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