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1 | /* -*-c-*- |
2 | * |
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3 | * $Id: mpbarrett.c,v 1.9 2004/04/01 12:50:09 mdw Exp $ |
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4 | * |
5 | * Barrett modular reduction |
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: mpbarrett.c,v $ |
34e4f738 |
33 | * Revision 1.9 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 1.8 2001/06/16 13:00:20 mdw |
41 | * Use the generic exponentiation functions. |
42 | * |
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43 | * Revision 1.7 2001/04/19 18:25:26 mdw |
44 | * Use sliding-window exponentiation. |
45 | * |
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46 | * Revision 1.6 2000/10/08 12:03:44 mdw |
47 | * (mpbarrett_reduce): Cope with negative numbers. |
48 | * |
419d33ed |
49 | * Revision 1.5 2000/07/29 17:04:33 mdw |
50 | * Change to use left-to-right bitwise exponentiation. This will improve |
51 | * performance when the base is small. |
52 | * |
d34decd2 |
53 | * Revision 1.4 2000/06/17 11:45:09 mdw |
54 | * Major memory management overhaul. Added arena support. Use the secure |
55 | * arena for secret integers. Replace and improve the MP management macros |
56 | * (e.g., replace MP_MODIFY by MP_DEST). |
57 | * |
0a5d0bc7 |
58 | * Revision 1.3 1999/12/12 15:08:52 mdw |
59 | * Don't bother shifting %$q$% in @mpbarrett_reduce@, just skip the least |
60 | * significant digits. |
61 | * |
ed6d1bd2 |
62 | * Revision 1.2 1999/12/11 01:50:56 mdw |
63 | * Improve initialization slightly. |
64 | * |
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65 | * Revision 1.1 1999/12/10 23:21:59 mdw |
66 | * Barrett reduction support: works with even moduli. |
67 | * |
68 | */ |
69 | |
70 | /*----- Header files ------------------------------------------------------*/ |
71 | |
72 | #include "mp.h" |
73 | #include "mpbarrett.h" |
74 | |
75 | /*----- Main code ---------------------------------------------------------*/ |
76 | |
77 | /* --- @mpbarrett_create@ --- * |
78 | * |
79 | * Arguments: @mpbarrett *mb@ = pointer to Barrett reduction context |
80 | * @mp *m@ = modulus to work to |
81 | * |
82 | * |
83 | * Returns: --- |
84 | * |
85 | * Use: Initializes a Barrett reduction context ready for use. |
86 | */ |
87 | |
88 | void mpbarrett_create(mpbarrett *mb, mp *m) |
89 | { |
90 | mp *b; |
91 | |
92 | /* --- Validate the arguments --- */ |
93 | |
94 | assert(((void)"Barrett modulus must be positive", (m->f & MP_NEG) == 0)); |
95 | |
96 | /* --- Compute %$\mu$% --- */ |
97 | |
98 | mp_shrink(m); |
99 | mb->k = MP_LEN(m); |
100 | mb->m = MP_COPY(m); |
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101 | b = mp_new(2 * mb->k + 1, 0); |
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102 | MPX_ZERO(b->v, b->vl - 1); |
103 | b->vl[-1] = 1; |
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104 | mp_div(&b, 0, b, m); |
105 | mb->mu = b; |
106 | } |
107 | |
108 | /* --- @mpbarrett_destroy@ --- * |
109 | * |
110 | * Arguments: @mpbarrett *mb@ = pointer to Barrett reduction context |
111 | * |
112 | * Returns: --- |
113 | * |
114 | * Use: Destroys a Barrett reduction context releasing any resources |
115 | * claimed. |
116 | */ |
117 | |
118 | void mpbarrett_destroy(mpbarrett *mb) |
119 | { |
120 | mp_drop(mb->m); |
121 | mp_drop(mb->mu); |
122 | } |
123 | |
124 | /* --- @mpbarrett_reduce@ --- * |
125 | * |
126 | * Arguments: @mpbarrett *mb@ = pointer to Barrett reduction context |
127 | * @mp *d@ = destination for result |
128 | * @mp *m@ = number to reduce |
129 | * |
130 | * Returns: The residue of @m@ modulo the number in the reduction |
131 | * context. |
132 | * |
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133 | * Use: Performs an efficient modular reduction. |
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134 | */ |
135 | |
136 | mp *mpbarrett_reduce(mpbarrett *mb, mp *d, mp *m) |
137 | { |
138 | mp *q; |
