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1 | /* -*-c-*- |
2 | * |
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3 | * Prime fields with Montgomery arithmetic |
4 | * |
5 | * (c) 2001 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 "mprand.h" |
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34 | #include "field-guts.h" |
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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_prime *f = (fctx_prime *)ff; |
42 | mpmont_destroy(&f->mm); |
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_prime *f = (fctx_prime *)ff; |
48 | return (mprand_range(d, f->mm.m, r, 0)); |
49 | } |
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50 | |
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51 | static mp *fin(field *ff, mp *d, mp *x) { |
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52 | fctx_prime *f = (fctx_prime *)ff; |
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53 | mp_div(0, &d, x, f->mm.m); |
54 | return (mpmont_mul(&f->mm, d, d, f->mm.r2)); |
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55 | } |
56 | |
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57 | static mp *fout(field *ff, mp *d, mp *x) { |
58 | fctx_prime *f = (fctx_prime *)ff; |
59 | return (mpmont_reduce(&f->mm, d, x)); |
60 | } |
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61 | |
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62 | static int fzerop(field *ff, mp *x) { return (MP_ZEROP(x)); } |
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63 | |
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64 | static mp *fneg(field *ff, mp *d, mp *x) { |
65 | fctx_prime *f = (fctx_prime *)ff; |
66 | return (mp_sub(d, f->mm.m, x)); |
67 | } |
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68 | |
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69 | static mp *fadd(field *ff, mp *d, mp *x, mp *y) { |
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70 | fctx_prime *f = (fctx_prime *)ff; d = mp_add(d, x, y); |
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71 | if (MP_NEGP(d)) d = mp_add(d, d, f->mm.m); |
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72 | else if (MP_CMP(d, >, f->mm.m)) d = mp_sub(d, d, f->mm.m); |
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73 | return (d); |
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74 | } |
75 | |
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76 | static mp *fsub(field *ff, mp *d, mp *x, mp *y) { |
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77 | fctx_prime *f = (fctx_prime *)ff; d = mp_sub(d, x, y); |
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78 | if (MP_NEGP(d)) d = mp_add(d, d, f->mm.m); |
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79 | else if (MP_CMP(d, >, f->mm.m)) d = mp_sub(d, d, f->mm.m); |
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80 | return (d); |
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81 | } |
82 | |
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83 | static mp *fmul(field *ff, mp *d, mp *x, mp *y) { |
84 | fctx_prime *f = (fctx_prime *)ff; |
85 | return (mpmont_mul(&f->mm, d, x, y)); |
86 | } |
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87 | |
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88 | static mp *fsqr(field *ff, mp *d, mp *x) { |
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89 | fctx_prime *f = (fctx_prime *)ff; d = mp_sqr(d, x); |
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90 | return (mpmont_reduce(&f->mm, d, d)); |
91 | } |
92 | |
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93 | static mp *finv(field *ff, mp *d, mp *x) { |
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94 | fctx_prime *f = (fctx_prime *)ff; d = mpmont_reduce(&f->mm, d, x); |
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95 | d = mp_modinv(d, d, f->mm.m); return (mpmont_mul(&f->mm, d, d, f->mm.r2)); |
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96 | } |
97 | |
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98 | static mp *freduce(field *ff, mp *d, mp *x) { |
99 | fctx_prime *f = (fctx_prime *)ff; |
100 | mp_div(0, &d, x, f->mm.m); |
101 | return (d); |
102 | } |
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103 | |
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104 | static mp *fsqrt(field *ff, mp *d, mp *x) { |
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105 | fctx_prime *f = (fctx_prime *)ff; d = mpmont_reduce(&f->mm, d, x); |
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106 | d = mp_modsqrt(d, d, f->mm.m); if (!d) return (d); |
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107 | return (mpmont_mul(&f->mm, d, d, f->mm.r2)); |
108 | } |
109 | |
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110 | static mp *fdbl(field *ff, mp *d, mp *x) { |
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111 | fctx_prime *f = (fctx_prime *)ff; d = mp_lsl(d, x, 1); |
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112 | if (MP_CMP(d, >=, f->mm.m)) d = mp_sub(d, d, f->mm.m); |
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113 | return (d); |
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114 | } |
115 | |
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116 | static mp *ftpl(field *ff, mp *d, mp *x) { |
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117 | fctx_prime *f = (fctx_prime *)ff; MP_DEST(d, MP_LEN(x) + 1, x->f); |
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118 | MPX_UMULN(d->v, d->vl, x->v, x->vl, 3); d->f &= ~MP_UNDEF; |
119 | while (MP_CMP(d, >=, f->mm.m)) d = mp_sub(d, d, f->mm.m); |
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120 | return (d); |
121 | } |
122 | |
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123 | static mp *fqdl(field *ff, mp *d, mp *x) { |
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124 | fctx_prime *f = (fctx_prime *)ff; d = mp_lsl(d, x, 2); |
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125 | while (MP_CMP(d, >=, f->mm.m)) d = mp_sub(d, d, f->mm.m); |
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126 | return (d); |
127 | } |
128 | |
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129 | static mp *fhlv(field *ff, mp *d, mp *x) { |
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130 | fctx_prime *f = (fctx_prime *)ff; |
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131 | if (MP_ZEROP(x)) { MP_COPY(x); MP_DROP(d); return (x); } |
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132 | if (x->v[0] & 1) { d = mp_add(d, x, f->mm.m); x = d; } |
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133 | return (mp_lsr(d, x, 1)); |
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134 | } |
135 | |
136 | /* --- Field operations table --- */ |
137 | |
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138 | static const field_ops fops = { |
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139 | FTY_PRIME, "prime", |
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140 | fdestroy, frand, field_stdsamep, |
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141 | fin, fout, |
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142 | fzerop, fneg, fadd, fsub, fmul, fsqr, finv, freduce, fsqrt, |
143 | 0, |
144 | fdbl, ftpl, fqdl, fhlv |
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145 | }; |
146 | |
147 | /* --- @field_prime@ --- * |
148 | * |
149 | * Arguments: @mp *p@ = the characteristic of the field |
150 | * |
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151 | * Returns: A pointer to the field or null. |
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152 | * |
153 | * Use: Creates a field structure for a prime field of size %$p$%, |
154 | * using Montgomery reduction for arithmetic. |
155 | */ |
156 | |
157 | field *field_prime(mp *p) |
158 | { |
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159 | fctx_prime *f; |
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160 | |
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161 | f = CREATE(fctx_prime); |
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162 | f->f.ops = &fops; |
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163 | if (mpmont_create(&f->mm, p)) { |
164 | DESTROY(f); |
165 | return (0); |
166 | } |
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167 | f->f.zero = MP_ZERO; |
168 | f->f.one = f->mm.r; |
432c4e18 |
169 | f->f.m = f->mm.m; |
170 | f->f.nbits = mp_bits(p); |
171 | f->f.noctets = (f->f.nbits + 7) >> 3; |
1d7857e7 |
172 | f->f.q = f->mm.m; |
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173 | return (&f->f); |
174 | } |
175 | |
176 | /*----- That's all, folks -------------------------------------------------*/ |