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Moved the Karatsuba macros into a separate file for better sharing.
[u/mdw/catacomb] / mpbarrett.c
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21a7c4b1 1/* -*-c-*-
2 *
0a5d0bc7 3 * $Id: mpbarrett.c,v 1.3 1999/12/12 15:08:52 mdw Exp $
21a7c4b1 4 *
5 * Barrett modular reduction
6 *
7 * (c) 1999 Straylight/Edgeware
8 */
9
10/*----- Licensing notice --------------------------------------------------*
11 *
12 * This file is part of Catacomb.
13 *
14 * Catacomb is free software; you can redistribute it and/or modify
15 * it under the terms of the GNU Library General Public License as
16 * published by the Free Software Foundation; either version 2 of the
17 * License, or (at your option) any later version.
18 *
19 * Catacomb is distributed in the hope that it will be useful,
20 * but WITHOUT ANY WARRANTY; without even the implied warranty of
21 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
22 * GNU Library General Public License for more details.
23 *
24 * You should have received a copy of the GNU Library General Public
25 * License along with Catacomb; if not, write to the Free
26 * Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
27 * MA 02111-1307, USA.
28 */
29
30/*----- Revision history --------------------------------------------------*
31 *
32 * $Log: mpbarrett.c,v $
0a5d0bc7 33 * Revision 1.3 1999/12/12 15:08:52 mdw
34 * Don't bother shifting %$q$% in @mpbarrett_reduce@, just skip the least
35 * significant digits.
36 *
ed6d1bd2 37 * Revision 1.2 1999/12/11 01:50:56 mdw
38 * Improve initialization slightly.
39 *
21a7c4b1 40 * Revision 1.1 1999/12/10 23:21:59 mdw
41 * Barrett reduction support: works with even moduli.
42 *
43 */
44
45/*----- Header files ------------------------------------------------------*/
46
47#include "mp.h"
48#include "mpbarrett.h"
49
50/*----- Main code ---------------------------------------------------------*/
51
52/* --- @mpbarrett_create@ --- *
53 *
54 * Arguments: @mpbarrett *mb@ = pointer to Barrett reduction context
55 * @mp *m@ = modulus to work to
56 *
57 *
58 * Returns: ---
59 *
60 * Use: Initializes a Barrett reduction context ready for use.
61 */
62
63void mpbarrett_create(mpbarrett *mb, mp *m)
64{
65 mp *b;
66
67 /* --- Validate the arguments --- */
68
69 assert(((void)"Barrett modulus must be positive", (m->f & MP_NEG) == 0));
70
71 /* --- Compute %$\mu$% --- */
72
73 mp_shrink(m);
74 mb->k = MP_LEN(m);
75 mb->m = MP_COPY(m);
ed6d1bd2 76 b = mp_create(2 * mb->k + 1);
77 MPX_ZERO(b->v, b->vl - 1);
78 b->vl[-1] = 1;
21a7c4b1 79 mp_div(&b, 0, b, m);
80 mb->mu = b;
81}
82
83/* --- @mpbarrett_destroy@ --- *
84 *
85 * Arguments: @mpbarrett *mb@ = pointer to Barrett reduction context
86 *
87 * Returns: ---
88 *
89 * Use: Destroys a Barrett reduction context releasing any resources
90 * claimed.
91 */
92
93void mpbarrett_destroy(mpbarrett *mb)
94{
95 mp_drop(mb->m);
96 mp_drop(mb->mu);
97}
98
99/* --- @mpbarrett_reduce@ --- *
100 *
101 * Arguments: @mpbarrett *mb@ = pointer to Barrett reduction context
102 * @mp *d@ = destination for result
103 * @mp *m@ = number to reduce
104 *
105 * Returns: The residue of @m@ modulo the number in the reduction
106 * context.
107 *
108 * Use: Performs an efficient modular reduction. The argument is
109 * assumed to be positive.
110 */
111
112mp *mpbarrett_reduce(mpbarrett *mb, mp *d, mp *m)
113{
114 mp *q;
115 size_t k = mb->k;
116
117 /* --- Special case if @m@ is too small --- */
118
119 if (MP_LEN(m) < k) {
120 m = MP_COPY(m);
121 MP_DROP(d);
122 return (m);
123 }
124
125 /* --- First stage --- */
126
127 {
128 mp qq;
129 mp_build(&qq, m->v + (k - 1), m->vl);
130 q = mp_mul(MP_NEW, &qq, mb->mu);
0a5d0bc7 131 if (MP_LEN(q) <= k) {
132 m = MP_COPY(m);
133 MP_DROP(d);
134 return (m);
135 }
21a7c4b1 136 }
137
138 /* --- Second stage --- */
139
140 {
141 mp *r;
142 mpw *mvl;
143
144 MP_COPY(m);
145 if (MP_LEN(m) <= k + 1)
146 mvl = m->vl;
147 else
148 mvl = m->v + k + 1;
149 r = mp_create(k + 1);
0a5d0bc7 150 mpx_umul(r->v, r->vl, q->v + k + 1, q->vl, mb->m->v, mb->m->vl);
21a7c4b1 151 r->f = (q->f | mb->m->f) & MP_BURN;
152 MP_MODIFY(d, k + 1);
153 mpx_usub(d->v, d->vl, m->v, mvl, r->v, r->vl);
154 d->f = (m->f | r->f) & MP_BURN;
155 MP_DROP(r);
156 MP_DROP(q);
157 MP_DROP(m);
158 }
159
160 /* --- Final stage --- */
161
162 MP_SHRINK(d);
163 while (MPX_UCMP(d->v, d->vl, >=, mb->m->v, mb->m->vl))
164 mpx_usub(d->v, d->vl, d->v, d->vl, mb->m->v, mb->m->vl);
165
166 MP_SHRINK(d);
167 return (d);
168}
169
170/* --- @mpbarrett_exp@ --- *
171 *
172 * Arguments: @mpbarrett *mb@ = pointer to Barrett reduction context
173 * @mp *d@ = fake destination
174 * @mp *a@ = base
175 * @mp *e@ = exponent
176 *
177 * Returns: Result, %$a^e \bmod m$%.
