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author Matt Johnston <matt@ucc.asn.au>
date Mon, 31 May 2004 18:23:46 +0000
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-1:000000000000 1:22d5cf7d4b1a
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 *
19 * This is an optimized implementation of mp_montgomery_reduce
20 * which uses the comba method to quickly calculate the columns of the
21 * reduction.
22 *
23 * Based on Algorithm 14.32 on pp.601 of HAC.
24 */
25 int
26 fast_mp_montgomery_reduce (mp_int * x, mp_int * n, mp_digit rho)
27 {
28 int ix, res, olduse;
29 mp_word W[MP_WARRAY];
30
31 /* get old used count */
32 olduse = x->used;
33
34 /* grow a as required */
35 if (x->alloc < n->used + 1) {
36 if ((res = mp_grow (x, n->used + 1)) != MP_OKAY) {
37 return res;
38 }
39 }
40
41 /* first we have to get the digits of the input into
42 * an array of double precision words W[...]
43 */
44 {
45 register mp_word *_W;
46 register mp_digit *tmpx;
47
48 /* alias for the W[] array */
49 _W = W;
50
51 /* alias for the digits of x*/
52 tmpx = x->dp;
53
54 /* copy the digits of a into W[0..a->used-1] */
55 for (ix = 0; ix < x->used; ix++) {
56 *_W++ = *tmpx++;
57 }
58
59 /* zero the high words of W[a->used..m->used*2] */
60 for (; ix < n->used * 2 + 1; ix++) {
61 *_W++ = 0;
62 }
63 }
64
65 /* now we proceed to zero successive digits
66 * from the least significant upwards
67 */
68 for (ix = 0; ix < n->used; ix++) {
69 /* mu = ai * m' mod b
70 *
71 * We avoid a double precision multiplication (which isn't required)
72 * by casting the value down to a mp_digit. Note this requires
73 * that W[ix-1] have the carry cleared (see after the inner loop)
74 */
75 register mp_digit mu;
76 mu = (mp_digit) (((W[ix] & MP_MASK) * rho) & MP_MASK);
77
78 /* a = a + mu * m * b**i
79 *
80 * This is computed in place and on the fly. The multiplication
81 * by b**i is handled by offseting which columns the results
82 * are added to.
83 *
84 * Note the comba method normally doesn't handle carries in the
85 * inner loop In this case we fix the carry from the previous
86 * column since the Montgomery reduction requires digits of the
87 * result (so far) [see above] to work. This is
88 * handled by fixing up one carry after the inner loop. The
89 * carry fixups are done in order so after these loops the
90 * first m->used words of W[] have the carries fixed
91 */
92 {
93 register int iy;
94 register mp_digit *tmpn;
95 register mp_word *_W;
96
97 /* alias for the digits of the modulus */
98 tmpn = n->dp;
99
100 /* Alias for the columns set by an offset of ix */
101 _W = W + ix;
102
103 /* inner loop */
104 for (iy = 0; iy < n->used; iy++) {
105 *_W++ += ((mp_word)mu) * ((mp_word)*tmpn++);
106 }
107 }
108
109 /* now fix carry for next digit, W[ix+1] */
110 W[ix + 1] += W[ix] >> ((mp_word) DIGIT_BIT);
111 }
112
113 /* now we have to propagate the carries and
114 * shift the words downward [all those least
115 * significant digits we zeroed].
116 */
117 {
118 register mp_digit *tmpx;
119 register mp_word *_W, *_W1;
120
121 /* nox fix rest of carries */
122
123 /* alias for current word */
124 _W1 = W + ix;
125
126 /* alias for next word, where the carry goes */
127 _W = W + ++ix;
128
129 for (; ix <= n->used * 2 + 1; ix++) {
130 *_W++ += *_W1++ >> ((mp_word) DIGIT_BIT);
131 }
132
133 /* copy out, A = A/b**n
134 *
135 * The result is A/b**n but instead of converting from an
136 * array of mp_word to mp_digit than calling mp_rshd
137 * we just copy them in the right order
138 */
139
140 /* alias for destination word */
141 tmpx = x->dp;
142
143 /* alias for shifted double precision result */
144 _W = W + n->used;
145
146 for (ix = 0; ix < n->used + 1; ix++) {
147 *tmpx++ = (mp_digit)(*_W++ & ((mp_word) MP_MASK));
148 }
149
150 /* zero oldused digits, if the input a was larger than
151 * m->used+1 we'll have to clear the digits
152 */
153 for (; ix < olduse; ix++) {
154 *tmpx++ = 0;
155 }
156 }
157
158 /* set the max used and clamp */
159 x->used = n->used + 1;
160 mp_clamp (x);
161
162 /* if A >= m then A = A - m */
163 if (mp_cmp_mag (x, n) != MP_LT) {
164 return s_mp_sub (x, n, x);
165 }
166 return MP_OKAY;
167 }