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