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1 | /* -*-c-*- |
2 | * |
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3 | * $Id: f-prime.c,v 1.8 2004/04/01 12:50:09 mdw Exp $ |
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4 | * |
5 | * Prime fields with Montgomery arithmetic |
6 | * |
7 | * (c) 2001 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: f-prime.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 2004/03/27 17:54:11 mdw |
41 | * Standard curves and curve checking. |
42 | * |
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43 | * Revision 1.6 2004/03/23 15:19:32 mdw |
44 | * Test elliptic curves more thoroughly. |
45 | * |
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46 | * Revision 1.5 2004/03/23 12:08:26 mdw |
47 | * Random field-element selection. |
48 | * |
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49 | * Revision 1.4 2004/03/21 22:52:06 mdw |
50 | * Merge and close elliptic curve branch. |
51 | * |
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52 | * Revision 1.3.4.3 2004/03/21 22:39:46 mdw |
53 | * Elliptic curves on binary fields work. |
54 | * |
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55 | * Revision 1.3.4.2 2004/03/20 00:13:31 mdw |
56 | * Projective coordinates for prime curves |
57 | * |
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58 | * Revision 1.3.4.1 2003/06/10 13:43:53 mdw |
59 | * Simple (non-projective) curves over prime fields now seem to work. |
60 | * |
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61 | * Revision 1.3 2003/05/15 23:25:59 mdw |
62 | * Make elliptic curve stuff build. |
63 | * |
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64 | * Revision 1.2 2002/01/13 13:48:44 mdw |
65 | * Further progress. |
66 | * |
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67 | * Revision 1.1 2001/04/29 18:12:33 mdw |
68 | * Prototype version. |
69 | * |
70 | */ |
71 | |
72 | /*----- Header files ------------------------------------------------------*/ |
73 | |
74 | #include <mLib/sub.h> |
75 | |
76 | #include "field.h" |
77 | #include "mpmont.h" |
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78 | #include "mprand.h" |
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79 | |
80 | /*----- Data structures ---------------------------------------------------*/ |
81 | |
82 | typedef struct fctx { |
83 | field f; |
84 | mpmont mm; |
85 | } fctx; |
86 | |
87 | /*----- Main code ---------------------------------------------------------*/ |
88 | |
89 | /* --- Field operations --- */ |
90 | |
91 | static void fdestroy(field *ff) |
92 | { |
93 | fctx *f = (fctx *)ff; |
94 | mpmont_destroy(&f->mm); |
95 | DESTROY(f); |
96 | } |
97 | |
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98 | static mp *frand(field *ff, mp *d, grand *r) |
99 | { |
100 | fctx *f = (fctx *)ff; |
101 | return (mprand_range(d, f->mm.m, r, 0)); |
102 | } |
103 | |
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104 | static mp *fin(field *ff, mp *d, mp *x) |
105 | { |
106 | fctx *f = (fctx *)ff; |
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107 | mp_div(0, &d, x, f->mm.m); |
108 | return (mpmont_mul(&f->mm, d, d, f->mm.r2)); |
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109 | } |
110 | |
111 | static mp *fout(field *ff, mp *d, mp *x) |
112 | { |
113 | fctx *f = (fctx *)ff; |
114 | return (mpmont_reduce(&f->mm, d, x)); |
115 | } |
116 | |
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117 | static int fzerop(field *ff, mp *x) |
118 | { |
119 | return (!MP_LEN(x)); |
120 | } |
121 | |
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122 | static mp *fneg(field *ff, mp *d, mp *x) |
123 | { |
124 | fctx *f = (fctx *)ff; |
125 | return (mp_sub(d, f->mm.m, x)); |
126 | } |
127 | |
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128 | static mp *fadd(field *ff, mp *d, mp *x, mp *y) |
129 | { |
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130 | fctx *f = (fctx *)ff; |
131 | d = mp_add(d, x, y); |
132 | if (d->f & MP_NEG) |
133 | d = mp_add(d, d, f->mm.m); |
134 | else if (MP_CMP(d, >, f->mm.m)) |
135 | d = mp_sub(d, d, f->mm.m); |
136 | return (d); |
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137 | } |
138 | |
139 | static mp *fsub(field *ff, mp *d, mp *x, mp *y) |
140 | { |
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141 | fctx *f = (fctx *)ff; |
142 | d = mp_sub(d, x, y); |
143 | if (d->f & MP_NEG) |
144 | d = mp_add(d, d, f->mm.m); |
145 | else if (MP_CMP(d, >, f->mm.m)) |
