1#include <tommath.h>
2#ifdef BN_MP_MONTGOMERY_REDUCE_C
3/* LibTomMath, multiple-precision integer library -- Tom St Denis
4 *
5 * LibTomMath is a library that provides multiple-precision
6 * integer arithmetic as well as number theoretic functionality.
7 *
8 * The library was designed directly after the MPI library by
9 * Michael Fromberger but has been written from scratch with
10 * additional optimizations in place.
11 *
12 * The library is free for all purposes without any express
13 * guarantee it works.
14 *
15 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
16 */
17
18/* computes xR**-1 == x (mod N) via Montgomery Reduction */
19int
20mp_montgomery_reduce (mp_int * x, mp_int * n, mp_digit rho)
21{
22  int     ix, res, digs;
23  mp_digit mu;
24
25  /* can the fast reduction [comba] method be used?
26   *
27   * Note that unlike in mul you're safely allowed *less*
28   * than the available columns [255 per default] since carries
29   * are fixed up in the inner loop.
30   */
31  digs = n->used * 2 + 1;
32  if ((digs < MP_WARRAY) &&
33      n->used <
34      (1 << ((CHAR_BIT * sizeof (mp_word)) - (2 * DIGIT_BIT)))) {
35    return fast_mp_montgomery_reduce (x, n, rho);
36  }
37
38  /* grow the input as required */
39  if (x->alloc < digs) {
40    if ((res = mp_grow (x, digs)) != MP_OKAY) {
41      return res;
42    }
43  }
44  x->used = digs;
45
46  for (ix = 0; ix < n->used; ix++) {
47    /* mu = ai * rho mod b
48     *
49     * The value of rho must be precalculated via
50     * montgomery_setup() such that
51     * it equals -1/n0 mod b this allows the
52     * following inner loop to reduce the
53     * input one digit at a time
54     */
55    mu = (mp_digit) (((mp_word)x->dp[ix]) * ((mp_word)rho) & MP_MASK);
56
57    /* a = a + mu * m * b**i */
58    {
59      register int iy;
60      register mp_digit *tmpn, *tmpx, u;
61      register mp_word r;
62
63      /* alias for digits of the modulus */
64      tmpn = n->dp;
65
66      /* alias for the digits of x [the input] */
67      tmpx = x->dp + ix;
68
69      /* set the carry to zero */
70      u = 0;
71
72      /* Multiply and add in place */
73      for (iy = 0; iy < n->used; iy++) {
74        /* compute product and sum */
75        r       = ((mp_word)mu) * ((mp_word)*tmpn++) +
76                  ((mp_word) u) + ((mp_word) * tmpx);
77
78        /* get carry */
79        u       = (mp_digit)(r >> ((mp_word) DIGIT_BIT));
80
81        /* fix digit */
82        *tmpx++ = (mp_digit)(r & ((mp_word) MP_MASK));
83      }
84      /* At this point the ix'th digit of x should be zero */
85
86
87      /* propagate carries upwards as required*/
88      while (u) {
89        *tmpx   += u;
90        u        = *tmpx >> DIGIT_BIT;
91        *tmpx++ &= MP_MASK;
92      }
93    }
94  }
95
96  /* at this point the n.used'th least
97   * significant digits of x are all zero
98   * which means we can shift x to the
99   * right by n.used digits and the
100   * residue is unchanged.
101   */
102
103  /* x = x/b**n.used */
104  mp_clamp(x);
105  mp_rshd (x, n->used);
106
107  /* if x >= n then x = x - n */
108  if (mp_cmp_mag (x, n) != MP_LT) {
109    return s_mp_sub (x, n, x);
110  }
111
112  return MP_OKAY;
113}
114#endif
115
116/* $Source: /cvs/libtom/libtommath/bn_mp_montgomery_reduce.c,v $ */
117/* $Revision: 1.3 $ */
118/* $Date: 2006/03/31 14:18:44 $ */
119