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1 | /* -*-c-*- |
2 | * |
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3 | * $Id: f-niceprime.c,v 1.5 2004/04/02 01:03:49 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 1.5 2004/04/02 01:03:49 mdw |
34 | * Miscellaneous constification. |
35 | * |
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36 | * Revision 1.4 2004/04/01 21:28:41 mdw |
37 | * Normal basis support (translates to poly basis internally). Rewrite |
38 | * EC and prime group table generators in awk, so that they can reuse data |
39 | * for repeated constants. |
40 | * |
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41 | * Revision 1.3 2004/04/01 12:50:09 mdw |
42 | * Add cyclic group abstraction, with test code. Separate off exponentation |
43 | * functions for better static linking. Fix a buttload of bugs on the way. |
44 | * Generally ensure that negative exponents do inversion correctly. Add |
45 | * table of standard prime-field subgroups. (Binary field subgroups are |
46 | * currently unimplemented but easy to add if anyone ever finds a good one.) |
47 | * |
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48 | * Revision 1.2 2004/03/27 17:54:11 mdw |
49 | * Standard curves and curve checking. |
50 | * |
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51 | * Revision 1.1 2004/03/27 00:04:46 mdw |
52 | * Implement efficient reduction for pleasant-looking primes. |
53 | * |
54 | */ |
55 | |
56 | /*----- Header files ------------------------------------------------------*/ |
57 | |
58 | #include <mLib/sub.h> |
59 | |
60 | #include "field.h" |
61 | #include "mpreduce.h" |
62 | #include "mprand.h" |
63 | |
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64 | /*----- Main code ---------------------------------------------------------*/ |
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65 | |
66 | typedef struct fctx { |
67 | field f; |
68 | mpreduce r; |
69 | } fctx; |
70 | |
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71 | /* --- Field operations --- */ |
72 | |
73 | static void fdestroy(field *ff) |
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74 | { fctx *f = (fctx *)ff; mpreduce_destroy(&f->r); DESTROY(f); } |
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75 | |
76 | static mp *frand(field *ff, mp *d, grand *r) |
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77 | { fctx *f = (fctx *)ff; return (mprand_range(d, f->r.p, r, 0)); } |
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78 | |
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79 | static int fzerop(field *ff, mp *x) { return (!MP_LEN(x)); } |
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80 | |
81 | static mp *fneg(field *ff, mp *d, mp *x) |
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82 | { fctx *f = (fctx *)ff; return (mp_sub(d, f->r.p, x)); } |
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83 | |
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84 | static mp *fadd(field *ff, mp *d, mp *x, mp *y) { |
85 | fctx *f = (fctx *)ff; d = mp_add(d, x, y); |
86 | if (d->f & MP_NEG) d = mp_add(d, d, f->r.p); |
87 | else if (MP_CMP(d, >, f->r.p)) d = mp_sub(d, d, f->r.p); |
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88 | return (d); |
89 | } |
90 | |
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91 | static mp *fsub(field *ff, mp *d, mp *x, mp *y) { |
92 | fctx *f = (fctx *)ff; d = mp_sub(d, x, y); |
93 | if (d->f & MP_NEG) d = mp_add(d, d, f->r.p); |
94 | else if (MP_CMP(d, >, f->r.p)) d = mp_sub(d, d, f->r.p); |
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95 | return (d); |
96 | } |
97 | |
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98 | static mp *fmul(field *ff, mp *d, mp *x, mp *y) { |
99 | fctx *f = (fctx *)ff; d = mp_mul(d, x, y); |
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100 | return (mpreduce_do(&f->r, d, d)); |
101 | } |
102 | |
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103 | static mp *fsqr(field *ff, mp *d, mp *x) { |
104 | fctx *f = (fctx *)ff; d = mp_sqr(d, x); |
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105 | return (mpreduce_do(&f->r, d, d)); |
106 | } |
107 | |
108 | static mp *finv(field *ff, mp *d, mp *x) |
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109 | { fctx *f = (fctx *)ff; mp_gcd(0, 0, &d, f->r.p, x); return (d); } |
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110 | |
111 | static mp *freduce(field *ff, mp *d, mp *x) |
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112 | { fctx *f = (fctx *)ff; return (mpreduce_do(&f->r, d, x)); } |
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113 | |
114 | static mp *fsqrt(field *ff, mp *d, mp *x) |
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115 | { fctx *f = (fctx *)ff; return (mp_modsqrt(d, x, f->r.p)); } |
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116 | |
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117 | static mp *fdbl(field *ff, mp *d, mp *x) { |
118 | fctx *f = (fctx *)ff; d = mp_lsl(d, x, 1); |
119 | if (MP_CMP(d, >, f->r.p)) d = mp_sub(d, d, f->r.p); |
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120 | return (d); |
121 | } |
122 | |
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123 | static mp *ftpl(field *ff, mp *d, mp *x) { |
124 | fctx *f = (fctx *)ff; MP_DEST(d, MP_LEN(x) + 1, x->f); |
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125 | MPX_UMULN(d->v, d->vl, x->v, x->vl, 3); |
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126 | while (MP_CMP(d, >, f->r.p)) d = mp_sub(d, d, f->r.p); |
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127 | return (d); |
128 | } |
129 | |
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130 | static mp *fqdl(field *ff, mp *d, mp *x) { |
131 | fctx *f = (fctx *)ff; d = mp_lsl(d, x, 2); |
132 | while (MP_CMP(d, >, f->r.p)) d = mp_sub(d, d, f->r.p); |
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133 | return (d); |
134 | } |
135 | |
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136 | static mp *fhlv(field *ff, mp *d, mp *x) { |
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137 | fctx *f = (fctx *)ff; |
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138 | if (!MP_LEN(x)) { MP_COPY(x); MP_DROP(d); return (x); } |
139 | if (x->v[0] & 1) { d = mp_add(d, x, f->r.p); x = d; } |
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140 | return (mp_lsr(d, x, 1)); |
141 | } |
142 | |
143 | /* --- Field operations table --- */ |
144 | |
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145 | static const field_ops fops = { |
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146 | FTY_PRIME, "niceprime", |
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147 | fdestroy, frand, field_stdsamep, |
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148 | freduce, field_id, |
149 | fzerop, fneg, fadd, fsub, fmul, fsqr, finv, freduce, fsqrt, |
150 | 0, |
151 | fdbl, ftpl, fqdl, fhlv |
152 | }; |
153 | |
154 | /* --- @field_niceprime@ --- * |
155 | * |
156 | * Arguments: @mp *p@ = the characteristic of the field |
157 | * |
158 | * Returns: A pointer to the field. |
159 | * |
160 | * Use: Creates a field structure for a prime field of size %$p$%, |
161 | * using efficient reduction for nice primes. |
162 | */ |
163 | |
164 | field *field_niceprime(mp *p) |
165 | { |
166 | fctx *f = CREATE(fctx); |
167 | f->f.ops = &fops; |
168 | f->f.zero = MP_ZERO; |
169 | f->f.one = MP_ONE; |
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170 | f->f.nbits = mp_bits(p); |
171 | f->f.noctets = (f->f.nbits + 7) >> 3; |
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172 | mpreduce_create(&f->r, p); |
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173 | f->f.m = f->r.p; |
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174 | return (&f->f); |
175 | } |
176 | |
177 | /*----- That's all, folks -------------------------------------------------*/ |