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