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1 | /* -*-c-*- |
2 | * |
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3 | * $Id: mpmont-mexp.c,v 1.3 1999/12/10 23:18:39 mdw Exp $ |
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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 $ |
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33 | * Revision 1.3 1999/12/10 23:18:39 mdw |
34 | * Change interface for suggested destinations. |
35 | * |
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36 | * Revision 1.2 1999/11/21 11:35:10 mdw |
37 | * Performance improvement: use @mp_sqr@ and @mpmont_reduce@ instead of |
38 | * @mpmont_mul@ for squaring in exponentiation. |
39 | * |
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40 | * Revision 1.1 1999/11/19 13:19:29 mdw |
41 | * Simultaneous exponentiation support. |
42 | * |
43 | */ |
44 | |
45 | /*----- Header files ------------------------------------------------------*/ |
46 | |
47 | #include "mp.h" |
48 | #include "mpmont.h" |
49 | |
50 | /*----- Main code ---------------------------------------------------------*/ |
51 | |
52 | /* --- @mpmont_mexpr@ --- * |
53 | * |
54 | * Arguments: @mpmont *mm@ = pointer to Montgomery reduction context |
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55 | * @mp *d@ = fake destination |
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56 | * @mpmont_factor *f@ = pointer to array of factors |
57 | * @size_t n@ = number of factors supplied |
58 | * |
59 | * Returns: If the bases are %$g_0, g_1, \ldots, g_{n-1}$% and the |
60 | * exponents are %$e_0, e_1, \ldots, e_{n-1}$% then the result |
61 | * is: |
62 | * |
63 | * %$g_0^{e_0} g_1^{e_1} \ldots g_{n-1}^{e_{n-1}} R \bmod m$% |
64 | */ |
65 | |
66 | typedef struct scan { |
67 | size_t len; |
68 | mpw w; |
69 | } scan; |
70 | |
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71 | mp *mpmont_mexpr(mpmont *mm, mp *d, mpmont_factor *f, size_t n) |
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72 | { |
73 | size_t vn = 1 << n; |
74 | mp **v = xmalloc(vn * sizeof(mp *)); |
75 | scan *s; |
76 | size_t o; |
77 | unsigned b; |
78 | mp *a = MP_COPY(mm->r); |
79 | mp *spare = MP_NEW; |
80 | |
81 | /* --- Perform the precomputation --- */ |
82 | |
83 | { |
84 | size_t i, j; |
85 | size_t mask; |
86 | |
87 | /* --- Fill in the rest of the array --- * |
88 | * |
89 | * Zero never gets used. |
90 | */ |
91 | |
92 | j = 0; |
93 | mask = 0; |
94 | for (i = 1; i < vn; i++) { |
95 | |
96 | /* --- Check for a new bit entering --- * |
97 | * |
98 | * If a bit gets set that wasn't set before, then all the lower bits |
99 | * are zeroes and I've got to introduce a new base into the array. |
100 | */ |
101 | |
102 | if ((i & mask) == 0) { |
103 | v[i] = mpmont_mul(mm, MP_NEW, f[j++].base, mm->r2); |
104 | mask = i; |
105 | } |
106 | |
107 | /* --- Otherwise I can get away with a single multiplication --- * |
108 | * |
109 | * In particular, if %$i$% has more than one bit set, then I only need |
110 | * to calculate %$v_i = v_{\mathit{mask}} v_{i - \mathit{mask}}$%. |
111 | * Since both are less than %$i$%, they must have already been |
112 | * computed. |
113 | */ |
114 | |
115 | else |
116 | v[i] = mpmont_mul(mm, MP_NEW, v[mask], v[i & ~mask]); |
117 | } |
118 | } |
119 | |
120 | /* --- Set up the bitscanners --- * |
121 | * |
122 | * I must scan the exponents from left to right, which is a shame. It |
123 | * means that I can't use the standard @mpscan@ stuff, in particular. |
124 | */ |
125 | |
126 | { |
127 | size_t i; |
128 | |
129 | s = xmalloc(n * sizeof(scan)); |
130 | o = 0; |
131 | for (i = 0; i < n; i++) { |
132 | s[i].len = MP_LEN(f[i].exp); |
133 | if (s[i].len > o) |
134 | o = s[i].len; |
135 | } |
136 | b = 0; |
137 | } |
138 | |
139 | /* --- Now do the actual calculation --- */ |
140 | |
141 | b = 0; |
142 | for (;;) { |
143 | size_t i; |
144 | size_t j; |
145 | mp *dd; |
146 | |
147 | /* --- If no more bits, get some more --- */ |
148 | |
149 | if (!b) { |
150 | if (!o) |
151 | break; |
152 | o--; |
153 | b = MPW_BITS; |
154 | } |
155 | |
156 | /* --- Work out the next index --- */ |
157 | |
158 | j = 0; |
159 | b--; |
160 | for (i = 0; i < n; i++) { |
161 | if (o < s[i].len) |
162 | j |= (((f[i].exp->v[o] >> b) & 1) << i); |
163 | } |
164 | |
165 | /* --- Accumulate the result --- */ |
166 | |
167 | if (spare) { |
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168 | dd = mp_sqr(spare, a); |
169 | dd = mpmont_reduce(mm, dd, dd); |
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170 | spare = a; |
171 | a = dd; |
