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1 | /* -*-c-*- |
2 | * |
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3 | * $Id: f-prime.c,v 1.7 2004/03/27 17:54:11 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 1.7 2004/03/27 17:54:11 mdw |
34 | * Standard curves and curve checking. |
35 | * |
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36 | * Revision 1.6 2004/03/23 15:19:32 mdw |
37 | * Test elliptic curves more thoroughly. |
38 | * |
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39 | * Revision 1.5 2004/03/23 12:08:26 mdw |
40 | * Random field-element selection. |
41 | * |
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42 | * Revision 1.4 2004/03/21 22:52:06 mdw |
43 | * Merge and close elliptic curve branch. |
44 | * |
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45 | * Revision 1.3.4.3 2004/03/21 22:39:46 mdw |
46 | * Elliptic curves on binary fields work. |
47 | * |
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48 | * Revision 1.3.4.2 2004/03/20 00:13:31 mdw |
49 | * Projective coordinates for prime curves |
50 | * |
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51 | * Revision 1.3.4.1 2003/06/10 13:43:53 mdw |
52 | * Simple (non-projective) curves over prime fields now seem to work. |
53 | * |
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54 | * Revision 1.3 2003/05/15 23:25:59 mdw |
55 | * Make elliptic curve stuff build. |
56 | * |
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57 | * Revision 1.2 2002/01/13 13:48:44 mdw |
58 | * Further progress. |
59 | * |
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60 | * Revision 1.1 2001/04/29 18:12:33 mdw |
61 | * Prototype version. |
62 | * |
63 | */ |
64 | |
65 | /*----- Header files ------------------------------------------------------*/ |
66 | |
67 | #include <mLib/sub.h> |
68 | |
69 | #include "field.h" |
70 | #include "mpmont.h" |
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71 | #include "mprand.h" |
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72 | |
73 | /*----- Data structures ---------------------------------------------------*/ |
74 | |
75 | typedef struct fctx { |
76 | field f; |
77 | mpmont mm; |
78 | } fctx; |
79 | |
80 | /*----- Main code ---------------------------------------------------------*/ |
81 | |
82 | /* --- Field operations --- */ |
83 | |
84 | static void fdestroy(field *ff) |
85 | { |
86 | fctx *f = (fctx *)ff; |
87 | mpmont_destroy(&f->mm); |
88 | DESTROY(f); |
89 | } |
90 | |
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91 | static mp *frand(field *ff, mp *d, grand *r) |
92 | { |
93 | fctx *f = (fctx *)ff; |
94 | return (mprand_range(d, f->mm.m, r, 0)); |
95 | } |
96 | |
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97 | static mp *fin(field *ff, mp *d, mp *x) |
98 | { |
99 | fctx *f = (fctx *)ff; |
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100 | mp_div(0, &d, x, f->mm.m); |
101 | return (mpmont_mul(&f->mm, d, d, f->mm.r2)); |
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102 | } |
103 | |
104 | static mp *fout(field *ff, mp *d, mp *x) |
105 | { |
106 | fctx *f = (fctx *)ff; |
107 | return (mpmont_reduce(&f->mm, d, x)); |
108 | } |
109 | |
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110 | static int fzerop(field *ff, mp *x) |
111 | { |
112 | return (!MP_LEN(x)); |
113 | } |
114 | |
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115 | static mp *fneg(field *ff, mp *d, mp *x) |
116 | { |
117 | fctx *f = (fctx *)ff; |
118 | return (mp_sub(d, f->mm.m, x)); |
119 | } |
120 | |
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121 | static mp *fadd(field *ff, mp *d, mp *x, mp *y) |
122 | { |
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123 | fctx *f = (fctx *)ff; |
124 | d = mp_add(d, x, y); |
125 | if (d->f & MP_NEG) |
126 | d = mp_add(d, d, f->mm.m); |
127 | else if (MP_CMP(d, >, f->mm.m)) |
128 | d = mp_sub(d, d, f->mm.m); |
129 | return (d); |
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130 | } |
131 | |
132 | static mp *fsub(field *ff, mp *d, mp *x, mp *y) |
133 | { |
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134 | fctx *f = (fctx *)ff; |
135 | d = mp_sub(d, x, y); |
136 | if (d->f & MP_NEG) |
137 | d = mp_add(d, d, f->mm.m); |
138 | else if (MP_CMP(d, >, f->mm.m)) |
139 | d = mp_sub(d, d, f->mm.m); |
140 | return (d); |
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141 | } |
