mdw@git.distorted.org.uk Git - catacomb/blob - math/f-prime.c

   1 /* -*-c-*-
   2  *
   3  * Prime fields with Montgomery arithmetic
   4  *
   5  * (c) 2001 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 "mprand.h"
  34 #include "field-guts.h"
  35
  36 /*----- Main code ---------------------------------------------------------*/
  37
  38 /* --- Field operations --- */
  39
  40 static void fdestroy(field *ff) {
  41   fctx_prime *f = (fctx_prime *)ff;
  42   mpmont_destroy(&f->mm);
  43   DESTROY(f);
  44 }
  45
  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 }
  50
  51 static mp *fin(field *ff, mp *d, mp *x) {
  52   fctx_prime *f = (fctx_prime *)ff;
  53   mp_div(0, &d, x, f->mm.m);
  54   return (mpmont_mul(&f->mm, d, d, f->mm.r2));
  55 }
  56
  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 }
  61
  62 static int fzerop(field *ff, mp *x) { return (MP_ZEROP(x)); }
  63
  64 static mp *fneg(field *ff, mp *d, mp *x) {
  65   fctx_prime *f = (fctx_prime *)ff;
  66   if (MP_ZEROP(x)) { if (d != x) mp_drop(d); return (MP_COPY(x)); }
  67   else return (mp_sub(d, f->mm.m, x));
  68 }
  69
  70 static mp *fadd(field *ff, mp *d, mp *x, mp *y) {
  71   fctx_prime *f = (fctx_prime *)ff; d = mp_add(d, x, y);
  72   if (MP_NEGP(d)) d = mp_add(d, d, f->mm.m);
  73   else if (MP_CMP(d, >=, f->mm.m)) d = mp_sub(d, d, f->mm.m);
  74   return (d);
  75 }
  76
  77 static mp *fsub(field *ff, mp *d, mp *x, mp *y) {
  78   fctx_prime *f = (fctx_prime *)ff; d = mp_sub(d, x, y);
  79   if (MP_NEGP(d)) d = mp_add(d, d, f->mm.m);
  80   else if (MP_CMP(d, >=, f->mm.m)) d = mp_sub(d, d, f->mm.m);
  81   return (d);
  82 }
  83
  84 static mp *fmul(field *ff, mp *d, mp *x, mp *y) {
  85   fctx_prime *f = (fctx_prime *)ff;
  86   return (mpmont_mul(&f->mm, d, x, y));
  87 }
  88
  89 static mp *fsqr(field *ff, mp *d, mp *x) {
  90   fctx_prime *f = (fctx_prime *)ff; d = mp_sqr(d, x);
  91   return (mpmont_reduce(&f->mm, d, d));
  92 }
  93
  94 static mp *finv(field *ff, mp *d, mp *x) {
  95   fctx_prime *f = (fctx_prime *)ff; d = mpmont_reduce(&f->mm, d, x);
  96   d = mp_modinv(d, d, f->mm.m); return (mpmont_mul(&f->mm, d, d, f->mm.r2));
  97 }
  98
  99 static mp *freduce(field *ff, mp *d, mp *x) {
 100   fctx_prime *f = (fctx_prime *)ff;
 101   mp_div(0, &d, x, f->mm.m);
 102   return (d);
 103 }
 104
 105 static mp *fsqrt(field *ff, mp *d, mp *x) {
 106   fctx_prime *f = (fctx_prime *)ff; d = mpmont_reduce(&f->mm, d, x);
 107   d = mp_modsqrt(d, d, f->mm.m); if (!d) return (d);
 108   return (mpmont_mul(&f->mm, d, d, f->mm.r2));
 109 }
 110
 111 static mp *fdbl(field *ff, mp *d, mp *x) {
 112   fctx_prime *f = (fctx_prime *)ff; d = mp_lsl(d, x, 1);
 113   if (MP_CMP(d, >=, f->mm.m)) d = mp_sub(d, d, f->mm.m);
 114   return (d);
 115 }
 116
 117 static mp *ftpl(field *ff, mp *d, mp *x) {
 118   fctx_prime *f = (fctx_prime *)ff; MP_DEST(d, MP_LEN(x) + 1, x->f);
 119   MPX_UMULN(d->v, d->vl, x->v, x->vl, 3); d->f &= ~MP_UNDEF;
 120   while (MP_CMP(d, >=, f->mm.m)) d = mp_sub(d, d, f->mm.m);
 121   return (d);
 122 }
 123
 124 static mp *fqdl(field *ff, mp *d, mp *x) {
 125   fctx_prime *f = (fctx_prime *)ff; d = mp_lsl(d, x, 2);
 126   while (MP_CMP(d, >=, f->mm.m)) d = mp_sub(d, d, f->mm.m);
 127   return (d);
 128 }
 129
 130 static mp *fhlv(field *ff, mp *d, mp *x) {
 131   fctx_prime *f = (fctx_prime *)ff;
 132   if (MP_ZEROP(x)) { MP_COPY(x); MP_DROP(d); return (x); }
 133   if (x->v[0] & 1) { d = mp_add(d, x, f->mm.m); x = d; }
 134   return (mp_lsr(d, x, 1));
 135 }
 136
 137 /* --- Field operations table --- */
 138
 139 static const field_ops fops = {
 140   FTY_PRIME, "prime",
 141   fdestroy, frand, field_stdsamep,
 142   fin, fout,
 143   fzerop, fneg, fadd, fsub, fmul, fsqr, finv, freduce, fsqrt,
 144   0,
 145   fdbl, ftpl, fqdl, fhlv
 146 };
 147
 148 /* --- @field_prime@ --- *
 149  *
 150  * Arguments:   @mp *p@ = the characteristic of the field
 151  *
 152  * Returns:     A pointer to the field or null.
 153  *
 154  * Use:         Creates a field structure for a prime field of size %$p$%,
 155  *              using Montgomery reduction for arithmetic.
 156  */
 157
 158 field *field_prime(mp *p)
 159 {
 160   fctx_prime *f;
 161
 162   f = CREATE(fctx_prime);
 163   f->f.ops = &fops;
 164   if (mpmont_create(&f->mm, p)) {
 165     DESTROY(f);
 166     return (0);
 167   }
 168   f->f.zero = MP_ZERO;
 169   f->f.one = f->mm.r;
 170   f->f.m = f->mm.m;
 171   f->f.nbits = mp_bits(p);
 172   f->f.noctets = (f->f.nbits + 7) >> 3;
 173   f->f.q = f->mm.m;
 174   return (&f->f);
 175 }
 176
 177 /*----- That's all, folks -------------------------------------------------*/