172 | } |
173 | |
174 | if (j) { |
175 | dd = mpmont_mul(mm, spare, a, v[j]); |
176 | spare = a; |
177 | a = dd; |
178 | } |
179 | } |
180 | |
181 | /* --- Tidy up afterwards --- */ |
182 | |
183 | { |
184 | size_t i; |
185 | for (i = 1; i < vn; i++) |
186 | MP_DROP(v[i]); |
187 | if (spare) |
188 | MP_DROP(spare); |
189 | free(v); |
190 | free(s); |
191 | } |
192 | |
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193 | if (d != MP_NEW) |
194 | MP_DROP(d); |
195 | |
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196 | return (a); |
197 | } |
198 | |
199 | /* --- @mpmont_mexp@ --- * |
200 | * |
201 | * Arguments: @mpmont *mm@ = pointer to Montgomery reduction context |
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202 | * @mp *d@ = fake destination |
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203 | * @mpmont_factor *f@ = pointer to array of factors |
204 | * @size_t n@ = number of factors supplied |
205 | * |
206 | * Returns: Product of bases raised to exponents, all mod @m@. |
207 | * |
208 | * Use: Convenient interface over @mpmont_mexpr@. |
209 | */ |
210 | |
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211 | mp *mpmont_mexp(mpmont *mm, mp *d, mpmont_factor *f, size_t n) |
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212 | { |
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213 | d = mpmont_mexpr(mm, d, f, n); |
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214 | d = mpmont_reduce(mm, d, d); |
215 | return (d); |
216 | } |
217 | |
218 | /*----- Test rig ----------------------------------------------------------*/ |
219 | |
220 | #ifdef TEST_RIG |
221 | |
222 | #include <mLib/testrig.h> |
223 | |
224 | static int verify(size_t n, dstr *v) |
225 | { |
226 | mp *m = *(mp **)v[0].buf; |
227 | mpmont_factor *f = xmalloc(n * sizeof(*f)); |
228 | mp *r, *rr; |
229 | size_t i, j; |
230 | mpmont mm; |
231 | int ok = 1; |
232 | |
233 | j = 1; |
234 | for (i = 0; i < n; i++) { |
235 | f[i].base = *(mp **)v[j++].buf; |
236 | f[i].exp = *(mp **)v[j++].buf; |
237 | } |
238 | |
239 | rr = *(mp **)v[j].buf; |
240 | mpmont_create(&mm, m); |
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241 | r = mpmont_mexp(&mm, MP_NEW, f, n); |
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242 | if (MP_CMP(r, !=, rr)) { |
243 | fputs("\n*** mexp failed\n", stderr); |
244 | fputs("m = ", stderr); mp_writefile(m, stderr, 10); |
245 | for (i = 0; i < n; i++) { |
246 | fprintf(stderr, "\ng_%u = ", i); |
247 | mp_writefile(f[i].base, stderr, 10); |
248 | fprintf(stderr, "\ne_%u = ", i); |
249 | mp_writefile(f[i].exp, stderr, 10); |
250 | } |
251 | fputs("\nr = ", stderr); mp_writefile(r, stderr, 10); |
252 | fputs("\nR = ", stderr); mp_writefile(rr, stderr, 10); |
253 | fputc('\n', stderr); |
254 | ok = 0; |
255 | } |
256 | |
257 | for (i = 0; i < n; i++) { |
258 | MP_DROP(f[i].base); |
259 | MP_DROP(f[i].exp); |
260 | } |
261 | MP_DROP(m); |
262 | MP_DROP(r); |
263 | MP_DROP(rr); |
264 | mpmont_destroy(&mm); |
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265 | assert(mparena_count(MPARENA_GLOBAL) == 0); |
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266 | return (ok); |
267 | } |
268 | |
269 | static int t1(dstr *v) { return verify(1, v); } |
270 | static int t2(dstr *v) { return verify(2, v); } |
271 | static int t3(dstr *v) { return verify(3, v); } |
272 | static int t4(dstr *v) { return verify(4, v); } |
273 | static int t5(dstr *v) { return verify(5, v); } |
274 | |
275 | static test_chunk tests[] = { |
276 | { "mexp-1", t1, { &type_mp, |
277 | &type_mp, &type_mp, |
278 | &type_mp, 0 } }, |
279 | { "mexp-2", t2, { &type_mp, |
280 | &type_mp, &type_mp, |
281 | &type_mp, &type_mp, |
282 | &type_mp, 0 } }, |
283 | { "mexp-3", t3, { &type_mp, |
284 | &type_mp, &type_mp, |
285 | &type_mp, &type_mp, |
286 | &type_mp, &type_mp, |
287 | &type_mp, 0 } }, |
288 | { "mexp-4", t4, { &type_mp, |
289 | &type_mp, &type_mp, |
290 | &type_mp, &type_mp, |
291 | &type_mp, &type_mp, |
292 | &type_mp, &type_mp, |
293 | &type_mp, 0 } }, |
294 | { "mexp-5", t5, { &type_mp, |
295 | &type_mp, &type_mp, |
296 | &type_mp, &type_mp, |
297 | &type_mp, &type_mp, |
298 | &type_mp, &type_mp, |
299 | &type_mp, &type_mp, |
300 | &type_mp, 0 } }, |
301 | { 0, 0, { 0 } } |
302 | }; |
303 | |
304 | int main(int argc, char *argv[]) |
305 | { |
306 | sub_init(); |
307 | test_run(argc, argv, tests, SRCDIR "/tests/mpmont"); |
308 | return (0); |
309 | } |
310 | |
311 | #endif |
312 | |
313 | /*----- That's all, folks -------------------------------------------------*/ |