4cc02d06 |
1 | /* -*-c-*- |
2 | * |
3 | * $Id: mpmont-mexp.c,v 1.1 1999/11/19 13:19:29 mdw Exp $ |
4 | * |
5 | * Multiplle simultaneous exponentiations |
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: mpmont-mexp.c,v $ |
33 | * Revision 1.1 1999/11/19 13:19:29 mdw |
34 | * Simultaneous exponentiation support. |
35 | * |
36 | */ |
37 | |
38 | /*----- Header files ------------------------------------------------------*/ |
39 | |
40 | #include "mp.h" |
41 | #include "mpmont.h" |
42 | |
43 | /*----- Main code ---------------------------------------------------------*/ |
44 | |
45 | /* --- @mpmont_mexpr@ --- * |
46 | * |
47 | * Arguments: @mpmont *mm@ = pointer to Montgomery reduction context |
48 | * @mpmont_factor *f@ = pointer to array of factors |
49 | * @size_t n@ = number of factors supplied |
50 | * |
51 | * Returns: If the bases are %$g_0, g_1, \ldots, g_{n-1}$% and the |
52 | * exponents are %$e_0, e_1, \ldots, e_{n-1}$% then the result |
53 | * is: |
54 | * |
55 | * %$g_0^{e_0} g_1^{e_1} \ldots g_{n-1}^{e_{n-1}} R \bmod m$% |
56 | */ |
57 | |
58 | typedef struct scan { |
59 | size_t len; |
60 | mpw w; |
61 | } scan; |
62 | |
63 | mp *mpmont_mexpr(mpmont *mm, mpmont_factor *f, size_t n) |
64 | { |
65 | size_t vn = 1 << n; |
66 | mp **v = xmalloc(vn * sizeof(mp *)); |
67 | scan *s; |
68 | size_t o; |
69 | unsigned b; |
70 | mp *a = MP_COPY(mm->r); |
71 | mp *spare = MP_NEW; |
72 | |
73 | /* --- Perform the precomputation --- */ |
74 | |
75 | { |
76 | size_t i, j; |
77 | size_t mask; |
78 | |
79 | /* --- Fill in the rest of the array --- * |
80 | * |
81 | * Zero never gets used. |
82 | */ |
83 | |
84 | j = 0; |
85 | mask = 0; |
86 | for (i = 1; i < vn; i++) { |
87 | |
88 | /* --- Check for a new bit entering --- * |
89 | * |
90 | * If a bit gets set that wasn't set before, then all the lower bits |
91 | * are zeroes and I've got to introduce a new base into the array. |
92 | */ |
93 | |
94 | if ((i & mask) == 0) { |
95 | v[i] = mpmont_mul(mm, MP_NEW, f[j++].base, mm->r2); |
96 | mask = i; |
97 | } |
98 | |
99 | /* --- Otherwise I can get away with a single multiplication --- * |
100 | * |
101 | * In particular, if %$i$% has more than one bit set, then I only need |
102 | * to calculate %$v_i = v_{\mathit{mask}} v_{i - \mathit{mask}}$%. |
103 | * Since both are less than %$i$%, they must have already been |
104 | * computed. |
105 | */ |
106 | |
107 | else |
108 | v[i] = mpmont_mul(mm, MP_NEW, v[mask], v[i & ~mask]); |
109 | } |
110 | } |
111 | |
112 | /* --- Set up the bitscanners --- * |
113 | * |
114 | * I must scan the exponents from left to right, which is a shame. It |
115 | * means that I can't use the standard @mpscan@ stuff, in particular. |
116 | */ |
117 | |
118 | { |
119 | size_t i; |
120 | |
121 | s = xmalloc(n * sizeof(scan)); |
122 | o = 0; |
123 | for (i = 0; i < n; i++) { |
124 | s[i].len = MP_LEN(f[i].exp); |
125 | if (s[i].len > o) |
126 | o = s[i].len; |
127 | } |
128 | b = 0; |
129 | } |
130 | |
131 | /* --- Now do the actual calculation --- */ |
132 | |
133 | b = 0; |
134 | for (;;) { |
135 | size_t i; |
136 | size_t j; |
137 | mp *dd; |
138 | |
139 | /* --- If no more bits, get some more --- */ |
140 | |
141 | if (!b) { |
142 | if (!o) |
143 | break; |
144 | o--; |
145 | b = MPW_BITS; |
146 | } |
147 | |
148 | /* --- Work out the next index --- */ |
149 | |
150 | j = 0; |
151 | b--; |
152 | for (i = 0; i < n; i++) { |
153 | if (o < s[i].len) |
154 | j |= (((f[i].exp->v[o] >> b) & 1) << i); |
155 | } |
156 | |
157 | /* --- Accumulate the result --- */ |
158 | |
159 | if (spare) { |
160 | dd = mpmont_mul(mm, spare, a, a); |
161 | spare = a; |
162 | a = dd; |
163 | } |
164 | |
