| 1 | /* -*-c-*- |
| 2 | * |
| 3 | * Prime fields with efficient reduction for special-form primes |
| 4 | * |
| 5 | * (c) 2004 Straylight/Edgeware |
| 6 | */ |
| 7 | |
| 8 | /*----- Licensing notice --------------------------------------------------* |
| 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. |
| 16 | * |
| 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. |
| 21 | * |
| 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 | |
| 28 | /*----- Header files ------------------------------------------------------*/ |
| 29 | |
| 30 | #include <mLib/sub.h> |
| 31 | |
| 32 | #include "field.h" |
| 33 | #include "field-guts.h" |
| 34 | #include "mprand.h" |
| 35 | |
| 36 | /*----- Main code ---------------------------------------------------------*/ |
| 37 | |
| 38 | /* --- Field operations --- */ |
| 39 | |
| 40 | static void fdestroy(field *ff) { |
| 41 | fctx_niceprime *f = (fctx_niceprime *)ff; |
| 42 | mpreduce_destroy(&f->r); |
| 43 | DESTROY(f); |
| 44 | } |
| 45 | |
| 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 | } |
| 50 | |
| 51 | static int fzerop(field *ff, mp *x) { return (MP_ZEROP(x)); } |
| 52 | |
| 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 | } |
| 57 | |
| 58 | static mp *fadd(field *ff, mp *d, mp *x, mp *y) { |
| 59 | fctx_niceprime *f = (fctx_niceprime *)ff; d = mp_add(d, x, y); |
| 60 | if (MP_NEGP(d)) d = mp_add(d, d, f->r.p); |
| 61 | else if (MP_CMP(d, >, f->r.p)) d = mp_sub(d, d, f->r.p); |
| 62 | return (d); |
| 63 | } |
| 64 | |
| 65 | static mp *fsub(field *ff, mp *d, mp *x, mp *y) { |
| 66 | fctx_niceprime *f = (fctx_niceprime *)ff; d = mp_sub(d, x, y); |
| 67 | if (MP_NEGP(d)) d = mp_add(d, d, f->r.p); |
| 68 | else if (MP_CMP(d, >, f->r.p)) d = mp_sub(d, d, f->r.p); |
| 69 | return (d); |
| 70 | } |
| 71 | |
| 72 | static mp *fmul(field *ff, mp *d, mp *x, mp *y) { |
| 73 | fctx_niceprime *f = (fctx_niceprime *)ff; d = mp_mul(d, x, y); |
| 74 | return (mpreduce_do(&f->r, d, d)); |
| 75 | } |
| 76 | |
| 77 | static mp *fsqr(field *ff, mp *d, mp *x) { |
| 78 | fctx_niceprime *f = (fctx_niceprime *)ff; d = mp_sqr(d, x); |
| 79 | return (mpreduce_do(&f->r, d, d)); |
| 80 | } |
| 81 | |
| 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 | } |
| 87 | |
| 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 | } |
| 92 | |
| 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 | } |
| 97 | |
| 98 | static mp *fdbl(field *ff, mp *d, mp *x) { |
| 99 | fctx_niceprime *f = (fctx_niceprime *)ff; d = mp_lsl(d, x, 1); |
| 100 | if (MP_CMP(d, >=, f->r.p)) d = mp_sub(d, d, f->r.p); |
| 101 | return (d); |
| 102 | } |
| 103 | |
| 104 | static mp *ftpl(field *ff, mp *d, mp *x) { |
| 105 | fctx_niceprime *f = (fctx_niceprime *)ff; MP_DEST(d, MP_LEN(x) + 1, x->f); |
| 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); |
| 108 | return (d); |
| 109 | } |
| 110 | |
| 111 | static mp *fqdl(field *ff, mp *d, mp *x) { |
| 112 | fctx_niceprime *f = (fctx_niceprime *)ff; d = mp_lsl(d, x, 2); |
| 113 | while (MP_CMP(d, >=, f->r.p)) d = mp_sub(d, d, f->r.p); |
| 114 | return (d); |
| 115 | } |
| 116 | |
| 117 | static mp *fhlv(field *ff, mp *d, mp *x) { |
| 118 | fctx_niceprime *f = (fctx_niceprime *)ff; |
| 119 | if (MP_ZEROP(x)) { MP_COPY(x); MP_DROP(d); return (x); } |
| 120 | if (x->v[0] & 1) { d = mp_add(d, x, f->r.p); x = d; } |
| 121 | return (mp_lsr(d, x, 1)); |
| 122 | } |
| 123 | |
| 124 | /* --- Field operations table --- */ |
| 125 | |
| 126 | static const field_ops fops = { |
| 127 | FTY_PRIME, "niceprime", |
| 128 | fdestroy, frand, field_stdsamep, |
| 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 | * |
| 139 | * Returns: A pointer to the field, or null. |
| 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 | { |
| 147 | fctx_niceprime *f = CREATE(fctx_niceprime); |
| 148 | f->f.ops = &fops; |
| 149 | f->f.zero = MP_ZERO; |
| 150 | f->f.one = MP_ONE; |
| 151 | f->f.nbits = mp_bits(p); |
| 152 | f->f.noctets = (f->f.nbits + 7) >> 3; |
| 153 | if (mpreduce_create(&f->r, p)) { |
| 154 | DESTROY(f); |
| 155 | return (0); |
| 156 | } |
| 157 | f->f.m = f->r.p; |
| 158 | f->f.q = f->r.p; |
| 159 | return (&f->f); |
| 160 | } |
| 161 | |
| 162 | /*----- That's all, folks -------------------------------------------------*/ |