as required */ if (x->alloc < digs) { if ((res = mp_grow (x, digs)) != MP_OKAY) { return res; } } x->used = digs; for (ix = 0; ix < n->used; ix++) { /* mu = ai * m' mod b */ mu = (x->dp[ix] * rho) & MP_MASK; /* a = a + mu * m * b**i */ { register int iy; register mp_digit *tmpn, *tmpx, u; register mp_word r; /* aliases */ tmpn = n->dp; tmpx = x->dp + ix; /* set the carry to zero */ u = 0; /* Multiply and add in place */ for (iy = 0; iy < n->used; iy++) { r = ((mp_word) mu) * ((mp_word) * tmpn++) + ((mp_word) u) + ((mp_word) * tmpx); u = (mp_digit)(r >> ((mp_word) DIGIT_BIT)); *tmpx++ = (mp_digit)(r & ((mp_word) MP_MASK)); } /* propagate carries */ while (u) { *tmpx += u; u = *tmpx >> DIGIT_BIT; *tmpx++ &= MP_MASK; } } } /* x = x/b**n.used */ mp_clamp(x); mp_rshd (x, n->used); /* 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; }