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