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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" |
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35 | #include "field-guts.h" |
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36 | #include "mprand.h" |
37 | |
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38 | /*----- Main code ---------------------------------------------------------*/ |
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39 | |
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40 | /* --- Field operations --- */ |
41 | |
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42 | static void fdestroy(field *ff) { |
43 | fctx_niceprime *f = (fctx_niceprime *)ff; |
44 | mpreduce_destroy(&f->r); |
45 | DESTROY(f); |
46 | } |
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47 | |
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48 | static mp *frand(field *ff, mp *d, grand *r) { |
49 | fctx_niceprime *f = (fctx_niceprime *)ff; |
50 | return (mprand_range(d, f->r.p, r, 0)); |
51 | } |
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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 | |
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55 | static mp *fneg(field *ff, mp *d, mp *x) { |
56 | fctx_niceprime *f = (fctx_niceprime *)ff; |
57 | return (mp_sub(d, f->r.p, x)); |
58 | } |
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59 | |
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60 | static mp *fadd(field *ff, mp *d, mp *x, mp *y) { |
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61 | fctx_niceprime *f = (fctx_niceprime *)ff; d = mp_add(d, x, y); |
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62 | if (MP_NEGP(d)) d = mp_add(d, d, f->r.p); |
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63 | else if (MP_CMP(d, >, f->r.p)) d = mp_sub(d, d, f->r.p); |
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64 | return (d); |
65 | } |
66 | |
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67 | static mp *fsub(field *ff, mp *d, mp *x, mp *y) { |
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68 | fctx_niceprime *f = (fctx_niceprime *)ff; d = mp_sub(d, x, y); |
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69 | if (MP_NEGP(d)) d = mp_add(d, d, f->r.p); |
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70 | else if (MP_CMP(d, >, f->r.p)) d = mp_sub(d, d, f->r.p); |
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71 | return (d); |
72 | } |
73 | |
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74 | static mp *fmul(field *ff, mp *d, mp *x, mp *y) { |
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75 | fctx_niceprime *f = (fctx_niceprime *)ff; d = mp_mul(d, x, y); |
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76 | return (mpreduce_do(&f->r, d, d)); |
77 | } |
78 | |
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79 | static mp *fsqr(field *ff, mp *d, mp *x) { |
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80 | fctx_niceprime *f = (fctx_niceprime *)ff; d = mp_sqr(d, x); |
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81 | return (mpreduce_do(&f->r, d, d)); |
82 | } |
83 | |
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84 | static mp *finv(field *ff, mp *d, mp *x) { |
85 | fctx_niceprime *f = (fctx_niceprime *)ff; |
86 | d = mp_modinv(d, x, f->r.p); |
87 | return (d); |
88 | } |
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89 | |
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90 | static mp *freduce(field *ff, mp *d, mp *x) { |
91 | fctx_niceprime *f = (fctx_niceprime *)ff; |
92 | return (mpreduce_do(&f->r, d, x)); |
93 | } |
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94 | |
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95 | static mp *fsqrt(field *ff, mp *d, mp *x) { |
96 | fctx_niceprime *f = (fctx_niceprime *)ff; |
97 | return (mp_modsqrt(d, x, f->r.p)); |
98 | } |
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99 | |
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100 | static mp *fdbl(field *ff, mp *d, mp *x) { |
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101 | fctx_niceprime *f = (fctx_niceprime *)ff; d = mp_lsl(d, x, 1); |
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102 | if (MP_CMP(d, >=, f->r.p)) d = mp_sub(d, d, f->r.p); |
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103 | return (d); |
104 | } |
105 | |
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106 | static mp *ftpl(field *ff, mp *d, mp *x) { |
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107 | fctx_niceprime *f = (fctx_niceprime *)ff; MP_DEST(d, MP_LEN(x) + 1, x->f); |
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108 | MPX_UMULN(d->v, d->vl, x->v, x->vl, 3); d->f &= ~MP_UNDEF; |
109 | while (MP_CMP(d, >=, f->r.p)) d = mp_sub(d, d, f->r.p); |
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110 | return (d); |
111 | } |
112 | |
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113 | static mp *fqdl(field *ff, mp *d, mp *x) { |
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114 | fctx_niceprime *f = (fctx_niceprime *)ff; d = mp_lsl(d, x, 2); |
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115 | while (MP_CMP(d, >=, f->r.p)) d = mp_sub(d, d, f->r.p); |
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116 | return (d); |
117 | } |
118 | |
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119 | static mp *fhlv(field *ff, mp *d, mp *x) { |
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120 | fctx_niceprime *f = (fctx_niceprime *)ff; |
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121 | if (MP_ZEROP(x)) { MP_COPY(x); MP_DROP(d); return (x); } |
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122 | if (x->v[0] & 1) { d = mp_add(d, x, f->r.p); x = d; } |
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123 | return (mp_lsr(d, x, 1)); |
124 | } |
125 | |
126 | /* --- Field operations table --- */ |
127 | |
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128 | static const field_ops fops = { |
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129 | FTY_PRIME, "niceprime", |
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130 | fdestroy, frand, field_stdsamep, |
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131 | freduce, field_id, |
132 | fzerop, fneg, fadd, fsub, fmul, fsqr, finv, freduce, fsqrt, |
133 | 0, |
134 | fdbl, ftpl, fqdl, fhlv |
135 | }; |
136 | |
137 | /* --- @field_niceprime@ --- * |
138 | * |
139 | * Arguments: @mp *p@ = the characteristic of the field |
140 | * |
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141 | * Returns: A pointer to the field, or null. |
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142 | * |
143 | * Use: Creates a field structure for a prime field of size %$p$%, |
144 | * using efficient reduction for nice primes. |
145 | */ |
146 | |
147 | field *field_niceprime(mp *p) |
148 | { |
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149 | fctx_niceprime *f = CREATE(fctx_niceprime); |
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150 | f->f.ops = &fops; |
151 | f->f.zero = MP_ZERO; |
152 | f->f.one = MP_ONE; |
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153 | f->f.nbits = mp_bits(p); |
154 | f->f.noctets = (f->f.nbits + 7) >> 3; |
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155 | if (mpreduce_create(&f->r, p)) { |
156 | DESTROY(f); |
157 | return (0); |
158 | } |
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159 | f->f.m = f->r.p; |
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160 | f->f.q = f->r.p; |
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161 | return (&f->f); |
162 | } |
163 | |
164 | /*----- That's all, folks -------------------------------------------------*/ |