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1 | /* -*-c-*- |
2 | * |
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3 | * $Id: mpmont-mexp.c,v 1.8 2004/04/01 12:50:09 mdw Exp $ |
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4 | * |
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5 | * Multiple simultaneous exponentiations |
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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 1.8 2004/04/01 12:50:09 mdw |
34 | * Add cyclic group abstraction, with test code. Separate off exponentation |
35 | * functions for better static linking. Fix a buttload of bugs on the way. |
36 | * Generally ensure that negative exponents do inversion correctly. Add |
37 | * table of standard prime-field subgroups. (Binary field subgroups are |
38 | * currently unimplemented but easy to add if anyone ever finds a good one.) |
39 | * |
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40 | * Revision 1.7 2002/01/13 13:49:14 mdw |
41 | * Make @const@-correct. |
42 | * |
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43 | * Revision 1.6 2001/06/16 13:00:20 mdw |
44 | * Use the generic exponentiation functions. |
45 | * |
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46 | * Revision 1.5 2000/10/08 12:11:22 mdw |
47 | * Use @MP_EQ@ instead of @MP_CMP@. |
48 | * |
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49 | * Revision 1.4 2000/06/17 11:45:09 mdw |
50 | * Major memory management overhaul. Added arena support. Use the secure |
51 | * arena for secret integers. Replace and improve the MP management macros |
52 | * (e.g., replace MP_MODIFY by MP_DEST). |
53 | * |
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54 | * Revision 1.3 1999/12/10 23:18:39 mdw |
55 | * Change interface for suggested destinations. |
56 | * |
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57 | * Revision 1.2 1999/11/21 11:35:10 mdw |
58 | * Performance improvement: use @mp_sqr@ and @mpmont_reduce@ instead of |
59 | * @mpmont_mul@ for squaring in exponentiation. |
60 | * |
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61 | * Revision 1.1 1999/11/19 13:19:29 mdw |
62 | * Simultaneous exponentiation support. |
63 | * |
64 | */ |
65 | |
66 | /*----- Header files ------------------------------------------------------*/ |
67 | |
68 | #include "mp.h" |
69 | #include "mpmont.h" |
70 | |
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71 | #define EXP_WINSZ 3 |
72 | #include "mpmont-exp.h" |
73 | |
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74 | /*----- Main code ---------------------------------------------------------*/ |
75 | |
76 | /* --- @mpmont_mexpr@ --- * |
77 | * |
78 | * Arguments: @mpmont *mm@ = pointer to Montgomery reduction context |
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79 | * @mp *d@ = fake destination |
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80 | * @const mp_expfactor *f@ = pointer to array of factors |
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81 | * @size_t n@ = number of factors supplied |
82 | * |
83 | * Returns: If the bases are %$g_0, g_1, \ldots, g_{n-1}$% and the |
84 | * exponents are %$e_0, e_1, \ldots, e_{n-1}$% then the result |
85 | * is: |
86 | * |
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87 | * %$g_0^{e_0} g_1^{e_1} \ldots g_{n-1}^{e_{n-1}} \bmod m$% |
88 | * |
89 | * except that the %$g_i$% and result are in Montgomery form. |
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90 | */ |
91 | |
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92 | static mp *mexpr(mpmont *mm, mp *d, mp_expfactor *f, size_t n) |
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93 | { |
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94 | mp *a = MP_COPY(mm->r); |
95 | mp *spare = MP_NEW; |
96 | mp *g = MP_NEW; |
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97 | size_t i; |
98 | |
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99 | for (i = 0; i < n; i++) { |
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100 | mp *t; |
101 | if (f[i].exp->f & MP_BURN) |
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102 | spare = MP_NEWSEC; |
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103 | if (f[i].exp->f & MP_NEG) { |
104 | t = mpmont_reduce(mm, f[i].base, f[i].base); |
105 | mp_gcd(&g, 0, &t, mm->m, t); |
106 | assert(MP_EQ(g, MP_ONE)); |
107 | f[i].base = mpmont_mul(mm, t, t, mm->r2); |
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108 | } |
109 | } |
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110 | mp_drop(g); |
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111 | EXP_SIMUL(a, f, n); |
112 | mp_drop(d); |
113 | mp_drop(spare); |
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114 | for (i = 0; i < n; i++) |
115 | MP_DROP(f[i].base); |
116 | xfree(f); |
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117 | return (a); |
118 | } |
119 | |
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120 | mp *mpmont_mexpr(mpmont *mm, mp *d, const mp_expfactor *f, size_t n) |
