| 1 | /* -*-c-*- |
| 2 | * |
| 3 | * $Id: f-prime.c,v 1.11 2004/04/03 03:32:05 mdw Exp $ |
| 4 | * |
| 5 | * Prime fields with Montgomery arithmetic |
| 6 | * |
| 7 | * (c) 2001 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 | |
| 30 | /*----- Revision history --------------------------------------------------* |
| 31 | * |
| 32 | * $Log: f-prime.c,v $ |
| 33 | * Revision 1.11 2004/04/03 03:32:05 mdw |
| 34 | * General robustification. |
| 35 | * |
| 36 | * Revision 1.10 2004/04/02 01:03:49 mdw |
| 37 | * Miscellaneous constification. |
| 38 | * |
| 39 | * Revision 1.9 2004/04/01 21:28:41 mdw |
| 40 | * Normal basis support (translates to poly basis internally). Rewrite |
| 41 | * EC and prime group table generators in awk, so that they can reuse data |
| 42 | * for repeated constants. |
| 43 | * |
| 44 | * Revision 1.8 2004/04/01 12:50:09 mdw |
| 45 | * Add cyclic group abstraction, with test code. Separate off exponentation |
| 46 | * functions for better static linking. Fix a buttload of bugs on the way. |
| 47 | * Generally ensure that negative exponents do inversion correctly. Add |
| 48 | * table of standard prime-field subgroups. (Binary field subgroups are |
| 49 | * currently unimplemented but easy to add if anyone ever finds a good one.) |
| 50 | * |
| 51 | * Revision 1.7 2004/03/27 17:54:11 mdw |
| 52 | * Standard curves and curve checking. |
| 53 | * |
| 54 | * Revision 1.6 2004/03/23 15:19:32 mdw |
| 55 | * Test elliptic curves more thoroughly. |
| 56 | * |
| 57 | * Revision 1.5 2004/03/23 12:08:26 mdw |
| 58 | * Random field-element selection. |
| 59 | * |
| 60 | * Revision 1.4 2004/03/21 22:52:06 mdw |
| 61 | * Merge and close elliptic curve branch. |
| 62 | * |
| 63 | * Revision 1.3.4.3 2004/03/21 22:39:46 mdw |
| 64 | * Elliptic curves on binary fields work. |
| 65 | * |
| 66 | * Revision 1.3.4.2 2004/03/20 00:13:31 mdw |
| 67 | * Projective coordinates for prime curves |
| 68 | * |
| 69 | * Revision 1.3.4.1 2003/06/10 13:43:53 mdw |
| 70 | * Simple (non-projective) curves over prime fields now seem to work. |
| 71 | * |
| 72 | * Revision 1.3 2003/05/15 23:25:59 mdw |
| 73 | * Make elliptic curve stuff build. |
| 74 | * |
| 75 | * Revision 1.2 2002/01/13 13:48:44 mdw |
| 76 | * Further progress. |
| 77 | * |
| 78 | * Revision 1.1 2001/04/29 18:12:33 mdw |
| 79 | * Prototype version. |
| 80 | * |
| 81 | */ |
| 82 | |
| 83 | /*----- Header files ------------------------------------------------------*/ |
| 84 | |
| 85 | #include <mLib/sub.h> |
| 86 | |
| 87 | #include "field.h" |
| 88 | #include "mpmont.h" |
| 89 | #include "mprand.h" |
| 90 | |
| 91 | /*----- Main code ---------------------------------------------------------*/ |
| 92 | |
| 93 | typedef struct fctx { |
| 94 | field f; |
| 95 | mpmont mm; |
| 96 | } fctx; |
| 97 | |
| 98 | /* --- Field operations --- */ |
| 99 | |
| 100 | static void fdestroy(field *ff) |
| 101 | { fctx *f = (fctx *)ff; mpmont_destroy(&f->mm); DESTROY(f); } |
| 102 | |
| 103 | static mp *frand(field *ff, mp *d, grand *r) |
| 104 | { fctx *f = (fctx *)ff; return (mprand_range(d, f->mm.m, r, 0)); } |
| 105 | |
| 106 | static mp *fin(field *ff, mp *d, mp *x) { |
| 107 | fctx *f = (fctx *)ff; |
| 108 | mp_div(0, &d, x, f->mm.m); |
| 109 | return (mpmont_mul(&f->mm, d, d, f->mm.r2)); |
| 110 | } |
| 111 | |
| 112 | static mp *fout(field *ff, mp *d, mp *x) |
| 113 | { fctx *f = (fctx *)ff; return (mpmont_reduce(&f->mm, d, x)); } |
| 114 | |
| 115 | static int fzerop(field *ff, mp *x) { return (!MP_LEN(x)); } |
| 116 | |
| 117 | static mp *fneg(field *ff, mp *d, mp *x) |
| 118 | { fctx *f = (fctx *)ff; return (mp_sub(d, f->mm.m, x)); } |
| 119 | |
