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1 | /* -*-c-*- |
2 | * |
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3 | * $Id: mpcrt.c,v 1.4 2001/04/19 18:25:38 mdw Exp $ |
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4 | * |
5 | * Chinese Remainder Theorem computations (Gauss's algorithm) |
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: mpcrt.c,v $ |
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33 | * Revision 1.4 2001/04/19 18:25:38 mdw |
34 | * Use mpmul for the multiplication. |
35 | * |
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36 | * Revision 1.3 2000/10/08 12:11:22 mdw |
37 | * Use @MP_EQ@ instead of @MP_CMP@. |
38 | * |
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39 | * Revision 1.2 1999/12/10 23:22:32 mdw |
40 | * Interface changes for suggested destinations. Use Barrett reduction. |
41 | * |
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42 | * Revision 1.1 1999/11/22 20:50:57 mdw |
43 | * Add support for solving Chinese Remainder Theorem problems. |
44 | * |
45 | */ |
46 | |
47 | /*----- Header files ------------------------------------------------------*/ |
48 | |
49 | #include "mp.h" |
50 | #include "mpcrt.h" |
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51 | #include "mpmul.h" |
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52 | #include "mpbarrett.h" |
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53 | |
54 | /*----- Main code ---------------------------------------------------------*/ |
55 | |
56 | /* --- @mpcrt_create@ --- * |
57 | * |
58 | * Arguments: @mpcrt *c@ = pointer to CRT context |
59 | * @mpcrt_mod *v@ = pointer to vector of moduli |
60 | * @size_t k@ = number of moduli |
61 | * @mp *n@ = product of all moduli (@MP_NEW@ if unknown) |
62 | * |
63 | * Returns: --- |
64 | * |
65 | * Use: Initializes a context for solving Chinese Remainder Theorem |
66 | * problems. The vector of moduli can be incomplete. Omitted |
67 | * items must be left as null pointers. Not all combinations of |
68 | * missing things can be coped with, even if there is |
69 | * technically enough information to cope. For example, if @n@ |
70 | * is unspecified, all the @m@ values must be present, even if |
71 | * there is one modulus with both @m@ and @n@ (from which the |
72 | * product of all moduli could clearly be calculated). |
73 | */ |
74 | |
75 | void mpcrt_create(mpcrt *c, mpcrt_mod *v, size_t k, mp *n) |
76 | { |
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77 | size_t i; |
78 | |
79 | /* --- Simple initialization things --- */ |
80 | |
81 | c->k = k; |
82 | c->v = v; |
83 | |
84 | /* --- Work out @n@ if I don't have it already --- */ |
85 | |
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86 | if (n != MP_NEW) |
87 | n = MP_COPY(n); |
88 | else { |
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89 | mpmul mm; |
90 | mpmul_init(&mm); |
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91 | n = MP_COPY(v[0].m); |
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92 | for (i = 0; i < k; i++) |
93 | mpmul_add(&mm, v[i].m); |
94 | n = mpmul_done(&mm); |
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95 | } |
96 | |
97 | /* --- A quick hack if %$k = 2$% --- */ |
98 | |
99 | if (k == 2) { |
100 | |
101 | /* --- The %$n / n_i$% values are trivial in this case --- */ |
102 | |
103 | if (!v[0].n) |
104 | v[0].n = MP_COPY(v[1].m); |
105 | if (!v[1].n) |
106 | v[1].n = MP_COPY(v[0].m); |
107 | |
108 | /* --- Now sort out the inverses --- * |
109 | * |
110 | * @mp_gcd@ will ensure that the first argument is negative. |
111 | */ |
112 | |
113 | if (!v[0].ni && !v[1].ni) { |
114 | mp_gcd(0, &v[0].ni, &v[1].ni, v[0].n, v[1].n); |
