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1 | /* -*-c-*- |
2 | * |
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3 | * $Id: f-prime.c,v 1.11 2004/04/03 03:32:05 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 1.11 2004/04/03 03:32:05 mdw |
34 | * General robustification. |
35 | * |
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36 | * Revision 1.10 2004/04/02 01:03:49 mdw |
37 | * Miscellaneous constification. |
38 | * |
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39 | * Revision 1.9 2004/04/01 21:28:41 mdw |
40 | * Normal basis support (translates to poly basis internally). Rewrite |
41 | * EC and prime group table generators in awk, so that they can reuse data |
42 | * for repeated constants. |
43 | * |
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44 | * Revision 1.8 2004/04/01 12:50:09 mdw |
45 | * Add cyclic group abstraction, with test code. Separate off exponentation |
46 | * functions for better static linking. Fix a buttload of bugs on the way. |
47 | * Generally ensure that negative exponents do inversion correctly. Add |
48 | * table of standard prime-field subgroups. (Binary field subgroups are |
49 | * currently unimplemented but easy to add if anyone ever finds a good one.) |
50 | * |
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51 | * Revision 1.7 2004/03/27 17:54:11 mdw |
52 | * Standard curves and curve checking. |
53 | * |
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54 | * Revision 1.6 2004/03/23 15:19:32 mdw |
55 | * Test elliptic curves more thoroughly. |
56 | * |
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57 | * Revision 1.5 2004/03/23 12:08:26 mdw |
58 | * Random field-element selection. |
59 | * |
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60 | * Revision 1.4 2004/03/21 22:52:06 mdw |
61 | * Merge and close elliptic curve branch. |
62 | * |
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63 | * Revision 1.3.4.3 2004/03/21 22:39:46 mdw |
64 | * Elliptic curves on binary fields work. |
65 | * |
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66 | * Revision 1.3.4.2 2004/03/20 00:13:31 mdw |
67 | * Projective coordinates for prime curves |
68 | * |
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69 | * Revision 1.3.4.1 2003/06/10 13:43:53 mdw |
70 | * Simple (non-projective) curves over prime fields now seem to work. |
71 | * |
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72 | * Revision 1.3 2003/05/15 23:25:59 mdw |
73 | * Make elliptic curve stuff build. |
74 | * |
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75 | * Revision 1.2 2002/01/13 13:48:44 mdw |
76 | * Further progress. |
77 | * |
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78 | * Revision 1.1 2001/04/29 18:12:33 mdw |
79 | * Prototype version. |
80 | * |
81 | */ |
82 | |
83 | /*----- Header files ------------------------------------------------------*/ |
84 | |
85 | #include <mLib/sub.h> |
86 | |
87 | #include "field.h" |
88 | #include "mpmont.h" |
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89 | #include "mprand.h" |
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90 | |
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91 | /*----- Main code ---------------------------------------------------------*/ |
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92 | |
93 | typedef struct fctx { |
94 | field f; |
95 | mpmont mm; |
96 | } fctx; |
97 | |
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98 | /* --- Field operations --- */ |
99 | |
100 | static void fdestroy(field *ff) |
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101 | { fctx *f = (fctx *)ff; mpmont_destroy(&f->mm); DESTROY(f); } |
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102 | |
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103 | static mp *frand(field *ff, mp *d, grand *r) |
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104 | { fctx *f = (fctx *)ff; return (mprand_range(d, f->mm.m, r, 0)); } |
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105 | |
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106 | static mp *fin(field *ff, mp *d, mp *x) { |
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107 | fctx *f = (fctx *)ff; |
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108 | mp_div(0, &d, x, f->mm.m); |
109 | return (mpmont_mul(&f->mm, d, d, f->mm.r2)); |
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110 | } |
111 | |
112 | static mp *fout(field *ff, mp *d, mp *x) |
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113 | { fctx *f = (fctx *)ff; return (mpmont_reduce(&f->mm, d, x)); } |
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114 | |
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115 | static int fzerop(field *ff, mp *x) { return (!MP_LEN(x)); } |
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116 | |
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117 | static mp *fneg(field *ff, mp *d, mp *x) |
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118 | { fctx *f = (fctx *)ff; return (mp_sub(d, f->mm.m, x)); } |
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119 | |
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120 | static mp *fadd(field *ff, mp *d, mp *x, mp *y) { |
121 | fctx *f = (fctx *)ff; d = mp_add(d, x, y); |
122 | if (d->f & MP_NEG) d = mp_add(d, d, f->mm.m); |
123 | else if (MP_CMP(d, >, f->mm.m)) d = mp_sub(d, d, f->mm.m); |
