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1 | /* -*-c-*- |
2 | * |
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3 | * $Id: f-niceprime.c,v 1.3 2004/04/01 12:50:09 mdw Exp $ |
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4 | * |
5 | * Prime fields with efficient reduction for special-form primes |
6 | * |
7 | * (c) 2004 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-niceprime.c,v $ |
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33 | * Revision 1.3 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 1.2 2004/03/27 17:54:11 mdw |
41 | * Standard curves and curve checking. |
42 | * |
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43 | * Revision 1.1 2004/03/27 00:04:46 mdw |
44 | * Implement efficient reduction for pleasant-looking primes. |
45 | * |
46 | */ |
47 | |
48 | /*----- Header files ------------------------------------------------------*/ |
49 | |
50 | #include <mLib/sub.h> |
51 | |
52 | #include "field.h" |
53 | #include "mpreduce.h" |
54 | #include "mprand.h" |
55 | |
56 | /*----- Data structures ---------------------------------------------------*/ |
57 | |
58 | typedef struct fctx { |
59 | field f; |
60 | mpreduce r; |
61 | } fctx; |
62 | |
63 | /*----- Main code ---------------------------------------------------------*/ |
64 | |
65 | /* --- Field operations --- */ |
66 | |
67 | static void fdestroy(field *ff) |
68 | { |
69 | fctx *f = (fctx *)ff; |
70 | mpreduce_destroy(&f->r); |
71 | DESTROY(f); |
72 | } |
73 | |
74 | static mp *frand(field *ff, mp *d, grand *r) |
75 | { |
76 | fctx *f = (fctx *)ff; |
77 | return (mprand_range(d, f->r.p, r, 0)); |
78 | } |
79 | |
80 | static int fzerop(field *ff, mp *x) |
81 | { |
82 | return (!MP_LEN(x)); |
83 | } |
84 | |
85 | static mp *fneg(field *ff, mp *d, mp *x) |
86 | { |
87 | fctx *f = (fctx *)ff; |
88 | return (mp_sub(d, f->r.p, x)); |
89 | } |
90 | |
91 | static mp *fadd(field *ff, mp *d, mp *x, mp *y) |
92 | { |
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->r.p); |
97 | else if (MP_CMP(d, >, f->r.p)) |
98 | d = mp_sub(d, d, f->r.p); |
99 | return (d); |
100 | } |
101 | |
102 | static mp *fsub(field *ff, mp *d, mp *x, mp *y) |
103 | { |
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->r.p); |
108 | else if (MP_CMP(d, >, f->r.p)) |
109 | d = mp_sub(d, d, f->r.p); |
110 | return (d); |
111 | } |
112 | |
113 | static mp *fmul(field *ff, mp *d, mp *x, mp *y) |
114 | { |
115 | fctx *f = (fctx *)ff; |
116 | d = mp_mul(d, x, y); |
117 | return (mpreduce_do(&f->r, d, d)); |
118 | } |
119 | |
120 | static mp *fsqr(field *ff, mp *d, mp *x) |
121 | { |
122 | fctx *f = (fctx *)ff; |
123 | d = mp_sqr(d, x); |
124 | return (mpreduce_do(&f->r, d, d)); |
125 | } |
126 | |
127 | static mp *finv(field *ff, mp *d, mp *x) |
128 | { |
129 | fctx *f = (fctx *)ff; |
130 | mp_gcd(0, 0, &d, f->r.p, x); |
131 | return (d); |
132 | } |
133 | |
134 | static mp *freduce(field *ff, mp *d, mp *x) |
135 | { |
136 | fctx *f = (fctx *)ff; |
137 | return (mpreduce_do(&f->r, d, x)); |
138 | } |
139 | |
140 | static mp *fsqrt(field *ff, mp *d, mp *x) |
141 | { |
142 | fctx *f = (fctx *)ff; |
143 | return (mp_modsqrt(d, x, f->r.p)); |
144 | } |
145 | |
146 | static mp *fdbl(field *ff, mp *d, mp *x) |
147 | { |
148 | fctx *f = (fctx *)ff; |
149 | d = mp_lsl(d, x, 1); |
150 | if (MP_CMP(d, >, f->r.p)) |
151 | d = mp_sub(d, d, f->r.p); |
152 | return (d); |
153 | } |
154 | |
155 | static mp *ftpl(field *ff, mp *d, mp *x) |
156 | { |
157 | fctx *f = (fctx *)ff; |
158 | MP_DEST(d, MP_LEN(x) + 1, x->f); |
159 | MPX_UMULN(d->v, d->vl, x->v, x->vl, 3); |
160 | while (MP_CMP(d, >, f->r.p)) |
161 | d = mp_sub(d, d, f->r.p); |
162 | return (d); |
163 | } |
164 | |
165 | static mp *fqdl(field *ff, mp *d, mp *x) |
166 | { |
167 | fctx *f = (fctx *)ff; |
168 | d = mp_lsl(d, x, 2); |
169 | while (MP_CMP(d, >, f->r.p)) |
170 | d = mp_sub(d, d, f->r.p); |
171 | return (d); |
172 | } |
173 | |
174 | static mp *fhlv(field *ff, mp *d, mp *x) |
175 | { |
176 | fctx *f = (fctx *)ff; |
177 | if (!MP_LEN(x)) { |
178 | MP_COPY(x); |
179 | MP_DROP(d); |
180 | return (x); |
181 | } |
182 | if (x->v[0] & 1) { |
183 | d = mp_add(d, x, f->r.p); |
184 | x = d; |
185 | } |
186 | return (mp_lsr(d, x, 1)); |
187 | } |
188 | |
189 | /* --- Field operations table --- */ |
190 | |
191 | static field_ops fops = { |
192 | FTY_PRIME, "niceprime", |
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193 | fdestroy, frand, field_stdsamep, |
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194 | freduce, field_id, |
195 | fzerop, fneg, fadd, fsub, fmul, fsqr, finv, freduce, fsqrt, |
196 | 0, |
197 | fdbl, ftpl, fqdl, fhlv |
198 | }; |
199 | |
200 | /* --- @field_niceprime@ --- * |
201 | * |
202 | * Arguments: @mp *p@ = the characteristic of the field |
203 | * |
204 | * Returns: A pointer to the field. |
205 | * |
206 | * Use: Creates a field structure for a prime field of size %$p$%, |
207 | * using efficient reduction for nice primes. |
208 | */ |
209 | |
210 | field *field_niceprime(mp *p) |
211 | { |
212 | fctx *f = CREATE(fctx); |
213 | f->f.ops = &fops; |
214 | f->f.zero = MP_ZERO; |
215 | f->f.one = MP_ONE; |
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216 | f->f.nbits = mp_bits(p); |
217 | f->f.noctets = (f->f.nbits + 7) >> 3; |
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218 | mpreduce_create(&f->r, p); |
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219 | f->f.m = f->r.p; |
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220 | return (&f->f); |
221 | } |
222 | |
223 | /*----- That's all, folks -------------------------------------------------*/ |