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

   1 /* -*-apcalc-*-
   2  *
   3  * $Id: ec2.cal,v 1.2 2004/03/21 22:52:06 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 1.2  2004/03/21 22:52:06  mdw
  34  * Merge and close elliptic curve branch.
  35  *
  36  * Revision 1.1.2.1  2004/03/21 22:39:46  mdw
  37  * Elliptic curves on binary fields work.
  38  *
  39  * Revision 1.1.4.2  2004/03/20 00:13:31  mdw
  40  * Projective coordinates for prime curves
  41  *
  42  * Revision 1.1.4.1  2003/06/10 13:43:53  mdw
  43  * Simple (non-projective) curves over prime fields now seem to work.
  44  *
  45  * Revision 1.1  2000/10/08 16:01:37  mdw
  46  * Prototypes of various bits of code.
  47  *
  48  */
  49
  50 /*----- Object types ------------------------------------------------------*/
  51
  52 obj ec2_curve { a, b, p };
  53 obj ec2_pt { x, y, e };
  54 obj ecpp_pt { x, y, z, e };
  55
  56 /*----- Main code ---------------------------------------------------------*/
  57
  58 define ec2_curve(a, b, p)
  59 {
  60   local obj ec2_curve e;
  61   e.a = a;
  62   e.b = b;
  63   e.p = p;
  64   return (e);
  65 }
  66
  67 define ec2_pt(x, y, e)
  68 {
  69   local obj ec2_pt p;
  70   p.x = x % e.p;
  71   p.y = y % e.p;
  72   p.e = e;
  73   return (p);
  74 }
  75
  76 define ec2_pt_print(a)
  77 {
  78   print "(" : a.x : ", " : a.y : ")" :;
  79 }
  80
  81 define ec2_pt_add(a, b)
  82 {
  83   local e, alpha;
  84   local obj ec2_pt d;
  85
  86   print "> ecadd: ", a, b;
  87   if (a == 0)
  88     d = b;
  89   else if (b == 0)
  90     d = a;
  91   else if (!istype(a, b))
  92     quit "bad type arguments to ec2_pt_add";
  93   else if (a.e != b.e)
  94     quit "points from different curves in ec2_pt_add";
  95   else {
  96     e = a.e;
  97     if (a.x != b.x) {
  98       alpha = ((a.y + b.y) * gf_inv(a.x + b.x, e.p)) % e.p;
  99       d.x = (e.a + alpha^2 + alpha + a.x + b.x) % e.p;
 100     } else if (a.y != b.y || a.x == gf(0))
 101       return 0;
 102     else {
 103       alpha = a.x + a.y * gf_inv(a.x, e.p) % e.p;
 104       d.x = (e.a + alpha^2 + alpha) % e.p;
 105     }
 106     d.y = ((a.x + d.x) * alpha + d.x + a.y) % e.p;
 107     d.e = e;
 108   }
 109
 110   print "< ecadd: ", d;
 111   return (d);
 112 }
 113
 114 define ec2_pt_dbl(a)
 115 {
 116   local e, alpha;
 117   local obj ec2_pt d;
 118   print "> ecdbl: ", a;
 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   print "< ecdbl: ", d;
 127   return (d);
 128 }
 129
 130 define ec2_pt_sub(a, b) { return ec2_pt_add(a, ec2_pt_neg(b)); }
 131
 132 define ec2_pt_neg(a)
 133 {
 134   local obj ec2_pt d;
 135   d.x = a.x;
 136   d.y = a.x + a.y;
 137   d.e = a.e;
 138   return (d);
 139 }
 140
 141 define ec2_pt_check(a)
 142 {
 143   local e;
 144
 145   e = a.e;
 146   if ((a.y^2 + a.x * a.y) % e.p != (a.x^3 + e.a * a.x^2 + e.b) % e.p)
 147     quit "bad curve point";
 148 }
 149
 150 define ec2_pt_mul(a, b)
 151 {
 152   local p, n;
 153   local d;
 154
 155   if (istype(a, 1)) {
 156     n = a;
 157     p = b;
 158   } else if (istype(b, 1)) {
 159     n = b;
 160     p = a;
 161   } else
 162     return (newerror("bad arguments to ec2_pt_mul"));
 163
 164   d = 0;
 165   while (n) {
 166     if (n & 1)
 167       d += p;
 168     n >>= 1;
 169     p = ec2_pt_dbl(p);
 170   }
 171   return (d);
 172 }
 173
 174 /*----- FIPS186-2 standard curves -----------------------------------------*/
 175
 176 b163 = ec2_curve(gf(1),gf(0x20a601907b8c953ca1481eb10512f78744a3205fd),
 177                  gf(0x800000000000000000000000000000000000000c9));
 178 b163_r = 5846006549323611672814742442876390689256843201587;
 179 b163_g = ec2_pt(0x3f0eba16286a2d57ea0991168d4994637e8343e36,
 180                 0x0d51fbc6c71a0094fa2cdd545b11c5c0c797324f1, b163);
 181
 182 /*----- That's all, folks -------------------------------------------------*/
 183