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

   1 /* -*-apcalc-*-
   2  *
   3  * Testbed for elliptic curve arithmetic over binary fields
   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 /*----- Object types ------------------------------------------------------*/
  29
  30 obj ec2_curve { a, b, p };
  31 obj ec2_pt { x, y, e };
  32 obj ecpp_pt { x, y, z, e };
  33
  34 /*----- Main code ---------------------------------------------------------*/
  35
  36 define ec2_curve(a, b, p)
  37 {
  38   local obj ec2_curve e;
  39   e.a = a;
  40   e.b = b;
  41   e.p = p;
  42   return (e);
  43 }
  44
  45 define ec2_pt(x, y, e)
  46 {
  47   local obj ec2_pt p;
  48   p.x = x % e.p;
  49   p.y = y % e.p;
  50   p.e = e;
  51   return (p);
  52 }
  53
  54 define ec2_pt_print(a)
  55 {
  56   print "(" : a.x : ", " : a.y : ")" :;
  57 }
  58
  59 define ec2_pt_add(a, b)
  60 {
  61   local e, alpha;
  62   local obj ec2_pt d;
  63
  64   if (a == 0)
  65     d = b;
  66   else if (b == 0)
  67     d = a;
  68   else if (!istype(a, b))
  69     quit "bad type arguments to ec2_pt_add";
  70   else if (a.e != b.e)
  71     quit "points from different curves in ec2_pt_add";
  72   else {
  73     e = a.e;
  74     if (a.x != b.x) {
  75       alpha = ((a.y + b.y) * gf_inv(a.x + b.x, e.p)) % e.p;
  76       d.x = (e.a + alpha^2 + alpha + a.x + b.x) % e.p;
  77     } else if (a.y != b.y || a.x == gf(0))
  78       return 0;
  79     else {
  80       alpha = a.x + a.y * gf_inv(a.x, e.p) % e.p;
  81       d.x = (e.a + alpha^2 + alpha) % e.p;
  82     }
  83     d.y = ((a.x + d.x) * alpha + d.x + a.y) % e.p;
  84     d.e = e;
  85   }
  86
  87   return (d);
  88 }
  89
  90 define ec2_pt_dbl(a)
  91 {
  92   local e, alpha;
  93   local obj ec2_pt d;
  94   if (istype(a, 1))
  95     return (0);
  96   e = a.e;
  97   alpha = a.x + a.y * gf_inv(a.x, e.p) % e.p;
  98   d.x = (e.a + alpha^2 + alpha) % e.p;
  99   d.y = ((a.x + d.x) * alpha + d.x + a.y) % e.p;
 100   d.e = e;
 101   return (d);
 102 }
 103
 104 define ec2_pt_sub(a, b) { return ec2_pt_add(a, ec2_pt_neg(b)); }
 105
 106 define ec2_pt_neg(a)
 107 {
 108   local obj ec2_pt d;
 109   d.x = a.x;
 110   d.y = a.x + a.y;
 111   d.e = a.e;
 112   return (d);
 113 }
 114
 115 define ec2_pt_check(a)
 116 {
 117   local e;
 118
 119   e = a.e;
 120   if ((a.y^2 + a.x * a.y) % e.p != (a.x^3 + e.a * a.x^2 + e.b) % e.p)
 121     quit "bad curve point";
 122 }
 123
 124 define ec2_pt_mul(a, b)
 125 {
 126   local p, n;
 127   local d;
 128
 129   if (istype(a, 1)) {
 130     n = a;
 131     p = b;
 132   } else if (istype(b, 1)) {
 133     n = b;
 134     p = a;
 135   } else
 136     return (newerror("bad arguments to ec2_pt_mul"));
 137
 138   d = 0;
 139   while (n) {
 140     if (n & 1)
 141       d += p;
 142     n >>= 1;
 143     p = ec2_pt_dbl(p);
 144   }
 145   return (d);
 146 }
 147
 148 /*----- FIPS186-2 standard curves -----------------------------------------*/
 149
 150 b163 = ec2_curve(gf(1),gf(0x20a601907b8c953ca1481eb10512f78744a3205fd),
 151                  gf(0x800000000000000000000000000000000000000c9));
 152 b163_r = 5846006549323611672814742442876390689256843201587;
 153 b163_g = ec2_pt(0x3f0eba16286a2d57ea0991168d4994637e8343e36,
 154                 0x0d51fbc6c71a0094fa2cdd545b11c5c0c797324f1, b163);
 155
 156 /*----- That's all, folks -------------------------------------------------*/
 157