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1 | /* -*-c-*- |
2 | * |
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3 | * $Id$ |
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4 | * |
5 | * Chinese Remainder Theorem computations (Gauss's algorithm) |
6 | * |
7 | * (c) 1999 Straylight/Edgeware |
8 | */ |
9 | |
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10 | /*----- Licensing notice --------------------------------------------------* |
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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. |
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18 | * |
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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. |
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23 | * |
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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 | |
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30 | /*----- Header files ------------------------------------------------------*/ |
31 | |
32 | #include "mp.h" |
33 | #include "mpcrt.h" |
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34 | #include "mpmul.h" |
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35 | #include "mpbarrett.h" |
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36 | |
37 | /*----- Main code ---------------------------------------------------------*/ |
38 | |
39 | /* --- @mpcrt_create@ --- * |
40 | * |
41 | * Arguments: @mpcrt *c@ = pointer to CRT context |
42 | * @mpcrt_mod *v@ = pointer to vector of moduli |
43 | * @size_t k@ = number of moduli |
44 | * @mp *n@ = product of all moduli (@MP_NEW@ if unknown) |
45 | * |
46 | * Returns: --- |
47 | * |
48 | * Use: Initializes a context for solving Chinese Remainder Theorem |
49 | * problems. The vector of moduli can be incomplete. Omitted |
50 | * items must be left as null pointers. Not all combinations of |
51 | * missing things can be coped with, even if there is |
52 | * technically enough information to cope. For example, if @n@ |
53 | * is unspecified, all the @m@ values must be present, even if |
54 | * there is one modulus with both @m@ and @n@ (from which the |
55 | * product of all moduli could clearly be calculated). |
56 | */ |
57 | |
58 | void mpcrt_create(mpcrt *c, mpcrt_mod *v, size_t k, mp *n) |
59 | { |
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60 | size_t i; |
61 | |
62 | /* --- Simple initialization things --- */ |
63 | |
64 | c->k = k; |
65 | c->v = v; |
66 | |
67 | /* --- Work out @n@ if I don't have it already --- */ |
68 | |
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69 | if (n != MP_NEW) |
70 | n = MP_COPY(n); |
71 | else { |
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72 | mpmul mm; |
73 | mpmul_init(&mm); |
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74 | for (i = 0; i < k; i++) |
75 | mpmul_add(&mm, v[i].m); |
76 | n = mpmul_done(&mm); |
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77 | } |
78 | |
79 | /* --- A quick hack if %$k = 2$% --- */ |
80 | |
81 | if (k == 2) { |
82 | |
83 | /* --- The %$n / n_i$% values are trivial in this case --- */ |
84 | |
85 | if (!v[0].n) |
86 | v[0].n = MP_COPY(v[1].m); |
87 | if (!v[1].n) |
88 | v[1].n = MP_COPY(v[0].m); |
89 | |
90 | /* --- Now sort out the inverses --- * |
91 | * |
92 | * @mp_gcd@ will ensure that the first argument is negative. |
93 | */ |
94 | |
95 | if (!v[0].ni && !v[1].ni) { |
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96 | mp *g = MP_NEW; |
97 | mp_gcd(&g, &v[0].ni, &v[1].ni, v[0].n, v[1].n); |
98 | assert(MP_EQ(g, MP_ONE)); |
99 | mp_drop(g); |
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100 | v[0].ni = mp_add(v[0].ni, v[0].ni, v[1].n); |
101 | } else { |
102 | int i, j; |
103 | mp *x; |
104 | |
105 | if (!v[0].ni) |
106 | i = 0, j = 1; |
107 | else |
108 | i = 1, j = 0; |
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109 | |
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110 | x = mp_mul(MP_NEW, v[j].n, v[j].ni); |
111 | x = mp_sub(x, x, MP_ONE); |
112 | mp_div(&x, 0, x, v[i].n); |
113 | v[i].ni = x; |
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114 | } |
115 | } |
116 | |
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117 | /* --- Set up the Barrett context --- */ |
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118 | |
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119 | mpbarrett_create(&c->mb, n); |
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120 | |
121 | /* --- Walk through filling in @n@, @ni@ and @nnir@ --- */ |
122 | |
123 | for (i = 0; i < k; i++) { |
124 | if (!v[i].n) |
125 | mp_div(&v[i].n, 0, n, v[i].m); |
126 | if (!v[i].ni) |
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127 | v[i].ni = mp_modinv(MP_NEW, v[i].n, v[i].m); |
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128 | if (!v[i].nni) |
129 | v[i].nni = mp_mul(MP_NEW, v[i].n, v[i].ni); |
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130 | } |
131 | |
132 | /* --- Done --- */ |
133 | |
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134 | mp_drop(n); |
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135 | } |
136 | |
137 | /* --- @mpcrt_destroy@ --- * |
138 | * |
139 | * Arguments: @mpcrt *c@ - pointer to CRT context |
140 | * |
141 | * Returns: --- |
142 | * |
143 | * Use: Destroys a CRT context, releasing all the resources it holds. |
144 | */ |
145 | |
146 | void mpcrt_destroy(mpcrt *c) |
147 | { |
148 | size_t i; |
149 | |
150 | for (i = 0; i < c->k; i++) { |
151 | if (c->v[i].m) mp_drop(c->v[i].m); |
152 | if (c->v[i].n) mp_drop(c->v[i].n); |
