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1 | /* -*-c-*- |
2 | * |
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3 | * Prime fields with efficient reduction for special-form primes |
4 | * |
5 | * (c) 2004 Straylight/Edgeware |
6 | */ |
7 | |
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8 | /*----- Licensing notice --------------------------------------------------* |
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9 | * |
10 | * This file is part of Catacomb. |
11 | * |
12 | * Catacomb is free software; you can redistribute it and/or modify |
13 | * it under the terms of the GNU Library General Public License as |
14 | * published by the Free Software Foundation; either version 2 of the |
15 | * License, or (at your option) any later version. |
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16 | * |
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17 | * Catacomb is distributed in the hope that it will be useful, |
18 | * but WITHOUT ANY WARRANTY; without even the implied warranty of |
19 | * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the |
20 | * GNU Library General Public License for more details. |
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21 | * |
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22 | * You should have received a copy of the GNU Library General Public |
23 | * License along with Catacomb; if not, write to the Free |
24 | * Software Foundation, Inc., 59 Temple Place - Suite 330, Boston, |
25 | * MA 02111-1307, USA. |
26 | */ |
27 | |
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28 | /*----- Header files ------------------------------------------------------*/ |
29 | |
30 | #include <mLib/sub.h> |
31 | |
32 | #include "field.h" |
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33 | #include "field-guts.h" |
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34 | #include "mprand.h" |
35 | |
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36 | /*----- Main code ---------------------------------------------------------*/ |
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37 | |
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38 | /* --- Field operations --- */ |
39 | |
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40 | static void fdestroy(field *ff) { |
41 | fctx_niceprime *f = (fctx_niceprime *)ff; |
42 | mpreduce_destroy(&f->r); |
43 | DESTROY(f); |
44 | } |
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45 | |
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46 | static mp *frand(field *ff, mp *d, grand *r) { |
47 | fctx_niceprime *f = (fctx_niceprime *)ff; |
48 | return (mprand_range(d, f->r.p, r, 0)); |
49 | } |
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50 | |
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51 | static int fzerop(field *ff, mp *x) { return (MP_ZEROP(x)); } |
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52 | |
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53 | static mp *fneg(field *ff, mp *d, mp *x) { |
54 | fctx_niceprime *f = (fctx_niceprime *)ff; |
55 | return (mp_sub(d, f->r.p, x)); |
56 | } |
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57 | |
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58 | static mp *fadd(field *ff, mp *d, mp *x, mp *y) { |
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59 | fctx_niceprime *f = (fctx_niceprime *)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) { |
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66 | fctx_niceprime *f = (fctx_niceprime *)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) { |
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73 | fctx_niceprime *f = (fctx_niceprime *)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) { |
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78 | fctx_niceprime *f = (fctx_niceprime *)ff; d = mp_sqr(d, x); |
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79 | return (mpreduce_do(&f->r, d, d)); |
80 | } |
81 | |
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82 | static mp *finv(field *ff, mp *d, mp *x) { |
83 | fctx_niceprime *f = (fctx_niceprime *)ff; |
84 | d = mp_modinv(d, x, f->r.p); |
85 | return (d); |
86 | } |
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87 | |
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88 | static mp *freduce(field *ff, mp *d, mp *x) { |
89 | fctx_niceprime *f = (fctx_niceprime *)ff; |
90 | return (mpreduce_do(&f->r, d, x)); |
91 | } |
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92 | |
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93 | static mp *fsqrt(field *ff, mp *d, mp *x) { |
94 | fctx_niceprime *f = (fctx_niceprime *)ff; |
95 | return (mp_modsqrt(d, x, f->r.p)); |
96 | } |
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97 | |
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98 | static mp *fdbl(field *ff, mp *d, mp *x) { |
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99 | fctx_niceprime *f = (fctx_niceprime *)ff; d = mp_lsl(d, x, 1); |
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100 | if (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 *ftpl(field *ff, mp *d, mp *x) { |
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105 | fctx_niceprime *f = (fctx_niceprime *)ff; MP_DEST(d, MP_LEN(x) + 1, x->f); |
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106 | MPX_UMULN(d->v, d->vl, x->v, x->vl, 3); d->f &= ~MP_UNDEF; |
107 | while (MP_CMP(d, >=, f->r.p)) d = mp_sub(d, d, f->r.p); |
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108 | return (d); |
109 | } |
110 | |
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111 | static mp *fqdl(field *ff, mp *d, mp *x) { |
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112 | fctx_niceprime *f = (fctx_niceprime *)ff; d = mp_lsl(d, x, 2); |
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113 | while (MP_CMP(d, >=, f->r.p)) d = mp_sub(d, d, f->r.p); |
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114 | return (d); |
115 | } |
116 | |
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117 | static mp *fhlv(field *ff, mp *d, mp *x) { |
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118 | fctx_niceprime *f = (fctx_niceprime *)ff; |
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119 | if (MP_ZEROP(x)) { MP_COPY(x); MP_DROP(d); return (x); } |
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120 | if (x->v[0] & 1) { d = mp_add(d, x, f->r.p); x = d; } |
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121 | return (mp_lsr(d, x, 1)); |
122 | } |
123 | |
124 | /* --- Field operations table --- */ |
125 | |
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126 | static const field_ops fops = { |
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127 | FTY_PRIME, "niceprime", |
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128 | fdestroy, frand, field_stdsamep, |
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129 | freduce, field_id, |
130 | fzerop, fneg, fadd, fsub, fmul, fsqr, finv, freduce, fsqrt, |
131 | 0, |
132 | fdbl, ftpl, fqdl, fhlv |
133 | }; |
134 | |
135 | /* --- @field_niceprime@ --- * |
136 | * |
137 | * Arguments: @mp *p@ = the characteristic of the field |
138 | * |
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139 | * Returns: A pointer to the field, or null. |
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140 | * |
141 | * Use: Creates a field structure for a prime field of size %$p$%, |
142 | * using efficient reduction for nice primes. |
143 | */ |
144 | |
145 | field *field_niceprime(mp *p) |
146 | { |
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147 | fctx_niceprime *f = CREATE(fctx_niceprime); |
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148 | f->f.ops = &fops; |
149 | f->f.zero = MP_ZERO; |
150 | f->f.one = MP_ONE; |
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151 | f->f.nbits = mp_bits(p); |
152 | f->f.noctets = (f->f.nbits + 7) >> 3; |
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153 | if (mpreduce_create(&f->r, p)) { |
154 | DESTROY(f); |
155 | return (0); |
156 | } |
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157 | f->f.m = f->r.p; |
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158 | f->f.q = f->r.p; |
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159 | return (&f->f); |
160 | } |
161 | |
162 | /*----- That's all, folks -------------------------------------------------*/ |