142 | |
143 | static mp *fmul(field *ff, mp *d, mp *x, mp *y) |
144 | { |
145 | fctx *f = (fctx *)ff; |
146 | return (mpmont_mul(&f->mm, d, x, y)); |
147 | } |
148 | |
149 | static mp *fsqr(field *ff, mp *d, mp *x) |
150 | { |
151 | fctx *f = (fctx *)ff; |
152 | d = mp_sqr(d, x); |
153 | return (mpmont_reduce(&f->mm, d, d)); |
154 | } |
155 | |
156 | static mp *finv(field *ff, mp *d, mp *x) |
157 | { |
158 | fctx *f = (fctx *)ff; |
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159 | d = mpmont_reduce(&f->mm, d, x); |
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160 | mp_gcd(0, 0, &d, f->mm.m, d); |
161 | return (mpmont_mul(&f->mm, d, d, f->mm.r2)); |
162 | } |
163 | |
164 | static mp *freduce(field *ff, mp *d, mp *x) |
165 | { |
166 | fctx *f = (fctx *)ff; |
167 | mp_div(0, &d, x, f->mm.m); |
168 | return (d); |
169 | } |
170 | |
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171 | static mp *fsqrt(field *ff, mp *d, mp *x) |
172 | { |
173 | fctx *f = (fctx *)ff; |
174 | d = mpmont_reduce(&f->mm, d, x); |
175 | d = mp_modsqrt(d, d, f->mm.m); |
176 | if (!d) |
177 | return (d); |
178 | return (mpmont_mul(&f->mm, d, d, f->mm.r2)); |
179 | } |
180 | |
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181 | static mp *fdbl(field *ff, mp *d, mp *x) |
182 | { |
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183 | fctx *f = (fctx *)ff; |
184 | d = mp_lsl(d, x, 1); |
185 | if (MP_CMP(d, >, f->mm.m)) |
186 | d = mp_sub(d, d, f->mm.m); |
187 | return (d); |
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188 | } |
189 | |
190 | static mp *ftpl(field *ff, mp *d, mp *x) |
191 | { |
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192 | fctx *f = (fctx *)ff; |
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193 | MP_DEST(d, MP_LEN(x) + 1, x->f); |
194 | MPX_UMULN(d->v, d->vl, x->v, x->vl, 3); |
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195 | while (MP_CMP(d, >, f->mm.m)) |
196 | d = mp_sub(d, d, f->mm.m); |
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197 | return (d); |
198 | } |
199 | |
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200 | static mp *fqdl(field *ff, mp *d, mp *x) |
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201 | { |
202 | fctx *f = (fctx *)ff; |
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203 | d = mp_lsl(d, x, 2); |
204 | while (MP_CMP(d, >, f->mm.m)) |
205 | d = mp_sub(d, d, f->mm.m); |
206 | return (d); |
207 | } |
208 | |
209 | static mp *fhlv(field *ff, mp *d, mp *x) |
210 | { |
211 | fctx *f = (fctx *)ff; |
212 | if (!MP_LEN(x)) { |
213 | MP_COPY(x); |
214 | MP_DROP(d); |
215 | return (x); |
216 | } |
217 | if (x->v[0] & 1) { |
218 | d = mp_add(d, x, f->mm.m); |
219 | x = d; |
220 | } |
221 | return (mp_lsr(d, x, 1)); |
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222 | } |
223 | |
224 | /* --- Field operations table --- */ |
225 | |
226 | static field_ops fops = { |
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227 | FTY_PRIME, "prime", |
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228 | fdestroy, frand, |
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229 | fin, fout, |
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230 | fzerop, fneg, fadd, fsub, fmul, fsqr, finv, freduce, fsqrt, |
231 | 0, |
232 | fdbl, ftpl, fqdl, fhlv |
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233 | }; |
234 | |
235 | /* --- @field_prime@ --- * |
236 | * |
237 | * Arguments: @mp *p@ = the characteristic of the field |
238 | * |
239 | * Returns: A pointer to the field. |
240 | * |
241 | * Use: Creates a field structure for a prime field of size %$p$%, |
242 | * using Montgomery reduction for arithmetic. |
243 | */ |
244 | |
245 | field *field_prime(mp *p) |
246 | { |
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247 | fctx *f = CREATE(fctx); |
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248 | f->f.ops = &fops; |
249 | mpmont_create(&f->mm, p); |
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250 | f->f.zero = MP_ZERO; |
251 | f->f.one = f->mm.r; |
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252 | f->f.m = f->mm.m; |
253 | f->f.nbits = mp_bits(p); |
254 | f->f.noctets = (f->f.nbits + 7) >> 3; |
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255 | return (&f->f); |
256 | } |
257 | |
258 | /*----- That's all, folks -------------------------------------------------*/ |