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comparison bn_mp_montgomery_reduce.c @ 2:86e0b50a9b58 libtommath-orig ltm-0.30-orig

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ltm 0.30 orig import
author Matt Johnston <matt@ucc.asn.au>
date Mon, 31 May 2004 18:25:22 +0000
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-1:000000000000 2:86e0b50a9b58
1 /* LibTomMath, multiple-precision integer library -- Tom St Denis
2 *
3 * LibTomMath is a library that provides multiple-precision
4 * integer arithmetic as well as number theoretic functionality.
5 *
6 * The library was designed directly after the MPI library by
7 * Michael Fromberger but has been written from scratch with
8 * additional optimizations in place.
9 *
10 * The library is free for all purposes without any express
11 * guarantee it works.
12 *
13 * Tom St Denis, [email protected], http://math.libtomcrypt.org
14 */
15 #include <tommath.h>
16
17 /* computes xR**-1 == x (mod N) via Montgomery Reduction */
18 int
19 mp_montgomery_reduce (mp_int * x, mp_int * n, mp_digit rho)
20 {
21 int ix, res, digs;
22 mp_digit mu;
23
24 /* can the fast reduction [comba] method be used?
25 *
26 * Note that unlike in mp_mul you're safely allowed *less*
27 * than the available columns [255 per default] since carries
28 * are fixed up in the inner loop.
29 */
30 digs = n->used * 2 + 1;
31 if ((digs < MP_WARRAY) &&
32 n->used <
33 (1 << ((CHAR_BIT * sizeof (mp_word)) - (2 * DIGIT_BIT)))) {
34 return fast_mp_montgomery_reduce (x, n, rho);
35 }
36
37 /* grow the input as required */
38 if (x->alloc < digs) {
39 if ((res = mp_grow (x, digs)) != MP_OKAY) {
40 return res;
41 }
42 }
43 x->used = digs;
44
45 for (ix = 0; ix < n->used; ix++) {
46 /* mu = ai * rho mod b
47 *
48 * The value of rho must be precalculated via
49 * bn_mp_montgomery_setup() such that
50 * it equals -1/n0 mod b this allows the
51 * following inner loop to reduce the
52 * input one digit at a time
53 */
54 mu = (mp_digit) (((mp_word)x->dp[ix]) * ((mp_word)rho) & MP_MASK);
55
56 /* a = a + mu * m * b**i */
57 {
58 register int iy;
59 register mp_digit *tmpn, *tmpx, u;
60 register mp_word r;
61
62 /* alias for digits of the modulus */
63 tmpn = n->dp;
64
65 /* alias for the digits of x [the input] */
66 tmpx = x->dp + ix;
67
68 /* set the carry to zero */
69 u = 0;
70
71 /* Multiply and add in place */
72 for (iy = 0; iy < n->used; iy++) {
73 /* compute product and sum */
74 r = ((mp_word)mu) * ((mp_word)*tmpn++) +
75 ((mp_word) u) + ((mp_word) * tmpx);
76
77 /* get carry */
78 u = (mp_digit)(r >> ((mp_word) DIGIT_BIT));
79
80 /* fix digit */
81 *tmpx++ = (mp_digit)(r & ((mp_word) MP_MASK));
82 }
83 /* At this point the ix'th digit of x should be zero */
84
85
86 /* propagate carries upwards as required*/
87 while (u) {
88 *tmpx += u;
89 u = *tmpx >> DIGIT_BIT;
90 *tmpx++ &= MP_MASK;
91 }
92 }
93 }
94
95 /* at this point the n.used'th least
96 * significant digits of x are all zero
97 * which means we can shift x to the
98 * right by n.used digits and the
99 * residue is unchanged.
100 */
101
102 /* x = x/b**n.used */
103 mp_clamp(x);
104 mp_rshd (x, n->used);
105
106 /* if x >= n then x = x - n */
107 if (mp_cmp_mag (x, n) != MP_LT) {
108 return s_mp_sub (x, n, x);
109 }
110
111 return MP_OKAY;
112 }