139 | size_t k = mb->k; |
140 | |
141 | /* --- Special case if @m@ is too small --- */ |
142 | |
143 | if (MP_LEN(m) < k) { |
144 | m = MP_COPY(m); |
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145 | if (d) |
146 | MP_DROP(d); |
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147 | return (m); |
148 | } |
149 | |
150 | /* --- First stage --- */ |
151 | |
152 | { |
153 | mp qq; |
154 | mp_build(&qq, m->v + (k - 1), m->vl); |
155 | q = mp_mul(MP_NEW, &qq, mb->mu); |
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156 | if (MP_LEN(q) <= k) { |
157 | m = MP_COPY(m); |
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158 | if (d) |
159 | MP_DROP(d); |
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160 | return (m); |
161 | } |
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162 | } |
163 | |
164 | /* --- Second stage --- */ |
165 | |
166 | { |
167 | mp *r; |
168 | mpw *mvl; |
169 | |
170 | MP_COPY(m); |
171 | if (MP_LEN(m) <= k + 1) |
172 | mvl = m->vl; |
173 | else |
174 | mvl = m->v + k + 1; |
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175 | r = mp_new(k + 1, (q->f | mb->m->f) & MP_BURN); |
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176 | mpx_umul(r->v, r->vl, q->v + k + 1, q->vl, mb->m->v, mb->m->vl); |
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177 | MP_DEST(d, k + 1, r->f); |
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178 | mpx_usub(d->v, d->vl, m->v, mvl, r->v, r->vl); |
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179 | d->f = (m->f | r->f) & (MP_BURN | MP_NEG); |
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180 | MP_DROP(r); |
181 | MP_DROP(q); |
182 | MP_DROP(m); |
183 | } |
184 | |
185 | /* --- Final stage --- */ |
186 | |
187 | MP_SHRINK(d); |
188 | while (MPX_UCMP(d->v, d->vl, >=, mb->m->v, mb->m->vl)) |
189 | mpx_usub(d->v, d->vl, d->v, d->vl, mb->m->v, mb->m->vl); |
190 | |
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191 | /* --- Fix up the sign --- */ |
192 | |
193 | if (d->f & MP_NEG) { |
194 | mpx_usub(d->v, d->vl, mb->m->v, mb->m->vl, d->v, d->vl); |
195 | d->f &= ~MP_NEG; |
196 | } |
197 | |
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198 | MP_SHRINK(d); |
199 | return (d); |
200 | } |
201 | |
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202 | /*----- Test rig ----------------------------------------------------------*/ |
203 | |
204 | #ifdef TEST_RIG |
205 | |
206 | static int vmod(dstr *v) |
207 | { |
208 | mp *x = *(mp **)v[0].buf; |
209 | mp *n = *(mp **)v[1].buf; |
210 | mp *r = *(mp **)v[2].buf; |
211 | mp *s; |
212 | mpbarrett mb; |
213 | int ok = 1; |
214 | |
215 | mpbarrett_create(&mb, n); |
216 | s = mpbarrett_reduce(&mb, MP_NEW, x); |
217 | |
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218 | if (!MP_EQ(s, r)) { |
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219 | fputs("\n*** barrett reduction failure\n", stderr); |
220 | fputs("x = ", stderr); mp_writefile(x, stderr, 10); fputc('\n', stderr); |
221 | fputs("n = ", stderr); mp_writefile(n, stderr, 10); fputc('\n', stderr); |
222 | fputs("r = ", stderr); mp_writefile(r, stderr, 10); fputc('\n', stderr); |
223 | fputs("s = ", stderr); mp_writefile(s, stderr, 10); fputc('\n', stderr); |
224 | ok = 0; |
225 | } |
226 | |
227 | mpbarrett_destroy(&mb); |
228 | mp_drop(x); |
229 | mp_drop(n); |
230 | mp_drop(r); |
231 | mp_drop(s); |
232 | assert(mparena_count(MPARENA_GLOBAL) == 0); |
233 | return (ok); |
234 | } |
235 | |
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236 | static test_chunk tests[] = { |
237 | { "mpbarrett-reduce", vmod, { &type_mp, &type_mp, &type_mp, 0 } }, |
21a7c4b1 |
238 | { 0, 0, { 0 } } |
239 | }; |
240 | |
241 | int main(int argc, char *argv[]) |
242 | { |
243 | sub_init(); |
244 | test_run(argc, argv, tests, SRCDIR "/tests/mpbarrett"); |
245 | return (0); |
246 | } |
247 | |
248 | #endif |
249 | |
250 | /*----- That's all, folks -------------------------------------------------*/ |