153 | if (c->v[i].ni) mp_drop(c->v[i].ni); |
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154 | if (c->v[i].nni) mp_drop(c->v[i].nni); |
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155 | } |
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156 | mpbarrett_destroy(&c->mb); |
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157 | } |
158 | |
159 | /* --- @mpcrt_solve@ --- * |
160 | * |
161 | * Arguments: @mpcrt *c@ = pointer to CRT context |
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162 | * @mp *d@ = fake destination |
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163 | * @mp **v@ = array of residues |
164 | * |
165 | * Returns: The unique solution modulo the product of the individual |
166 | * moduli, which leaves the given residues. |
167 | * |
168 | * Use: Constructs a result given its residue modulo an array of |
169 | * coprime integers. This can be used to improve performance of |
170 | * RSA encryption or Blum-Blum-Shub generation if the factors |
171 | * of the modulus are known, since results can be computed mod |
172 | * each of the individual factors and then combined at the end. |
173 | * This is rather faster than doing the full-scale modular |
174 | * exponentiation. |
175 | */ |
176 | |
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177 | mp *mpcrt_solve(mpcrt *c, mp *d, mp **v) |
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178 | { |
179 | mp *a = MP_ZERO; |
180 | mp *x = MP_NEW; |
181 | size_t i; |
182 | |
183 | for (i = 0; i < c->k; i++) { |
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184 | x = mp_mul(x, c->v[i].nni, v[i]); |
185 | x = mpbarrett_reduce(&c->mb, x, x); |
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186 | a = mp_add(a, a, x); |
187 | } |
188 | if (x) |
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189 | MP_DROP(x); |
190 | a = mpbarrett_reduce(&c->mb, a, a); |
191 | if (d != MP_NEW) |
192 | MP_DROP(d); |
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193 | return (a); |
194 | } |
195 | |
196 | /*----- Test rig ----------------------------------------------------------*/ |
197 | |
198 | #ifdef TEST_RIG |
199 | |
200 | static int verify(size_t n, dstr *v) |
201 | { |
202 | mpcrt_mod *m = xmalloc(n * sizeof(mpcrt_mod)); |
203 | mp **r = xmalloc(n * sizeof(mp *)); |
204 | mpcrt c; |
205 | mp *a, *b; |
206 | size_t i; |
207 | int ok = 1; |
208 | |
209 | for (i = 0; i < n; i++) { |
210 | r[i] = *(mp **)v[2 * i].buf; |
211 | m[i].m = *(mp **)v[2 * i + 1].buf; |
212 | m[i].n = 0; |
213 | m[i].ni = 0; |
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214 | m[i].nni = 0; |
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215 | } |
216 | a = *(mp **)v[2 * n].buf; |
217 | |
218 | mpcrt_create(&c, m, n, 0); |
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219 | b = mpcrt_solve(&c, MP_NEW, r); |
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220 | |
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221 | if (!MP_EQ(a, b)) { |
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222 | fputs("\n*** failed\n", stderr); |
223 | fputs("n = ", stderr); |
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224 | mp_writefile(c.mb.m, stderr, 10); |
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225 | for (i = 0; i < n; i++) { |
226 | fprintf(stderr, "\nr[%u] = ", i); |
227 | mp_writefile(r[i], stderr, 10); |
228 | fprintf(stderr, "\nm[%u] = ", i); |
229 | mp_writefile(m[i].m, stderr, 10); |
230 | fprintf(stderr, "\nN[%u] = ", i); |
231 | mp_writefile(m[i].n, stderr, 10); |
232 | fprintf(stderr, "\nM[%u] = ", i); |
233 | mp_writefile(m[i].ni, stderr, 10); |
234 | } |
235 | fputs("\nresult = ", stderr); |
236 | mp_writefile(b, stderr, 10); |
237 | fputs("\nexpect = ", stderr); |
238 | mp_writefile(a, stderr, 10); |
239 | fputc('\n', stderr); |
240 | ok = 0; |
241 | } |
242 | |
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243 | for (i = 0; i < n; i++) |
244 | mp_drop(r[i]); |
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245 | mp_drop(a); |
246 | mp_drop(b); |
247 | mpcrt_destroy(&c); |
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248 | xfree(m); |
249 | xfree(r); |
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250 | assert(mparena_count(MPARENA_GLOBAL) == 0); |
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251 | return (ok); |
252 | } |
253 | |
254 | static int crt1(dstr *v) { return verify(1, v); } |
255 | static int crt2(dstr *v) { return verify(2, v); } |
256 | static int crt3(dstr *v) { return verify(3, v); } |
257 | static int crt4(dstr *v) { return verify(4, v); } |
258 | static int crt5(dstr *v) { return verify(5, v); } |
259 | |
260 | static test_chunk tests[] = { |
261 | { "crt-1", crt1, { &type_mp, &type_mp, |
262 | &type_mp, 0 } }, |
263 | { "crt-2", crt2, { &type_mp, &type_mp, |
264 | &type_mp, &type_mp, |
265 | &type_mp, 0 } }, |
266 | { "crt-3", crt3, { &type_mp, &type_mp, |
267 | &type_mp, &type_mp, |
268 | &type_mp, &type_mp, |
269 | &type_mp, 0 } }, |
270 | { "crt-4", crt4, { &type_mp, &type_mp, |
271 | &type_mp, &type_mp, |
272 | &type_mp, &type_mp, |
273 | &type_mp, &type_mp, |
274 | &type_mp, 0 } }, |
275 | { "crt-5", crt5, { &type_mp, &type_mp, |
276 | &type_mp, &type_mp, |
277 | &type_mp, &type_mp, |
278 | &type_mp, &type_mp, |
279 | &type_mp, &type_mp, |
280 | &type_mp, 0 } }, |
281 | { 0, 0, { 0 } } |
282 | }; |
283 | |
284 | int main(int argc, char *argv[]) |
285 | { |
286 | sub_init(); |
287 | test_run(argc, argv, tests, SRCDIR "/tests/mpcrt"); |
288 | return (0); |
289 | } |
290 | |
291 | #endif |
292 | |
293 | /*----- That's all, folks -------------------------------------------------*/ |