165 | if (j) { |
166 | dd = mpmont_mul(mm, spare, a, v[j]); |
167 | spare = a; |
168 | a = dd; |
169 | } |
170 | } |
171 | |
172 | /* --- Tidy up afterwards --- */ |
173 | |
174 | { |
175 | size_t i; |
176 | for (i = 1; i < vn; i++) |
177 | MP_DROP(v[i]); |
178 | if (spare) |
179 | MP_DROP(spare); |
180 | free(v); |
181 | free(s); |
182 | } |
183 | |
184 | return (a); |
185 | } |
186 | |
187 | /* --- @mpmont_mexp@ --- * |
188 | * |
189 | * Arguments: @mpmont *mm@ = pointer to Montgomery reduction context |
190 | * @mpmont_factor *f@ = pointer to array of factors |
191 | * @size_t n@ = number of factors supplied |
192 | * |
193 | * Returns: Product of bases raised to exponents, all mod @m@. |
194 | * |
195 | * Use: Convenient interface over @mpmont_mexpr@. |
196 | */ |
197 | |
198 | mp *mpmont_mexp(mpmont *mm, mpmont_factor *f, size_t n) |
199 | { |
200 | mp *d = mpmont_mexpr(mm, f, n); |
201 | d = mpmont_reduce(mm, d, d); |
202 | return (d); |
203 | } |
204 | |
205 | /*----- Test rig ----------------------------------------------------------*/ |
206 | |
207 | #ifdef TEST_RIG |
208 | |
209 | #include <mLib/testrig.h> |
210 | |
211 | static int verify(size_t n, dstr *v) |
212 | { |
213 | mp *m = *(mp **)v[0].buf; |
214 | mpmont_factor *f = xmalloc(n * sizeof(*f)); |
215 | mp *r, *rr; |
216 | size_t i, j; |
217 | mpmont mm; |
218 | int ok = 1; |
219 | |
220 | j = 1; |
221 | for (i = 0; i < n; i++) { |
222 | f[i].base = *(mp **)v[j++].buf; |
223 | f[i].exp = *(mp **)v[j++].buf; |
224 | } |
225 | |
226 | rr = *(mp **)v[j].buf; |
227 | mpmont_create(&mm, m); |
228 | r = mpmont_mexp(&mm, f, n); |
229 | if (MP_CMP(r, !=, rr)) { |
230 | fputs("\n*** mexp failed\n", stderr); |
231 | fputs("m = ", stderr); mp_writefile(m, stderr, 10); |
232 | for (i = 0; i < n; i++) { |
233 | fprintf(stderr, "\ng_%u = ", i); |
234 | mp_writefile(f[i].base, stderr, 10); |
235 | fprintf(stderr, "\ne_%u = ", i); |
236 | mp_writefile(f[i].exp, stderr, 10); |
237 | } |
238 | fputs("\nr = ", stderr); mp_writefile(r, stderr, 10); |
239 | fputs("\nR = ", stderr); mp_writefile(rr, stderr, 10); |
240 | fputc('\n', stderr); |
241 | ok = 0; |
242 | } |
243 | |
244 | for (i = 0; i < n; i++) { |
245 | MP_DROP(f[i].base); |
246 | MP_DROP(f[i].exp); |
247 | } |
248 | MP_DROP(m); |
249 | MP_DROP(r); |
250 | MP_DROP(rr); |
251 | mpmont_destroy(&mm); |
252 | return (ok); |
253 | } |
254 | |
255 | static int t1(dstr *v) { return verify(1, v); } |
256 | static int t2(dstr *v) { return verify(2, v); } |
257 | static int t3(dstr *v) { return verify(3, v); } |
258 | static int t4(dstr *v) { return verify(4, v); } |
259 | static int t5(dstr *v) { return verify(5, v); } |
260 | |
261 | static test_chunk tests[] = { |
262 | { "mexp-1", t1, { &type_mp, |
263 | &type_mp, &type_mp, |
264 | &type_mp, 0 } }, |
265 | { "mexp-2", t2, { &type_mp, |
266 | &type_mp, &type_mp, |
267 | &type_mp, &type_mp, |
268 | &type_mp, 0 } }, |
269 | { "mexp-3", t3, { &type_mp, |
270 | &type_mp, &type_mp, |
271 | &type_mp, &type_mp, |
272 | &type_mp, &type_mp, |
273 | &type_mp, 0 } }, |
274 | { "mexp-4", t4, { &type_mp, |
275 | &type_mp, &type_mp, |
276 | &type_mp, &type_mp, |
277 | &type_mp, &type_mp, |
278 | &type_mp, &type_mp, |
279 | &type_mp, 0 } }, |
280 | { "mexp-5", t5, { &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, &type_mp, |
286 | &type_mp, 0 } }, |
287 | { 0, 0, { 0 } } |
288 | }; |
289 | |
290 | int main(int argc, char *argv[]) |
291 | { |
292 | sub_init(); |
293 | test_run(argc, argv, tests, SRCDIR "/tests/mpmont"); |
294 | return (0); |
295 | } |
296 | |
297 | #endif |
298 | |
299 | /*----- That's all, folks -------------------------------------------------*/ |