115 | v[0].ni = mp_add(v[0].ni, v[0].ni, v[1].n); |
116 | } else { |
117 | int i, j; |
118 | mp *x; |
119 | |
120 | if (!v[0].ni) |
121 | i = 0, j = 1; |
122 | else |
123 | i = 1, j = 0; |
124 | |
125 | x = mp_mul(MP_NEW, v[j].n, v[j].ni); |
126 | x = mp_sub(x, x, MP_ONE); |
127 | mp_div(&x, 0, x, v[i].n); |
128 | v[i].ni = x; |
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129 | } |
130 | } |
131 | |
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132 | /* --- Set up the Barrett context --- */ |
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133 | |
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134 | mpbarrett_create(&c->mb, n); |
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135 | |
136 | /* --- Walk through filling in @n@, @ni@ and @nnir@ --- */ |
137 | |
138 | for (i = 0; i < k; i++) { |
139 | if (!v[i].n) |
140 | mp_div(&v[i].n, 0, n, v[i].m); |
141 | if (!v[i].ni) |
142 | mp_gcd(0, &v[i].ni, 0, v[i].n, v[i].m); |
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143 | if (!v[i].nni) |
144 | v[i].nni = mp_mul(MP_NEW, v[i].n, v[i].ni); |
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145 | } |
146 | |
147 | /* --- Done --- */ |
148 | |
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149 | mp_drop(n); |
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150 | } |
151 | |
152 | /* --- @mpcrt_destroy@ --- * |
153 | * |
154 | * Arguments: @mpcrt *c@ - pointer to CRT context |
155 | * |
156 | * Returns: --- |
157 | * |
158 | * Use: Destroys a CRT context, releasing all the resources it holds. |
159 | */ |
160 | |
161 | void mpcrt_destroy(mpcrt *c) |
162 | { |
163 | size_t i; |
164 | |
165 | for (i = 0; i < c->k; i++) { |
166 | if (c->v[i].m) mp_drop(c->v[i].m); |
167 | if (c->v[i].n) mp_drop(c->v[i].n); |
168 | if (c->v[i].ni) mp_drop(c->v[i].ni); |
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169 | if (c->v[i].nni) mp_drop(c->v[i].nni); |
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170 | } |
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171 | mpbarrett_destroy(&c->mb); |
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172 | } |
173 | |
174 | /* --- @mpcrt_solve@ --- * |
175 | * |
176 | * Arguments: @mpcrt *c@ = pointer to CRT context |
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177 | * @mp *d@ = fake destination |
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178 | * @mp **v@ = array of residues |
179 | * |
180 | * Returns: The unique solution modulo the product of the individual |
181 | * moduli, which leaves the given residues. |
182 | * |
183 | * Use: Constructs a result given its residue modulo an array of |
184 | * coprime integers. This can be used to improve performance of |
185 | * RSA encryption or Blum-Blum-Shub generation if the factors |
186 | * of the modulus are known, since results can be computed mod |
187 | * each of the individual factors and then combined at the end. |
188 | * This is rather faster than doing the full-scale modular |
189 | * exponentiation. |
190 | */ |
191 | |
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192 | mp *mpcrt_solve(mpcrt *c, mp *d, mp **v) |
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193 | { |
194 | mp *a = MP_ZERO; |
195 | mp *x = MP_NEW; |
196 | size_t i; |
197 | |
198 | for (i = 0; i < c->k; i++) { |
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199 | x = mp_mul(x, c->v[i].nni, v[i]); |
200 | x = mpbarrett_reduce(&c->mb, x, x); |
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201 | a = mp_add(a, a, x); |
202 | } |
203 | if (x) |
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204 | MP_DROP(x); |
205 | a = mpbarrett_reduce(&c->mb, a, a); |
206 | if (d != MP_NEW) |
