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1 | /* -*-c-*- |
2 | * |
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3 | * $Id: f-binpoly.c,v 1.7 2004/04/01 21:28:41 mdw Exp $ |
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4 | * |
5 | * Binary fields with polynomial basis representation |
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-binpoly.c,v $ |
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33 | * Revision 1.7 2004/04/01 21:28:41 mdw |
34 | * Normal basis support (translates to poly basis internally). Rewrite |
35 | * EC and prime group table generators in awk, so that they can reuse data |
36 | * for repeated constants. |
37 | * |
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38 | * Revision 1.6 2004/04/01 12:50:09 mdw |
39 | * Add cyclic group abstraction, with test code. Separate off exponentation |
40 | * functions for better static linking. Fix a buttload of bugs on the way. |
41 | * Generally ensure that negative exponents do inversion correctly. Add |
42 | * table of standard prime-field subgroups. (Binary field subgroups are |
43 | * currently unimplemented but easy to add if anyone ever finds a good one.) |
44 | * |
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45 | * Revision 1.5 2004/03/27 17:54:11 mdw |
46 | * Standard curves and curve checking. |
47 | * |
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48 | * Revision 1.4 2004/03/23 15:19:32 mdw |
49 | * Test elliptic curves more thoroughly. |
50 | * |
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51 | * Revision 1.3 2004/03/23 12:08:26 mdw |
52 | * Random field-element selection. |
53 | * |
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54 | * Revision 1.2 2004/03/21 22:52:06 mdw |
55 | * Merge and close elliptic curve branch. |
56 | * |
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57 | * Revision 1.1.2.1 2004/03/21 22:39:46 mdw |
58 | * Elliptic curves on binary fields work. |
59 | * |
60 | */ |
61 | |
62 | /*----- Header files ------------------------------------------------------*/ |
63 | |
64 | #include <mLib/sub.h> |
65 | |
66 | #include "field.h" |
67 | #include "gf.h" |
68 | #include "gfreduce.h" |
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69 | #include "mprand.h" |
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70 | #include "gfn.h" |
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71 | |
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72 | /*----- Polynomial basis --------------------------------------------------*/ |
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73 | |
74 | typedef struct fctx { |
75 | field f; |
76 | gfreduce r; |
77 | } fctx; |
78 | |
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79 | /* --- Field operations --- */ |
80 | |
81 | static void fdestroy(field *ff) |
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82 | { fctx *f = (fctx *)ff; gfreduce_destroy(&f->r); DESTROY(f); } |
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83 | |
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84 | static mp *frand(field *f, mp *d, grand *r) |
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85 | { return (mprand(d, f->nbits, r, 0)); } |
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86 | |
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87 | static int fzerop(field *ff, mp *x) { return (!MP_LEN(x)); } |
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88 | |
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89 | static mp *fadd(field *ff, mp *d, mp *x, mp *y) { return (gf_add(d, x, y)); } |
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90 | |
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91 | static mp *fmul(field *ff, mp *d, mp *x, mp *y) { |
92 | fctx *f = (fctx *)ff; d = gf_mul(d, x, y); |
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93 | return (gfreduce_do(&f->r, d, d)); |
94 | } |
95 | |
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96 | static mp *fsqr(field *ff, mp *d, mp *x) { |
97 | fctx *f = (fctx *)ff; d = gf_sqr(d, x); |
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98 | return (gfreduce_do(&f->r, d, d)); |
99 | } |
100 | |
101 | static mp *finv(field *ff, mp *d, mp *x) |
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102 | { fctx *f = (fctx *)ff; gf_gcd(0, 0, &d, f->r.p, x); return (d); } |
