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

   1 /* -*-apcalc-*-
   2  *
   3  * $Id: ecp.cal,v 1.2 2004/03/21 22:52:06 mdw Exp $
   4  *
   5  * Testbed for elliptic curve arithmetic over prime fields
   6  *
   7  * (c) 2000 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: ecp.cal,v $
  33  * Revision 1.2  2004/03/21 22:52:06  mdw
  34  * Merge and close elliptic curve branch.
  35  *
  36  * Revision 1.1.4.2  2004/03/20 00:13:31  mdw
  37  * Projective coordinates for prime curves
  38  *
  39  * Revision 1.1.4.1  2003/06/10 13:43:53  mdw
  40  * Simple (non-projective) curves over prime fields now seem to work.
  41  *
  42  * Revision 1.1  2000/10/08 16:01:37  mdw
  43  * Prototypes of various bits of code.
  44  *
  45  */
  46
  47 /*----- Object types ------------------------------------------------------*/
  48
  49 obj ecp_curve { a, b, p };
  50 obj ecp_pt { x, y, e };
  51 obj ecpp_pt { x, y, z, e };
  52
  53 /*----- Main code ---------------------------------------------------------*/
  54
  55 define ecp_curve(a, b, p)
  56 {
  57   local obj ecp_curve e;
  58   e.a = a;
  59   e.b = b;
  60   e.p = p;
  61   return (e);
  62 }
  63
  64 define ecp_pt(x, y, e)
  65 {
  66   local obj ecp_pt p;
  67   p.x = x % e.p;
  68   p.y = y % e.p;
  69   p.e = e;
  70   return (p);
  71 }
  72
  73 define ecpp_pt(p)
  74 {
  75   local obj ecpp_pt pp;
  76   if (istype(p, 1))
  77     return (0);
  78   pp.x = p.x;
  79   pp.y = p.y;
  80   pp.z = 1;
  81   pp.e = p.e;
  82   return (pp);
  83 }
  84
  85 define ecpp_fix(pp)
  86 {
  87   local obj ecp_pt p;
  88   local e, zi, z2, z3;
  89   if (istype(pp, 1) || pp.z == 0)
  90     return (0);
  91   e = pp.e;
  92   zi = minv(pp.z, e.p);
  93   z2 = zi * zi;
  94   z3 = zi * z2;
  95   p.x = pp.x * z2 % e.p;
  96   p.y = pp.y * z3 % e.p;
  97   p.e = e;
  98   return (p);
  99 }
 100
 101 define ecpp_dbl(a)
 102 {
 103   local m, s, t, y2;
 104   local e;
 105   local obj ecpp_pt d;
 106   if (istype(a, 1) || a.y == 0)
 107     return (0);
 108   e = a.e;
 109   if (e.a % e.p == e.p - 3) {
 110     m = a.z^3 % e.p;
 111     m = 3 * (a.x + t4) * (a.x - t4) % e.p;
 112   } else {
 113     m = (3 * a.x^2 - e.a * a.z^4) % e.p;
 114   }
 115   d.z = 2 * a.y * a.z % e.p;
 116   y2 = a.y^2 % e.p;
 117   s = 4 * a.x * a.y % e.p;
 118   d.x = (m^2 - 2 * s) % e.p;
 119   d.y = (m * (s - d.x) - y * y2^2) % e.p;
 120   d.e = e;
 121   return (d);
 122 }
 123
 124 define ecpp_add(a, b)
 125 {
 126   if (a == 0)
 127     d = b;
 128   else if (b == 0)
 129     d = a;
 130   else if (!istype(a, b))
 131     quit "bad type arguments to ecp_pt_add";
 132   else if (a.e != b.e)
 133     quit "points from different curves in ecp_pt_add";
 134   else {
 135     e = a.e;
 136
 137 }
 138
 139 define ecp_pt_print(a)
 140 {
 141   print "(" : a.x : ", " : a.y : ")" :;
 142 }
 143
 144 define ecp_pt_add(a, b)
 145 {
 146   local e, alpha;
 147   local obj ecp_pt d;
 148
 149   if (a == 0)
 150     d = b;
 151   else if (b == 0)
 152     d = a;
 153   else if (!istype(a, b))
 154     quit "bad type arguments to ecp_pt_add";
 155   else if (a.e != b.e)
 156     quit "points from different curves in ecp_pt_add";
 157   else {
 158     e = a.e;
 159     if (a.x == b.x) {
 160       if (a.y != b.y) {
 161         return (0);
 162       }
 163       alpha = (3 * a.x^2 + e.a) * minv(2 * a.y, e.p) % e.p;
 164     } else
 165       alpha = (b.y - a.y) * minv(b.x - a.x, e.p) % e.p;
 166
 167     d.x = (alpha^2 - a.x - b.x) % e.p;
 168     d.y = (-a.y + alpha * (a.x - d.x)) % e.p;
 169     d.e = e;
 170   }
 171
 172   return (d);
 173 }
 174
 175 define ecp_pt_dbl(a)
 176 {
 177   local e, alpha;
 178   local obj ecp_pt d;
 179   if (istype(a, 1))
 180     return (0);
 181   e = a.e;
 182   alpha = (3 * a.x^2 + e.a) * minv(2 * a.y, e.p) % e.p;
 183   d.x = (alpha^2 - 2 * a.x) % e.p;
 184   d.y = (-a.y + alpha * (a.x - d.x)) % e.p;
 185   d.e = e;
 186   return (d);
 187 }
 188
 189 define ecp_pt_neg(a)
 190 {
 191   local obj ecp_pt d;
 192   d.x = a.x;
 193   d.y = -a.y;
 194   d.e = a.e;
 195   return (d);
 196 }
 197
 198 define ecp_pt_check(a)
 199 {
 200   local e;
 201
 202   e = a.e;
 203   if (a.y^2 % e.p != (a.x^3 + e.a * a.x + e.b) % e.p)
 204     quit "bad curve point";
 205 }
 206
 207 define ecp_pt_mul(a, b)
 208 {
 209   local p, n;
 210   local d;
 211
 212   if (istype(a, 1)) {
 213     n = a;
 214     p = b;
 215   } else if (istype(b, 1)) {
 216     n = b;
 217     p = a;
 218   } else
 219     return (newerror("bad arguments to ecp_pt_mul"));
 220
 221   d = 0;
 222   while (n) {
 223     if (n & 1)
 224       d += p;
 225     n >>= 1;
 226     p = ecp_pt_dbl(p);
 227   }
 228   return (d);
 229 }
 230
 231 /*----- FIPS186-2 standard curves -----------------------------------------*/
 232
 233 p192 = ecp_curve(-3, 0x64210519e59c80e70fa7e9ab72243049feb8deecc146b9b1,
 234                  6277101735386680763835789423207666416083908700390324961279);
 235 p192_r = 6277101735386680763835789423176059013767194773182842284081;
 236 p192_g = ecp_pt(0x188da80eb03090f67cbf20eb43a18800f4ff0afd82ff1012,
 237                 0x07192b95ffc8da78631011ed6b24cdd573f977a11e794811, p192);
 238
 239 /*----- That's all, folks -------------------------------------------------*/
 240