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