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1 | /* -*-apcalc-*- |
2 | * |
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3 | * $Id: ecp.cal,v 1.4 2004/04/01 13:37:07 mdw Exp $ |
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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 $ |
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33 | * Revision 1.4 2004/04/01 13:37:07 mdw |
34 | * Keep numbers positive. |
35 | * |
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36 | * Revision 1.3 2004/03/23 15:19:32 mdw |
37 | * Test elliptic curves more thoroughly. |
38 | * |
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39 | * Revision 1.2 2004/03/21 22:52:06 mdw |
40 | * Merge and close elliptic curve branch. |
41 | * |
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42 | * Revision 1.1.4.2 2004/03/20 00:13:31 mdw |
43 | * Projective coordinates for prime curves |
44 | * |
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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 | * |
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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 ecp_curve { a, b, p }; |
56 | obj ecp_pt { x, y, e }; |
57 | |
58 | /*----- Main code ---------------------------------------------------------*/ |
59 | |
60 | define ecp_curve(a, b, p) |
61 | { |
62 | local obj ecp_curve e; |
63 | e.a = a; |
64 | e.b = b; |
65 | e.p = p; |
66 | return (e); |
67 | } |
68 | |
69 | define ecp_pt(x, y, e) |
70 | { |
71 | local obj ecp_pt p; |
72 | p.x = x % e.p; |
73 | p.y = y % e.p; |
74 | p.e = e; |
75 | return (p); |
76 | } |
77 | |
78 | define ecp_pt_print(a) |
79 | { |
80 | print "(" : a.x : ", " : a.y : ")" :; |
81 | } |
82 | |
83 | define ecp_pt_add(a, b) |
84 | { |
85 | local e, alpha; |
86 | local obj ecp_pt d; |
87 | |
88 | if (a == 0) |
89 | d = b; |
90 | else if (b == 0) |
91 | d = a; |
92 | else if (!istype(a, b)) |
93 | quit "bad type arguments to ecp_pt_add"; |
94 | else if (a.e != b.e) |
95 | quit "points from different curves in ecp_pt_add"; |
96 | else { |
97 | e = a.e; |
98 | if (a.x == b.x) { |
99 | if (a.y != b.y) { |
100 | return (0); |
101 | } |
102 | alpha = (3 * a.x^2 + e.a) * minv(2 * a.y, e.p) % e.p; |
103 | } else |
104 | alpha = (b.y - a.y) * minv(b.x - a.x, e.p) % e.p; |
105 | |
106 | d.x = (alpha^2 - a.x - b.x) % e.p; |
107 | d.y = (-a.y + alpha * (a.x - d.x)) % e.p; |
108 | d.e = e; |
109 | } |
110 | |
111 | return (d); |
112 | } |
113 | |
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114 | define ecp_pt_dbl(a) |
115 | { |
116 | local e, alpha; |
117 | local obj ecp_pt d; |
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118 | if (istype(a, 1)) |
119 | return (0); |
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120 | e = a.e; |
121 | alpha = (3 * a.x^2 + e.a) * minv(2 * a.y, e.p) % e.p; |
122 | d.x = (alpha^2 - 2 * a.x) % e.p; |
123 | d.y = (-a.y + alpha * (a.x - d.x)) % e.p; |
124 | d.e = e; |
125 | return (d); |
126 | } |
127 | |
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128 | define ecp_pt_neg(a) |
129 | { |
130 | local obj ecp_pt d; |
131 | d.x = a.x; |
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132 | d.y = a.e.p - a.y; |
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133 | d.e = a.e; |
134 | return (d); |
135 | } |
136 | |
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137 | define ecp_pt_check(a) |
138 | { |
139 | local e; |
140 | |
141 | e = a.e; |
142 | if (a.y^2 % e.p != (a.x^3 + e.a * a.x + e.b) % e.p) |
143 | quit "bad curve point"; |
144 | } |
145 | |
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146 | define ecp_pt_mul(a, b) |
147 | { |
148 | local p, n; |
149 | local d; |
150 | |
151 | if (istype(a, 1)) { |
152 | n = a; |
153 | p = b; |
154 | } else if (istype(b, 1)) { |
155 | n = b; |
156 | p = a; |
157 | } else |
158 | return (newerror("bad arguments to ecp_pt_mul")); |
159 | |
160 | d = 0; |
161 | while (n) { |
162 | if (n & 1) |
163 | d += p; |
164 | n >>= 1; |
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165 | p = ecp_pt_dbl(p); |
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166 | } |
167 | return (d); |
168 | } |
169 | |
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170 | /*----- FIPS186-2 standard curves -----------------------------------------*/ |
171 | |
172 | p192 = ecp_curve(-3, 0x64210519e59c80e70fa7e9ab72243049feb8deecc146b9b1, |
173 | 6277101735386680763835789423207666416083908700390324961279); |
174 | p192_r = 6277101735386680763835789423176059013767194773182842284081; |
175 | p192_g = ecp_pt(0x188da80eb03090f67cbf20eb43a18800f4ff0afd82ff1012, |
176 | 0x07192b95ffc8da78631011ed6b24cdd573f977a11e794811, p192); |
177 | |
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178 | /*----- That's all, folks -------------------------------------------------*/ |
179 | |