5ee4c893 |
1 | /* -*-c-*- |
2 | * |
3 | * $Id: mpcrt.c,v 1.1 1999/11/22 20:50:57 mdw Exp $ |
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 $ |
33 | * Revision 1.1 1999/11/22 20:50:57 mdw |
34 | * Add support for solving Chinese Remainder Theorem problems. |
35 | * |
36 | */ |
37 | |
38 | /*----- Header files ------------------------------------------------------*/ |
39 | |
40 | #include "mp.h" |
41 | #include "mpcrt.h" |
42 | #include "mpmont.h" |
43 | |
44 | /*----- Main code ---------------------------------------------------------*/ |
45 | |
46 | /* --- @mpcrt_create@ --- * |
47 | * |
48 | * Arguments: @mpcrt *c@ = pointer to CRT context |
49 | * @mpcrt_mod *v@ = pointer to vector of moduli |
50 | * @size_t k@ = number of moduli |
51 | * @mp *n@ = product of all moduli (@MP_NEW@ if unknown) |
52 | * |
53 | * Returns: --- |
54 | * |
55 | * Use: Initializes a context for solving Chinese Remainder Theorem |
56 | * problems. The vector of moduli can be incomplete. Omitted |
57 | * items must be left as null pointers. Not all combinations of |
58 | * missing things can be coped with, even if there is |
59 | * technically enough information to cope. For example, if @n@ |
60 | * is unspecified, all the @m@ values must be present, even if |
61 | * there is one modulus with both @m@ and @n@ (from which the |
62 | * product of all moduli could clearly be calculated). |
63 | */ |
64 | |
65 | void mpcrt_create(mpcrt *c, mpcrt_mod *v, size_t k, mp *n) |
66 | { |
67 | mp *x = MP_NEW, *y = MP_NEW; |
68 | size_t i; |
69 | |
70 | /* --- Simple initialization things --- */ |
71 | |
72 | c->k = k; |
73 | c->v = v; |
74 | |
75 | /* --- Work out @n@ if I don't have it already --- */ |
76 | |
77 | if (n == MP_NEW) { |
78 | n = MP_COPY(v[0].m); |
79 | for (i = 1; i < k; i++) { |
80 | mp *d = mp_mul(x, n, v[i].m); |
81 | x = n; |
82 | n = d; |
83 | } |
84 | } |
85 | |
86 | /* --- Set up the Montgomery context --- */ |
87 | |
88 | mpmont_create(&c->mm, n); |
89 | |
90 | /* --- Walk through filling in @n@, @ni@ and @nnir@ --- */ |
91 | |
92 | for (i = 0; i < k; i++) { |
93 | if (!v[i].n) |
94 | mp_div(&v[i].n, 0, n, v[i].m); |
95 | if (!v[i].ni) |
96 | mp_gcd(0, &v[i].ni, 0, v[i].n, v[i].m); |
97 | if (!v[i].nnir) { |
98 | x = mpmont_mul(&c->mm, x, v[i].n, c->mm.r2); |
99 | y = mpmont_mul(&c->mm, y, v[i].ni, c->mm.r2); |
100 | v[i].nnir = mpmont_mul(&c->mm, MP_NEW, x, y); |
101 | } |
102 | } |
103 | |
104 | /* --- Done --- */ |
105 | |
106 | if (x) |
107 | mp_drop(x); |
108 | if (y) |
109 | mp_drop(y); |
110 | } |
111 | |
112 | /* --- @mpcrt_destroy@ --- * |
113 | * |
114 | * Arguments: @mpcrt *c@ - pointer to CRT context |
115 | * |
116 | * Returns: --- |
117 | * |
118 | * Use: Destroys a CRT context, releasing all the resources it holds. |
119 | */ |
120 | |
121 | void mpcrt_destroy(mpcrt *c) |
122 | { |
123 | size_t i; |
124 | |
125 | for (i = 0; i < c->k; i++) { |
126 | if (c->v[i].m) mp_drop(c->v[i].m); |
127 | if (c->v[i].n) mp_drop(c->v[i].n); |
128 | if (c->v[i].ni) mp_drop(c->v[i].ni); |
129 | if (c->v[i].nnir) mp_drop(c->v[i].nnir); |
130 | } |
131 | mpmont_destroy(&c->mm); |
132 | } |
133 | |
134 | /* --- @mpcrt_solve@ --- * |
135 | * |
136 | * Arguments: @mpcrt *c@ = pointer to CRT context |
137 | * @mp **v@ = array of residues |
138 | * |
139 | * Returns: The unique solution modulo the product of the individual |
140 | * moduli, which leaves the given residues. |
141 | * |
142 | * Use: Constructs a result given its residue modulo an array of |
143 | * coprime integers. This can be used to improve performance of |
