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1 | /* -*-c-*- |
2 | * |
0a5d0bc7 |
3 | * $Id: mpbarrett.c,v 1.3 1999/12/12 15:08:52 mdw Exp $ |
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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 | |
63 | void 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; |
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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 | |
93 | void 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 | |
112 | mp *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 | } |
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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); |
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150 | mpx_umul(r->v, r->vl, q->v + k + 1, q->vl, mb->m->v, mb->m->vl); |
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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 | |
180 | mp *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 | |
221 | static 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 | |
251 | static 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 | |
286 | static 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 | |
292 | int 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 -------------------------------------------------*/ |