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124 | return (d); |
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125 | } |
126 | |
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127 | static mp *fsub(field *ff, mp *d, mp *x, mp *y) { |
128 | fctx *f = (fctx *)ff; d = mp_sub(d, x, y); |
129 | if (d->f & MP_NEG) d = mp_add(d, d, f->mm.m); |
130 | else if (MP_CMP(d, >, f->mm.m)) d = mp_sub(d, d, f->mm.m); |
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131 | return (d); |
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132 | } |
133 | |
134 | static mp *fmul(field *ff, mp *d, mp *x, mp *y) |
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135 | { fctx *f = (fctx *)ff; return (mpmont_mul(&f->mm, d, x, y)); } |
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136 | |
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137 | static mp *fsqr(field *ff, mp *d, mp *x) { |
138 | fctx *f = (fctx *)ff; d = mp_sqr(d, x); |
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139 | return (mpmont_reduce(&f->mm, d, d)); |
140 | } |
141 | |
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142 | static mp *finv(field *ff, mp *d, mp *x) { |
143 | fctx *f = (fctx *)ff; d = mpmont_reduce(&f->mm, d, x); |
144 | mp_gcd(0, 0, &d, f->mm.m, d); return (mpmont_mul(&f->mm, d, d, f->mm.r2)); |
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145 | } |
146 | |
147 | static mp *freduce(field *ff, mp *d, mp *x) |
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148 | { fctx *f = (fctx *)ff; mp_div(0, &d, x, f->mm.m); return (d); } |
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149 | |
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150 | static mp *fsqrt(field *ff, mp *d, mp *x) { |
151 | fctx *f = (fctx *)ff; d = mpmont_reduce(&f->mm, d, x); |
152 | d = mp_modsqrt(d, d, f->mm.m); if (!d) return (d); |
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153 | return (mpmont_mul(&f->mm, d, d, f->mm.r2)); |
154 | } |
155 | |
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156 | static mp *fdbl(field *ff, mp *d, mp *x) { |
157 | fctx *f = (fctx *)ff; d = mp_lsl(d, x, 1); |
158 | if (MP_CMP(d, >, f->mm.m)) d = mp_sub(d, d, f->mm.m); |
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159 | return (d); |
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160 | } |
161 | |
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162 | static mp *ftpl(field *ff, mp *d, mp *x) { |
163 | fctx *f = (fctx *)ff; MP_DEST(d, MP_LEN(x) + 1, x->f); |
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164 | MPX_UMULN(d->v, d->vl, x->v, x->vl, 3); |
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165 | while (MP_CMP(d, >, f->mm.m)) d = mp_sub(d, d, f->mm.m); |
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166 | return (d); |
167 | } |
168 | |
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169 | static mp *fqdl(field *ff, mp *d, mp *x) { |
170 | fctx *f = (fctx *)ff; d = mp_lsl(d, x, 2); |
171 | while (MP_CMP(d, >, f->mm.m)) d = mp_sub(d, d, f->mm.m); |
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172 | return (d); |
173 | } |
174 | |
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175 | static mp *fhlv(field *ff, mp *d, mp *x) { |
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176 | fctx *f = (fctx *)ff; |
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177 | if (!MP_LEN(x)) { MP_COPY(x); MP_DROP(d); return (x); } |
178 | if (x->v[0] & 1) { d = mp_add(d, x, f->mm.m); x = d; } |
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179 | return (mp_lsr(d, x, 1)); |
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180 | } |
181 | |
182 | /* --- Field operations table --- */ |
183 | |
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184 | static const field_ops fops = { |
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185 | FTY_PRIME, "prime", |
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186 | fdestroy, frand, field_stdsamep, |
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187 | fin, fout, |
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188 | fzerop, fneg, fadd, fsub, fmul, fsqr, finv, freduce, fsqrt, |
189 | 0, |
190 | fdbl, ftpl, fqdl, fhlv |
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191 | }; |
192 | |
193 | /* --- @field_prime@ --- * |
194 | * |
195 | * Arguments: @mp *p@ = the characteristic of the field |
196 | * |
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197 | * Returns: A pointer to the field or null. |
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198 | * |
199 | * Use: Creates a field structure for a prime field of size %$p$%, |
200 | * using Montgomery reduction for arithmetic. |
201 | */ |
202 | |
203 | field *field_prime(mp *p) |
204 | { |
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205 | fctx *f; |
206 | |
207 | if (!MP_ISPOS(p) || !MP_ISODD(p)) |
208 | return (0); |
209 | f = CREATE(fctx); |
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210 | f->f.ops = &fops; |
211 | mpmont_create(&f->mm, p); |
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212 | f->f.zero = MP_ZERO; |
213 | f->f.one = f->mm.r; |
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214 | f->f.m = f->mm.m; |
215 | f->f.nbits = mp_bits(p); |
216 | f->f.noctets = (f->f.nbits + 7) >> 3; |
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217 | return (&f->f); |
218 | } |
219 | |
220 | /*----- That's all, folks -------------------------------------------------*/ |