144 | * RSA encryption or Blum-Blum-Shub generation if the factors |
145 | * of the modulus are known, since results can be computed mod |
146 | * each of the individual factors and then combined at the end. |
147 | * This is rather faster than doing the full-scale modular |
148 | * exponentiation. |
149 | */ |
150 | |
151 | mp *mpcrt_solve(mpcrt *c, mp **v) |
152 | { |
153 | mp *a = MP_ZERO; |
154 | mp *x = MP_NEW; |
155 | size_t i; |
156 | |
157 | for (i = 0; i < c->k; i++) { |
158 | x = mpmont_mul(&c->mm, x, c->v[i].nnir, v[i]); |
159 | a = mp_add(a, a, x); |
160 | } |
161 | if (x) |
162 | mp_drop(x); |
163 | if (MP_CMP(a, >=, c->mm.m)) |
164 | mp_div(0, &a, a, c->mm.m); |
165 | return (a); |
166 | } |
167 | |
168 | /*----- Test rig ----------------------------------------------------------*/ |
169 | |
170 | #ifdef TEST_RIG |
171 | |
172 | static int verify(size_t n, dstr *v) |
173 | { |
174 | mpcrt_mod *m = xmalloc(n * sizeof(mpcrt_mod)); |
175 | mp **r = xmalloc(n * sizeof(mp *)); |
176 | mpcrt c; |
177 | mp *a, *b; |
178 | size_t i; |
179 | int ok = 1; |
180 | |
181 | for (i = 0; i < n; i++) { |
182 | r[i] = *(mp **)v[2 * i].buf; |
183 | m[i].m = *(mp **)v[2 * i + 1].buf; |
184 | m[i].n = 0; |
185 | m[i].ni = 0; |
186 | m[i].nnir = 0; |
187 | } |
188 | a = *(mp **)v[2 * n].buf; |
189 | |
190 | mpcrt_create(&c, m, n, 0); |
191 | b = mpcrt_solve(&c, r); |
192 | |
193 | if (MP_CMP(a, !=, b)) { |
194 | fputs("\n*** failed\n", stderr); |
195 | fputs("n = ", stderr); |
196 | mp_writefile(c.mm.m, stderr, 10); |
197 | for (i = 0; i < n; i++) { |
198 | fprintf(stderr, "\nr[%u] = ", i); |
199 | mp_writefile(r[i], stderr, 10); |
200 | fprintf(stderr, "\nm[%u] = ", i); |
201 | mp_writefile(m[i].m, stderr, 10); |
202 | fprintf(stderr, "\nN[%u] = ", i); |
203 | mp_writefile(m[i].n, stderr, 10); |
204 | fprintf(stderr, "\nM[%u] = ", i); |
205 | mp_writefile(m[i].ni, stderr, 10); |
206 | } |
207 | fputs("\nresult = ", stderr); |
208 | mp_writefile(b, stderr, 10); |
209 | fputs("\nexpect = ", stderr); |
210 | mp_writefile(a, stderr, 10); |
211 | fputc('\n', stderr); |
212 | ok = 0; |
213 | } |
214 | |
215 | mp_drop(a); |
216 | mp_drop(b); |
217 | mpcrt_destroy(&c); |
218 | free(m); |
219 | free(r); |
220 | return (ok); |
221 | } |
222 | |
223 | static int crt1(dstr *v) { return verify(1, v); } |
224 | static int crt2(dstr *v) { return verify(2, v); } |
225 | static int crt3(dstr *v) { return verify(3, v); } |
226 | static int crt4(dstr *v) { return verify(4, v); } |
227 | static int crt5(dstr *v) { return verify(5, v); } |
228 | |
229 | static test_chunk tests[] = { |
230 | { "crt-1", crt1, { &type_mp, &type_mp, |
231 | &type_mp, 0 } }, |
232 | { "crt-2", crt2, { &type_mp, &type_mp, |
233 | &type_mp, &type_mp, |
234 | &type_mp, 0 } }, |
235 | { "crt-3", crt3, { &type_mp, &type_mp, |
236 | &type_mp, &type_mp, |
237 | &type_mp, &type_mp, |
238 | &type_mp, 0 } }, |
239 | { "crt-4", crt4, { &type_mp, &type_mp, |
240 | &type_mp, &type_mp, |
241 | &type_mp, &type_mp, |
242 | &type_mp, &type_mp, |
243 | &type_mp, 0 } }, |
244 | { "crt-5", crt5, { &type_mp, &type_mp, |
245 | &type_mp, &type_mp, |
246 | &type_mp, &type_mp, |
247 | &type_mp, &type_mp, |
248 | &type_mp, &type_mp, |
249 | &type_mp, 0 } }, |
250 | { 0, 0, { 0 } } |
251 | }; |
252 | |
253 | int main(int argc, char *argv[]) |
254 | { |
255 | sub_init(); |
256 | test_run(argc, argv, tests, SRCDIR "/tests/mpcrt"); |
257 | return (0); |
258 | } |
259 | |
260 | #endif |
261 | |
262 | /*----- That's all, folks -------------------------------------------------*/ |