207 | MP_DROP(d); |
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208 | return (a); |
209 | } |
210 | |
211 | /*----- Test rig ----------------------------------------------------------*/ |
212 | |
213 | #ifdef TEST_RIG |
214 | |
215 | static int verify(size_t n, dstr *v) |
216 | { |
217 | mpcrt_mod *m = xmalloc(n * sizeof(mpcrt_mod)); |
218 | mp **r = xmalloc(n * sizeof(mp *)); |
219 | mpcrt c; |
220 | mp *a, *b; |
221 | size_t i; |
222 | int ok = 1; |
223 | |
224 | for (i = 0; i < n; i++) { |
225 | r[i] = *(mp **)v[2 * i].buf; |
226 | m[i].m = *(mp **)v[2 * i + 1].buf; |
227 | m[i].n = 0; |
228 | m[i].ni = 0; |
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229 | m[i].nni = 0; |
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230 | } |
231 | a = *(mp **)v[2 * n].buf; |
232 | |
233 | mpcrt_create(&c, m, n, 0); |
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234 | b = mpcrt_solve(&c, MP_NEW, r); |
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235 | |
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236 | if (!MP_EQ(a, b)) { |
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237 | fputs("\n*** failed\n", stderr); |
238 | fputs("n = ", stderr); |
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239 | mp_writefile(c.mb.m, stderr, 10); |
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240 | for (i = 0; i < n; i++) { |
241 | fprintf(stderr, "\nr[%u] = ", i); |
242 | mp_writefile(r[i], stderr, 10); |
243 | fprintf(stderr, "\nm[%u] = ", i); |
244 | mp_writefile(m[i].m, stderr, 10); |
245 | fprintf(stderr, "\nN[%u] = ", i); |
246 | mp_writefile(m[i].n, stderr, 10); |
247 | fprintf(stderr, "\nM[%u] = ", i); |
248 | mp_writefile(m[i].ni, stderr, 10); |
249 | } |
250 | fputs("\nresult = ", stderr); |
251 | mp_writefile(b, stderr, 10); |
252 | fputs("\nexpect = ", stderr); |
253 | mp_writefile(a, stderr, 10); |
254 | fputc('\n', stderr); |
255 | ok = 0; |
256 | } |
257 | |
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258 | for (i = 0; i < n; i++) |
259 | mp_drop(r[i]); |
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260 | mp_drop(a); |
261 | mp_drop(b); |
262 | mpcrt_destroy(&c); |
263 | free(m); |
264 | free(r); |
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265 | assert(mparena_count(MPARENA_GLOBAL) == 0); |
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266 | return (ok); |
267 | } |
268 | |
269 | static int crt1(dstr *v) { return verify(1, v); } |
270 | static int crt2(dstr *v) { return verify(2, v); } |
271 | static int crt3(dstr *v) { return verify(3, v); } |
272 | static int crt4(dstr *v) { return verify(4, v); } |
273 | static int crt5(dstr *v) { return verify(5, v); } |
274 | |
275 | static test_chunk tests[] = { |
276 | { "crt-1", crt1, { &type_mp, &type_mp, |
277 | &type_mp, 0 } }, |
278 | { "crt-2", crt2, { &type_mp, &type_mp, |
279 | &type_mp, &type_mp, |
280 | &type_mp, 0 } }, |
281 | { "crt-3", crt3, { &type_mp, &type_mp, |
282 | &type_mp, &type_mp, |
283 | &type_mp, &type_mp, |
284 | &type_mp, 0 } }, |
285 | { "crt-4", crt4, { &type_mp, &type_mp, |
286 | &type_mp, &type_mp, |
287 | &type_mp, &type_mp, |
288 | &type_mp, &type_mp, |
289 | &type_mp, 0 } }, |
290 | { "crt-5", crt5, { &type_mp, &type_mp, |
291 | &type_mp, &type_mp, |
292 | &type_mp, &type_mp, |
293 | &type_mp, &type_mp, |
294 | &type_mp, &type_mp, |
295 | &type_mp, 0 } }, |
296 | { 0, 0, { 0 } } |
297 | }; |
298 | |
299 | int main(int argc, char *argv[]) |
300 | { |
301 | sub_init(); |
302 | test_run(argc, argv, tests, SRCDIR "/tests/mpcrt"); |
303 | return (0); |
304 | } |
305 | |
306 | #endif |
307 | |
308 | /*----- That's all, folks -------------------------------------------------*/ |