| 120 | static mp *fadd(field *ff, mp *d, mp *x, mp *y) { |
| 121 | fctx *f = (fctx *)ff; d = mp_add(d, x, y); |
| 122 | if (d->f & MP_NEG) d = mp_add(d, d, f->mm.m); |
| 123 | else if (MP_CMP(d, >, f->mm.m)) d = mp_sub(d, d, f->mm.m); |
| 124 | return (d); |
| 125 | } |
| 126 | |
| 127 | static mp *fsub(field *ff, mp *d, mp *x, mp *y) { |
| 128 | fctx *f = (fctx *)ff; d = mp_sub(d, x, y); |
| 129 | if (d->f & MP_NEG) d = mp_add(d, d, f->mm.m); |
| 130 | else if (MP_CMP(d, >, f->mm.m)) d = mp_sub(d, d, f->mm.m); |
| 131 | return (d); |
| 132 | } |
| 133 | |
| 134 | static mp *fmul(field *ff, mp *d, mp *x, mp *y) |
| 135 | { fctx *f = (fctx *)ff; return (mpmont_mul(&f->mm, d, x, y)); } |
| 136 | |
| 137 | static mp *fsqr(field *ff, mp *d, mp *x) { |
| 138 | fctx *f = (fctx *)ff; d = mp_sqr(d, x); |
| 139 | return (mpmont_reduce(&f->mm, d, d)); |
| 140 | } |
| 141 | |
| 142 | static mp *finv(field *ff, mp *d, mp *x) { |
| 143 | fctx *f = (fctx *)ff; d = mpmont_reduce(&f->mm, d, x); |
| 144 | mp_gcd(0, 0, &d, f->mm.m, d); return (mpmont_mul(&f->mm, d, d, f->mm.r2)); |
| 145 | } |
| 146 | |
| 147 | static mp *freduce(field *ff, mp *d, mp *x) |
| 148 | { fctx *f = (fctx *)ff; mp_div(0, &d, x, f->mm.m); return (d); } |
| 149 | |
| 150 | static mp *fsqrt(field *ff, mp *d, mp *x) { |
| 151 | fctx *f = (fctx *)ff; d = mpmont_reduce(&f->mm, d, x); |
| 152 | d = mp_modsqrt(d, d, f->mm.m); if (!d) return (d); |
| 153 | return (mpmont_mul(&f->mm, d, d, f->mm.r2)); |
| 154 | } |
| 155 | |
| 156 | static mp *fdbl(field *ff, mp *d, mp *x) { |
| 157 | fctx *f = (fctx *)ff; d = mp_lsl(d, x, 1); |
| 158 | if (MP_CMP(d, >, f->mm.m)) d = mp_sub(d, d, f->mm.m); |
| 159 | return (d); |
| 160 | } |
| 161 | |
| 162 | static mp *ftpl(field *ff, mp *d, mp *x) { |
| 163 | fctx *f = (fctx *)ff; MP_DEST(d, MP_LEN(x) + 1, x->f); |
| 164 | MPX_UMULN(d->v, d->vl, x->v, x->vl, 3); |
| 165 | while (MP_CMP(d, >, f->mm.m)) d = mp_sub(d, d, f->mm.m); |
| 166 | return (d); |
| 167 | } |
| 168 | |
| 169 | static mp *fqdl(field *ff, mp *d, mp *x) { |
| 170 | fctx *f = (fctx *)ff; d = mp_lsl(d, x, 2); |
| 171 | while (MP_CMP(d, >, f->mm.m)) d = mp_sub(d, d, f->mm.m); |
| 172 | return (d); |
| 173 | } |
| 174 | |
| 175 | static mp *fhlv(field *ff, mp *d, mp *x) { |
| 176 | fctx *f = (fctx *)ff; |
| 177 | if (!MP_LEN(x)) { MP_COPY(x); MP_DROP(d); return (x); } |
| 178 | if (x->v[0] & 1) { d = mp_add(d, x, f->mm.m); x = d; } |
| 179 | return (mp_lsr(d, x, 1)); |
| 180 | } |
| 181 | |
| 182 | /* --- Field operations table --- */ |
| 183 | |
| 184 | static const field_ops fops = { |
| 185 | FTY_PRIME, "prime", |
| 186 | fdestroy, frand, field_stdsamep, |
| 187 | fin, fout, |
| 188 | fzerop, fneg, fadd, fsub, fmul, fsqr, finv, freduce, fsqrt, |
| 189 | 0, |
| 190 | fdbl, ftpl, fqdl, fhlv |
| 191 | }; |
| 192 | |
| 193 | /* --- @field_prime@ --- * |
| 194 | * |
| 195 | * Arguments: @mp *p@ = the characteristic of the field |
| 196 | * |
| 197 | * Returns: A pointer to the field or null. |
| 198 | * |
| 199 | * Use: Creates a field structure for a prime field of size %$p$%, |
| 200 | * using Montgomery reduction for arithmetic. |
| 201 | */ |
| 202 | |
| 203 | field *field_prime(mp *p) |
| 204 | { |
| 205 | fctx *f; |
| 206 | |
| 207 | if (!MP_ISPOS(p) || !MP_ISODD(p)) |
| 208 | return (0); |
| 209 | f = CREATE(fctx); |
| 210 | f->f.ops = &fops; |
| 211 | mpmont_create(&f->mm, p); |
| 212 | f->f.zero = MP_ZERO; |
| 213 | f->f.one = f->mm.r; |
| 214 | f->f.m = f->mm.m; |
| 215 | f->f.nbits = mp_bits(p); |
| 216 | f->f.noctets = (f->f.nbits + 7) >> 3; |
| 217 | return (&f->f); |
| 218 | } |
| 219 | |
| 220 | /*----- That's all, folks -------------------------------------------------*/ |