146 | d = mp_sub(d, d, f->mm.m); |
147 | return (d); |
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148 | } |
149 | |
150 | static mp *fmul(field *ff, mp *d, mp *x, mp *y) |
151 | { |
152 | fctx *f = (fctx *)ff; |
153 | return (mpmont_mul(&f->mm, d, x, y)); |
154 | } |
155 | |
156 | static mp *fsqr(field *ff, mp *d, mp *x) |
157 | { |
158 | fctx *f = (fctx *)ff; |
159 | d = mp_sqr(d, x); |
160 | return (mpmont_reduce(&f->mm, d, d)); |
161 | } |
162 | |
163 | static mp *finv(field *ff, mp *d, mp *x) |
164 | { |
165 | fctx *f = (fctx *)ff; |
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166 | d = mpmont_reduce(&f->mm, d, x); |
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167 | mp_gcd(0, 0, &d, f->mm.m, d); |
168 | return (mpmont_mul(&f->mm, d, d, f->mm.r2)); |
169 | } |
170 | |
171 | static mp *freduce(field *ff, mp *d, mp *x) |
172 | { |
173 | fctx *f = (fctx *)ff; |
174 | mp_div(0, &d, x, f->mm.m); |
175 | return (d); |
176 | } |
177 | |
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178 | static mp *fsqrt(field *ff, mp *d, mp *x) |
179 | { |
180 | fctx *f = (fctx *)ff; |
181 | d = mpmont_reduce(&f->mm, d, x); |
182 | d = mp_modsqrt(d, d, f->mm.m); |
183 | if (!d) |
184 | return (d); |
185 | return (mpmont_mul(&f->mm, d, d, f->mm.r2)); |
186 | } |
187 | |
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188 | static mp *fdbl(field *ff, mp *d, mp *x) |
189 | { |
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190 | fctx *f = (fctx *)ff; |
191 | d = mp_lsl(d, x, 1); |
192 | if (MP_CMP(d, >, f->mm.m)) |
193 | d = mp_sub(d, d, f->mm.m); |
194 | return (d); |
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195 | } |
196 | |
197 | static mp *ftpl(field *ff, mp *d, mp *x) |
198 | { |
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199 | fctx *f = (fctx *)ff; |
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200 | MP_DEST(d, MP_LEN(x) + 1, x->f); |
201 | MPX_UMULN(d->v, d->vl, x->v, x->vl, 3); |
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202 | while (MP_CMP(d, >, f->mm.m)) |
203 | d = mp_sub(d, d, f->mm.m); |
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204 | return (d); |
205 | } |
206 | |
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207 | static mp *fqdl(field *ff, mp *d, mp *x) |
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208 | { |
209 | fctx *f = (fctx *)ff; |
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210 | d = mp_lsl(d, x, 2); |
211 | while (MP_CMP(d, >, f->mm.m)) |
212 | d = mp_sub(d, d, f->mm.m); |
213 | return (d); |
214 | } |
215 | |
216 | static mp *fhlv(field *ff, mp *d, mp *x) |
217 | { |
218 | fctx *f = (fctx *)ff; |
219 | if (!MP_LEN(x)) { |
220 | MP_COPY(x); |
221 | MP_DROP(d); |
222 | return (x); |
223 | } |
224 | if (x->v[0] & 1) { |
225 | d = mp_add(d, x, f->mm.m); |
226 | x = d; |
227 | } |
228 | return (mp_lsr(d, x, 1)); |
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229 | } |
230 | |
231 | /* --- Field operations table --- */ |
232 | |
233 | static field_ops fops = { |
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234 | FTY_PRIME, "prime", |
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235 | fdestroy, frand, field_stdsamep, |
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236 | fin, fout, |
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237 | fzerop, fneg, fadd, fsub, fmul, fsqr, finv, freduce, fsqrt, |
238 | 0, |
239 | fdbl, ftpl, fqdl, fhlv |
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240 | }; |
241 | |
242 | /* --- @field_prime@ --- * |
243 | * |
244 | * Arguments: @mp *p@ = the characteristic of the field |
245 | * |
246 | * Returns: A pointer to the field. |
247 | * |
248 | * Use: Creates a field structure for a prime field of size %$p$%, |
249 | * using Montgomery reduction for arithmetic. |
250 | */ |
251 | |
252 | field *field_prime(mp *p) |
253 | { |
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254 | fctx *f = CREATE(fctx); |
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255 | f->f.ops = &fops; |
256 | mpmont_create(&f->mm, p); |
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257 | f->f.zero = MP_ZERO; |
258 | f->f.one = f->mm.r; |
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259 | f->f.m = f->mm.m; |
260 | f->f.nbits = mp_bits(p); |
261 | f->f.noctets = (f->f.nbits + 7) >> 3; |
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262 | return (&f->f); |
263 | } |
264 | |
265 | /*----- That's all, folks -------------------------------------------------*/ |