1 /* $NetBSD: bn_mp_montgomery_reduce.c,v 1.2 2017/01/28 21:31:47 christos Exp $ */
2
3 #include <tommath.h>
4 #ifdef BN_MP_MONTGOMERY_REDUCE_C
5 /* LibTomMath, multiple-precision integer library -- Tom St Denis
6 *
7 * LibTomMath is a library that provides multiple-precision
8 * integer arithmetic as well as number theoretic functionality.
9 *
10 * The library was designed directly after the MPI library by
11 * Michael Fromberger but has been written from scratch with
12 * additional optimizations in place.
13 *
14 * The library is free for all purposes without any express
15 * guarantee it works.
16 *
17 * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
18 */
19
20 /* computes xR**-1 == x (mod N) via Montgomery Reduction */
21 int
mp_montgomery_reduce(mp_int * x,mp_int * n,mp_digit rho)22 mp_montgomery_reduce (mp_int * x, mp_int * n, mp_digit rho)
23 {
24 int ix, res, digs;
25 mp_digit mu;
26
27 /* can the fast reduction [comba] method be used?
28 *
29 * Note that unlike in mul you're safely allowed *less*
30 * than the available columns [255 per default] since carries
31 * are fixed up in the inner loop.
32 */
33 digs = n->used * 2 + 1;
34 if ((digs < MP_WARRAY) &&
35 n->used <
36 (1 << ((CHAR_BIT * sizeof (mp_word)) - (2 * DIGIT_BIT)))) {
37 return fast_mp_montgomery_reduce (x, n, rho);
38 }
39
40 /* grow the input as required */
41 if (x->alloc < digs) {
42 if ((res = mp_grow (x, digs)) != MP_OKAY) {
43 return res;
44 }
45 }
46 x->used = digs;
47
48 for (ix = 0; ix < n->used; ix++) {
49 /* mu = ai * rho mod b
50 *
51 * The value of rho must be precalculated via
52 * montgomery_setup() such that
53 * it equals -1/n0 mod b this allows the
54 * following inner loop to reduce the
55 * input one digit at a time
56 */
57 mu = (mp_digit) (((mp_word)x->dp[ix]) * ((mp_word)rho) & MP_MASK);
58
59 /* a = a + mu * m * b**i */
60 {
61 register int iy;
62 register mp_digit *tmpn, *tmpx, u;
63 register mp_word r;
64
65 /* alias for digits of the modulus */
66 tmpn = n->dp;
67
68 /* alias for the digits of x [the input] */
69 tmpx = x->dp + ix;
70
71 /* set the carry to zero */
72 u = 0;
73
74 /* Multiply and add in place */
75 for (iy = 0; iy < n->used; iy++) {
76 /* compute product and sum */
77 r = ((mp_word)mu) * ((mp_word)*tmpn++) +
78 ((mp_word) u) + ((mp_word) * tmpx);
79
80 /* get carry */
81 u = (mp_digit)(r >> ((mp_word) DIGIT_BIT));
82
83 /* fix digit */
84 *tmpx++ = (mp_digit)(r & ((mp_word) MP_MASK));
85 }
86 /* At this point the ix'th digit of x should be zero */
87
88
89 /* propagate carries upwards as required*/
90 while (u) {
91 *tmpx += u;
92 u = *tmpx >> DIGIT_BIT;
93 *tmpx++ &= MP_MASK;
94 }
95 }
96 }
97
98 /* at this point the n.used'th least
99 * significant digits of x are all zero
100 * which means we can shift x to the
101 * right by n.used digits and the
102 * residue is unchanged.
103 */
104
105 /* x = x/b**n.used */
106 mp_clamp(x);
107 mp_rshd (x, n->used);
108
109 /* if x >= n then x = x - n */
110 if (mp_cmp_mag (x, n) != MP_LT) {
111 return s_mp_sub (x, n, x);
112 }
113
114 return MP_OKAY;
115 }
116 #endif
117
118 /* Source: /cvs/libtom/libtommath/bn_mp_montgomery_reduce.c,v */
119 /* Revision: 1.4 */
120 /* Date: 2006/12/28 01:25:13 */
121