git.distorted.org.uk Git - u/mdw/catacomb/blob - calc/ec2.cal

   1 /* -*-apcalc-*-
   2  *
   3  * $Id: ec2.cal,v 1.3 2004/04/01 12:50:27 mdw Exp $
   4  *
   5  * Testbed for elliptic curve arithmetic over binary fields
   6  *
   7  * (c) 2004 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: ec2.cal,v $
  33  * Revision 1.3  2004/04/01 12:50:27  mdw
  34  * Remove debugging code.
  35  *
  36  * Revision 1.2  2004/03/21 22:52:06  mdw
  37  * Merge and close elliptic curve branch.
  38  *
  39  * Revision 1.1.2.1  2004/03/21 22:39:46  mdw
  40  * Elliptic curves on binary fields work.
  41  *
  42  * Revision 1.1.4.2  2004/03/20 00:13:31  mdw
  43  * Projective coordinates for prime curves
  44  *
  45  * Revision 1.1.4.1  2003/06/10 13:43:53  mdw
  46  * Simple (non-projective) curves over prime fields now seem to work.
  47  *
  48  * Revision 1.1  2000/10/08 16:01:37  mdw
  49  * Prototypes of various bits of code.
  50  *
  51  */
  52
  53 /*----- Object types ------------------------------------------------------*/
  54
  55 obj ec2_curve { a, b, p };
  56 obj ec2_pt { x, y, e };
  57 obj ecpp_pt { x, y, z, e };
  58
  59 /*----- Main code ---------------------------------------------------------*/
  60
  61 define ec2_curve(a, b, p)
  62 {
  63   local obj ec2_curve e;
  64   e.a = a;
  65   e.b = b;
  66   e.p = p;
  67   return (e);
  68 }
  69
  70 define ec2_pt(x, y, e)
  71 {
  72   local obj ec2_pt p;
  73   p.x = x % e.p;
  74   p.y = y % e.p;
  75   p.e = e;
  76   return (p);
  77 }
  78
  79 define ec2_pt_print(a)
  80 {
  81   print "(" : a.x : ", " : a.y : ")" :;
  82 }
  83
  84 define ec2_pt_add(a, b)
  85 {
  86   local e, alpha;
  87   local obj ec2_pt d;
  88
  89   if (a == 0)
  90     d = b;
  91   else if (b == 0)
  92     d = a;
  93   else if (!istype(a, b))
  94     quit "bad type arguments to ec2_pt_add";
  95   else if (a.e != b.e)
  96     quit "points from different curves in ec2_pt_add";
  97   else {
  98     e = a.e;
  99     if (a.x != b.x) {
 100       alpha = ((a.y + b.y) * gf_inv(a.x + b.x, e.p)) % e.p;
 101       d.x = (e.a + alpha^2 + alpha + a.x + b.x) % e.p;
 102     } else if (a.y != b.y || a.x == gf(0))
 103       return 0;
 104     else {
 105       alpha = a.x + a.y * gf_inv(a.x, e.p) % e.p;
 106       d.x = (e.a + alpha^2 + alpha) % e.p;
 107     }
 108     d.y = ((a.x + d.x) * alpha + d.x + a.y) % e.p;
 109     d.e = e;
 110   }
 111
 112   return (d);
 113 }
 114
 115 define ec2_pt_dbl(a)
 116 {
 117   local e, alpha;
 118   local obj ec2_pt d;
 119   if (istype(a, 1))
 120     return (0);
 121   e = a.e;
 122   alpha = a.x + a.y * gf_inv(a.x, e.p) % e.p;
 123   d.x = (e.a + alpha^2 + alpha) % e.p;
 124   d.y = ((a.x + d.x) * alpha + d.x + a.y) % e.p;
 125   d.e = e;
 126   return (d);
 127 }
 128
 129 define ec2_pt_sub(a, b) { return ec2_pt_add(a, ec2_pt_neg(b)); }
 130
 131 define ec2_pt_neg(a)
 132 {
 133   local obj ec2_pt d;
 134   d.x = a.x;
 135   d.y = a.x + a.y;
 136   d.e = a.e;
 137   return (d);
 138 }
 139
 140 define ec2_pt_check(a)
 141 {
 142   local e;
 143
 144   e = a.e;
 145   if ((a.y^2 + a.x * a.y) % e.p != (a.x^3 + e.a * a.x^2 + e.b) % e.p)
 146     quit "bad curve point";
 147 }
 148
 149 define ec2_pt_mul(a, b)
 150 {
 151   local p, n;
 152   local d;
 153
 154   if (istype(a, 1)) {
 155     n = a;
 156     p = b;
 157   } else if (istype(b, 1)) {
 158     n = b;
 159     p = a;
 160   } else
 161     return (newerror("bad arguments to ec2_pt_mul"));
 162
 163   d = 0;
 164   while (n) {
 165     if (n & 1)
 166       d += p;
 167     n >>= 1;
 168     p = ec2_pt_dbl(p);
 169   }
 170   return (d);
 171 }
 172
 173 /*----- FIPS186-2 standard curves -----------------------------------------*/
 174
 175 b163 = ec2_curve(gf(1),gf(0x20a601907b8c953ca1481eb10512f78744a3205fd),
 176                  gf(0x800000000000000000000000000000000000000c9));
 177 b163_r = 5846006549323611672814742442876390689256843201587;
 178 b163_g = ec2_pt(0x3f0eba16286a2d57ea0991168d4994637e8343e36,
 179                 0x0d51fbc6c71a0094fa2cdd545b11c5c0c797324f1, b163);
 180
 181 /*----- That's all, folks -------------------------------------------------*/
 182