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103 | |
104 | static mp *freduce(field *ff, mp *d, mp *x) |
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105 | { fctx *f = (fctx *)ff; return (gfreduce_do(&f->r, d, x)); } |
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106 | |
107 | static mp *fsqrt(field *ff, mp *d, mp *x) |
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108 | { fctx *f = (fctx *)ff; return (gfreduce_sqrt(&f->r, d, x)); } |
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109 | |
110 | static mp *fquadsolve(field *ff, mp *d, mp *x) |
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111 | { fctx *f = (fctx *)ff; return (gfreduce_quadsolve(&f->r, d, x)); } |
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112 | |
113 | /* --- Field operations table --- */ |
114 | |
115 | static field_ops fops = { |
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116 | FTY_BINARY, "binpoly", |
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117 | fdestroy, frand, field_stdsamep, |
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118 | freduce, field_id, |
119 | fzerop, field_id, fadd, fadd, fmul, fsqr, finv, freduce, fsqrt, |
120 | fquadsolve, |
121 | 0, 0, 0, 0 |
122 | }; |
123 | |
124 | /* --- @field_binpoly@ --- * |
125 | * |
126 | * Arguments: @mp *p@ = the reduction polynomial |
127 | * |
128 | * Returns: A pointer to the field. |
129 | * |
130 | * Use: Creates a field structure for a binary field mod @p@. |
131 | */ |
132 | |
133 | field *field_binpoly(mp *p) |
134 | { |
135 | fctx *f = CREATE(fctx); |
136 | f->f.ops = &fops; |
137 | f->f.zero = MP_ZERO; |
138 | f->f.one = MP_ONE; |
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139 | f->f.nbits = mp_bits(p) - 1; |
140 | f->f.noctets = (f->f.nbits + 7) >> 3; |
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141 | gfreduce_create(&f->r, p); |
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142 | f->f.m = f->r.p; |
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143 | return (&f->f); |
144 | } |
145 | |
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146 | /*----- Normal basis ------------------------------------------------------*/ |
147 | |
148 | typedef struct fnctx { |
149 | fctx f; |
150 | gfn ntop, pton; |
151 | } fnctx; |
152 | |
153 | /* --- Field operations --- */ |
154 | |
155 | static void fndestroy(field *ff) { |
156 | fnctx *f = (fnctx *)ff; gfreduce_destroy(&f->f.r); |
157 | gfn_destroy(&f->ntop); gfn_destroy(&f->pton); |
158 | DESTROY(f); |
159 | } |
160 | |
161 | static int fnsamep(field *ff, field *gg) { |
162 | fnctx *f = (fnctx *)ff, *g = (fnctx *)gg; |
163 | return (MP_EQ(f->ntop.r[0], g->ntop.r[0]) && field_stdsamep(ff, gg)); |
164 | } |
165 | |
166 | static mp *fnin(field *ff, mp *d, mp *x) |
167 | { fnctx *f = (fnctx *)ff; return (gfn_transform(&f->ntop, d, x)); } |
168 | |
169 | static mp *fnout(field *ff, mp *d, mp *x) |
170 | { fnctx *f = (fnctx *)ff; return (gfn_transform(&f->pton, d, x)); } |
171 | |
172 | /* --- Field operations table --- */ |
173 | |
174 | static field_ops fnops = { |
175 | FTY_BINARY, "binnorm", |
176 | fndestroy, frand, fnsamep, |
177 | fnin, fnout, |
178 | fzerop, field_id, fadd, fadd, fmul, fsqr, finv, freduce, fsqrt, |
179 | fquadsolve, |
180 | 0, 0, 0, 0 |
181 | }; |
182 | |
183 | /* --- @field_binnorm@ --- * |
184 | * |
185 | * Arguments: @mp *p@ = the reduction polynomial |
186 | * @mp *beta@ = representation of normal point |
187 | * |
188 | * Returns: A pointer to the field. |
189 | * |
190 | * Use: Creates a field structure for a binary field mod @p@ which |
191 | * uses a normal basis representation externally. Computations |
192 | * are still done on a polynomial-basis representation. |
193 | */ |
194 | |
195 | field *field_binnorm(mp *p, mp *beta) |
196 | { |
197 | fnctx *f = CREATE(fnctx); |
198 | f->f.f.ops = &fnops; |
199 | f->f.f.zero = MP_ZERO; |
200 | f->f.f.one = MP_ONE; |
201 | f->f.f.nbits = mp_bits(p) - 1; |
202 | f->f.f.noctets = (f->f.f.nbits + 7) >> 3; |
203 | gfreduce_create(&f->f.r, p); |
204 | f->f.f.m = f->f.r.p; |
205 | gfn_create(p, beta, &f->ntop, &f->pton); |
206 | return (&f->f.f); |
207 | } |
208 | |
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209 | /*----- That's all, folks -------------------------------------------------*/ |