121 | { |
122 | mp_expfactor *ff = xmalloc(n * sizeof(mp_expfactor)); |
123 | size_t i; |
124 | |
125 | for (i = 0; i < n; i++) { |
126 | ff[i].base = MP_COPY(f[i].base); |
127 | ff[i].exp = f[i].exp; |
128 | } |
129 | return (mexpr(mm, d, ff, n)); |
130 | } |
131 | |
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132 | /* --- @mpmont_mexp@ --- * |
133 | * |
134 | * Arguments: @mpmont *mm@ = pointer to Montgomery reduction context |
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135 | * @mp *d@ = fake destination |
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136 | * @const mp_expfactor *f@ = pointer to array of factors |
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137 | * @size_t n@ = number of factors supplied |
138 | * |
139 | * Returns: Product of bases raised to exponents, all mod @m@. |
140 | * |
141 | * Use: Convenient interface over @mpmont_mexpr@. |
142 | */ |
143 | |
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144 | mp *mpmont_mexp(mpmont *mm, mp *d, const mp_expfactor *f, size_t n) |
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145 | { |
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146 | mp_expfactor *ff = xmalloc(n * sizeof(mp_expfactor)); |
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147 | size_t i; |
148 | |
149 | for (i = 0; i < n; i++) { |
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150 | ff[i].base = mpmont_mul(mm, MP_NEW, f[i].base, mm->r2); |
151 | ff[i].exp = f[i].exp; |
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152 | } |
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153 | d = mexpr(mm, d, ff, n); |
154 | return (mpmont_reduce(mm, d, d)); |
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155 | } |
156 | |
157 | /*----- Test rig ----------------------------------------------------------*/ |
158 | |
159 | #ifdef TEST_RIG |
160 | |
161 | #include <mLib/testrig.h> |
162 | |
163 | static int verify(size_t n, dstr *v) |
164 | { |
165 | mp *m = *(mp **)v[0].buf; |
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166 | mp_expfactor *f = xmalloc(n * sizeof(*f)); |
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167 | mp *r, *rr; |
168 | size_t i, j; |
169 | mpmont mm; |
170 | int ok = 1; |
171 | |
172 | j = 1; |
173 | for (i = 0; i < n; i++) { |
174 | f[i].base = *(mp **)v[j++].buf; |
175 | f[i].exp = *(mp **)v[j++].buf; |
176 | } |
177 | |
178 | rr = *(mp **)v[j].buf; |
179 | mpmont_create(&mm, m); |
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180 | r = mpmont_mexp(&mm, MP_NEW, f, n); |
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181 | if (!MP_EQ(r, rr)) { |
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182 | fputs("\n*** mexp failed\n", stderr); |
183 | fputs("m = ", stderr); mp_writefile(m, stderr, 10); |
184 | for (i = 0; i < n; i++) { |
185 | fprintf(stderr, "\ng_%u = ", i); |
186 | mp_writefile(f[i].base, stderr, 10); |
187 | fprintf(stderr, "\ne_%u = ", i); |
188 | mp_writefile(f[i].exp, stderr, 10); |
189 | } |
190 | fputs("\nr = ", stderr); mp_writefile(r, stderr, 10); |
191 | fputs("\nR = ", stderr); mp_writefile(rr, stderr, 10); |
192 | fputc('\n', stderr); |
193 | ok = 0; |
194 | } |
195 | |
196 | for (i = 0; i < n; i++) { |
197 | MP_DROP(f[i].base); |
198 | MP_DROP(f[i].exp); |
199 | } |
200 | MP_DROP(m); |
201 | MP_DROP(r); |
202 | MP_DROP(rr); |
203 | mpmont_destroy(&mm); |
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204 | assert(mparena_count(MPARENA_GLOBAL) == 0); |
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205 | return (ok); |
206 | } |
207 | |
208 | static int t1(dstr *v) { return verify(1, v); } |
209 | static int t2(dstr *v) { return verify(2, v); } |
210 | static int t3(dstr *v) { return verify(3, v); } |
211 | static int t4(dstr *v) { return verify(4, v); } |
212 | static int t5(dstr *v) { return verify(5, v); } |
213 | |
214 | static test_chunk tests[] = { |
215 | { "mexp-1", t1, { &type_mp, |
216 | &type_mp, &type_mp, |
217 | &type_mp, 0 } }, |
218 | { "mexp-2", t2, { &type_mp, |
219 | &type_mp, &type_mp, |
220 | &type_mp, &type_mp, |
221 | &type_mp, 0 } }, |
222 | { "mexp-3", t3, { &type_mp, |
223 | &type_mp, &type_mp, |
224 | &type_mp, &type_mp, |
225 | &type_mp, &type_mp, |
226 | &type_mp, 0 } }, |
227 | { "mexp-4", t4, { &type_mp, |
228 | &type_mp, &type_mp, |
229 | &type_mp, &type_mp, |
230 | &type_mp, &type_mp, |
231 | &type_mp, &type_mp, |
232 | &type_mp, 0 } }, |
233 | { "mexp-5", t5, { &type_mp, |
234 | &type_mp, &type_mp, |
235 | &type_mp, &type_mp, |
236 | &type_mp, &type_mp, |
237 | &type_mp, &type_mp, |
238 | &type_mp, &type_mp, |
239 | &type_mp, 0 } }, |
240 | { 0, 0, { 0 } } |
241 | }; |
242 | |
243 | int main(int argc, char *argv[]) |
244 | { |
245 | sub_init(); |
246 | test_run(argc, argv, tests, SRCDIR "/tests/mpmont"); |
247 | return (0); |
248 | } |
249 | |
250 | #endif |
251 | |
252 | /*----- That's all, folks -------------------------------------------------*/ |