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1 | /* -*-c-*- |
2 | * |
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3 | * $Id$ |
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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 | |
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30 | /*----- Header files ------------------------------------------------------*/ |
31 | |
32 | #include <mLib/sub.h> |
33 | |
34 | #include "field.h" |
35 | #include "mpreduce.h" |
36 | #include "mprand.h" |
37 | |
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38 | /*----- Main code ---------------------------------------------------------*/ |
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39 | |
40 | typedef struct fctx { |
41 | field f; |
42 | mpreduce r; |
43 | } fctx; |
44 | |
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45 | /* --- Field operations --- */ |
46 | |
47 | static void fdestroy(field *ff) |
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48 | { fctx *f = (fctx *)ff; mpreduce_destroy(&f->r); DESTROY(f); } |
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49 | |
50 | static mp *frand(field *ff, mp *d, grand *r) |
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51 | { fctx *f = (fctx *)ff; return (mprand_range(d, f->r.p, r, 0)); } |
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52 | |
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53 | static int fzerop(field *ff, mp *x) { return (MP_ZEROP(x)); } |
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54 | |
55 | static mp *fneg(field *ff, mp *d, mp *x) |
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56 | { fctx *f = (fctx *)ff; return (mp_sub(d, f->r.p, x)); } |
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57 | |
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58 | static mp *fadd(field *ff, mp *d, mp *x, mp *y) { |
59 | fctx *f = (fctx *)ff; d = mp_add(d, x, y); |
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60 | if (MP_NEGP(d)) d = mp_add(d, d, f->r.p); |
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61 | else if (MP_CMP(d, >, f->r.p)) d = mp_sub(d, d, f->r.p); |
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62 | return (d); |
63 | } |
64 | |
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65 | static mp *fsub(field *ff, mp *d, mp *x, mp *y) { |
66 | fctx *f = (fctx *)ff; d = mp_sub(d, x, y); |
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67 | if (MP_NEGP(d)) d = mp_add(d, d, f->r.p); |
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68 | else if (MP_CMP(d, >, f->r.p)) d = mp_sub(d, d, f->r.p); |
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69 | return (d); |
70 | } |
71 | |
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72 | static mp *fmul(field *ff, mp *d, mp *x, mp *y) { |
73 | fctx *f = (fctx *)ff; d = mp_mul(d, x, y); |
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74 | return (mpreduce_do(&f->r, d, d)); |
75 | } |
76 | |
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77 | static mp *fsqr(field *ff, mp *d, mp *x) { |
78 | fctx *f = (fctx *)ff; d = mp_sqr(d, x); |
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79 | return (mpreduce_do(&f->r, d, d)); |
80 | } |
81 | |
82 | static mp *finv(field *ff, mp *d, mp *x) |
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83 | { fctx *f = (fctx *)ff; d = mp_modinv(d, x, f->r.p); return (d); } |
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84 | |
85 | static mp *freduce(field *ff, mp *d, mp *x) |
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86 | { fctx *f = (fctx *)ff; return (mpreduce_do(&f->r, d, x)); } |
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87 | |
88 | static mp *fsqrt(field *ff, mp *d, mp *x) |
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89 | { fctx *f = (fctx *)ff; return (mp_modsqrt(d, x, f->r.p)); } |
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90 | |
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91 | static mp *fdbl(field *ff, mp *d, mp *x) { |
92 | fctx *f = (fctx *)ff; d = mp_lsl(d, x, 1); |
93 | if (MP_CMP(d, >, f->r.p)) d = mp_sub(d, d, f->r.p); |
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94 | return (d); |
95 | } |
96 | |
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97 | static mp *ftpl(field *ff, mp *d, mp *x) { |
98 | fctx *f = (fctx *)ff; MP_DEST(d, MP_LEN(x) + 1, x->f); |
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99 | MPX_UMULN(d->v, d->vl, x->v, x->vl, 3); |
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100 | while (MP_CMP(d, >, f->r.p)) d = mp_sub(d, d, f->r.p); |
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101 | return (d); |
102 | } |
103 | |
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104 | static mp *fqdl(field *ff, mp *d, mp *x) { |
105 | fctx *f = (fctx *)ff; d = mp_lsl(d, x, 2); |
106 | while (MP_CMP(d, >, f->r.p)) d = mp_sub(d, d, f->r.p); |
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107 | return (d); |
108 | } |
109 | |
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110 | static mp *fhlv(field *ff, mp *d, mp *x) { |
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111 | fctx *f = (fctx *)ff; |
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112 | if (MP_ZEROP(x)) { MP_COPY(x); MP_DROP(d); return (x); } |
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113 | if (x->v[0] & 1) { d = mp_add(d, x, f->r.p); x = d; } |
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114 | return (mp_lsr(d, x, 1)); |
115 | } |
116 | |
117 | /* --- Field operations table --- */ |
118 | |
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119 | static const field_ops fops = { |
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120 | FTY_PRIME, "niceprime", |
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121 | fdestroy, frand, field_stdsamep, |
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122 | freduce, field_id, |
123 | fzerop, fneg, fadd, fsub, fmul, fsqr, finv, freduce, fsqrt, |
124 | 0, |
125 | fdbl, ftpl, fqdl, fhlv |
126 | }; |
127 | |
128 | /* --- @field_niceprime@ --- * |
129 | * |
130 | * Arguments: @mp *p@ = the characteristic of the field |
131 | * |
132 | * Returns: A pointer to the field. |
133 | * |
134 | * Use: Creates a field structure for a prime field of size %$p$%, |
135 | * using efficient reduction for nice primes. |
136 | */ |
137 | |
138 | field *field_niceprime(mp *p) |
139 | { |
140 | fctx *f = CREATE(fctx); |
141 | f->f.ops = &fops; |
142 | f->f.zero = MP_ZERO; |
143 | f->f.one = MP_ONE; |
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144 | f->f.nbits = mp_bits(p); |
145 | f->f.noctets = (f->f.nbits + 7) >> 3; |
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146 | mpreduce_create(&f->r, p); |
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147 | f->f.m = f->r.p; |
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148 | return (&f->f); |
149 | } |
150 | |
151 | /*----- That's all, folks -------------------------------------------------*/ |