178 */
179
180mp *mpbarrett_exp(mpbarrett *mb, mp *d, mp *a, mp *e)
181{
182 mpscan sc;
183 mp *x = MP_ONE;
184 mp *spare = MP_NEW;
185
186 a = MP_COPY(a);
187 mp_scan(&sc, e);
188 if (MP_STEP(&sc)) {
189 size_t sq = 0;
190 for (;;) {
191 mp *dd;
192 if (MP_BIT(&sc)) {
193 while (sq) {
194 dd = mp_sqr(spare, a);
195 dd = mpbarrett_reduce(mb, dd, dd);
196 spare = a; a = dd;
197 sq--;
198 }
199 dd = mp_mul(spare, x, a);
200 dd = mpbarrett_reduce(mb, dd, dd);
201 spare = x; x = dd;
202 }
203 sq++;
204 if (!MP_STEP(&sc))
205 break;
206 }
207 }
208
209 MP_DROP(a);
210 if (spare != MP_NEW)
211 MP_DROP(spare);
212 if (d != MP_NEW)
213 MP_DROP(d);
214 return (x);
215}
216
217/*----- Test rig ----------------------------------------------------------*/
218
219#ifdef TEST_RIG
220
221static int vmod(dstr *v)
222{
223 mp *x = *(mp **)v[0].buf;
224 mp *n = *(mp **)v[1].buf;
225 mp *r = *(mp **)v[2].buf;
226 mp *s;
227 mpbarrett mb;
228 int ok = 1;
229
230 mpbarrett_create(&mb, n);
231 s = mpbarrett_reduce(&mb, MP_NEW, x);
232
233 if (MP_CMP(s, !=, r)) {
234 fputs("\n*** barrett reduction failure\n", stderr);
235 fputs("x = ", stderr); mp_writefile(x, stderr, 10); fputc('\n', stderr);
236 fputs("n = ", stderr); mp_writefile(n, stderr, 10); fputc('\n', stderr);
237 fputs("r = ", stderr); mp_writefile(r, stderr, 10); fputc('\n', stderr);
238 fputs("s = ", stderr); mp_writefile(s, stderr, 10); fputc('\n', stderr);
239 ok = 0;
240 }
241
242 mpbarrett_destroy(&mb);
243 mp_drop(x);
244 mp_drop(n);
245 mp_drop(r);
246 mp_drop(s);
247 assert(mparena_count(MPARENA_GLOBAL) == 0);
248 return (ok);
249}
250
251static int vexp(dstr *v)
252{
253 mp *m = *(mp **)v[0].buf;
254 mp *a = *(mp **)v[1].buf;
255 mp *b = *(mp **)v[2].buf;
256 mp *r = *(mp **)v[3].buf;
257 mp *mr;
258 int ok = 1;
259
260 mpbarrett mb;
261 mpbarrett_create(&mb, m);
262
263 mr = mpbarrett_exp(&mb, MP_NEW, a, b);
264
265 if (MP_CMP(mr, !=, r)) {
266 fputs("\n*** barrett modexp failed", stderr);
267 fputs("\n m = ", stderr); mp_writefile(m, stderr, 10);
268 fputs("\n a = ", stderr); mp_writefile(a, stderr, 10);
269 fputs("\n e = ", stderr); mp_writefile(b, stderr, 10);
270 fputs("\n r = ", stderr); mp_writefile(r, stderr, 10);
271 fputs("\nmr = ", stderr); mp_writefile(mr, stderr, 10);
272 fputc('\n', stderr);
273 ok = 0;
274 }
275
276 mp_drop(m);
277 mp_drop(a);
278 mp_drop(b);
279 mp_drop(r);
280 mp_drop(mr);
281 mpbarrett_destroy(&mb);
282 assert(mparena_count(MPARENA_GLOBAL) == 0);
283 return ok;
284}
285
286static test_chunk tests[] = {
287 { "mpbarrett-reduce", vmod, { &type_mp, &type_mp, &type_mp, 0 } },
288 { "mpbarrett-exp", vexp, { &type_mp, &type_mp, &type_mp, &type_mp, 0 } },
289 { 0, 0, { 0 } }
290};
291
292int main(int argc, char *argv[])
293{
294 sub_init();
295 test_run(argc, argv, tests, SRCDIR "/tests/mpbarrett");
296 return (0);
297}
298
299#endif
300
301/*----- That's all, folks -------------------------------------------------*/
Catacomb cryptographic library (downstream of http://git.distorted.org.uk/~mdw/catacomb/)