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1 | /* -*-apcalc-*- |
2 | * |
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3 | * $Id: ecp.cal,v 1.5 2004/04/08 01:36:15 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 | |
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30 | /*----- Object types ------------------------------------------------------*/ |
31 | |
32 | obj ecp_curve { a, b, p }; |
33 | obj ecp_pt { x, y, e }; |
34 | |
35 | /*----- Main code ---------------------------------------------------------*/ |
36 | |
37 | define ecp_curve(a, b, p) |
38 | { |
39 | local obj ecp_curve e; |
40 | e.a = a; |
41 | e.b = b; |
42 | e.p = p; |
43 | return (e); |
44 | } |
45 | |
46 | define ecp_pt(x, y, e) |
47 | { |
48 | local obj ecp_pt p; |
49 | p.x = x % e.p; |
50 | p.y = y % e.p; |
51 | p.e = e; |
52 | return (p); |
53 | } |
54 | |
55 | define ecp_pt_print(a) |
56 | { |
57 | print "(" : a.x : ", " : a.y : ")" :; |
58 | } |
59 | |
60 | define ecp_pt_add(a, b) |
61 | { |
62 | local e, alpha; |
63 | local obj ecp_pt d; |
64 | |
65 | if (a == 0) |
66 | d = b; |
67 | else if (b == 0) |
68 | d = a; |
69 | else if (!istype(a, b)) |
70 | quit "bad type arguments to ecp_pt_add"; |
71 | else if (a.e != b.e) |
72 | quit "points from different curves in ecp_pt_add"; |
73 | else { |
74 | e = a.e; |
75 | if (a.x == b.x) { |
76 | if (a.y != b.y) { |
77 | return (0); |
78 | } |
79 | alpha = (3 * a.x^2 + e.a) * minv(2 * a.y, e.p) % e.p; |
80 | } else |
81 | alpha = (b.y - a.y) * minv(b.x - a.x, e.p) % e.p; |
82 | |
83 | d.x = (alpha^2 - a.x - b.x) % e.p; |
84 | d.y = (-a.y + alpha * (a.x - d.x)) % e.p; |
85 | d.e = e; |
86 | } |
87 | |
88 | return (d); |
89 | } |
90 | |
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91 | define ecp_pt_dbl(a) |
92 | { |
93 | local e, alpha; |
94 | local obj ecp_pt d; |
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95 | if (istype(a, 1)) |
96 | return (0); |
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97 | e = a.e; |
98 | alpha = (3 * a.x^2 + e.a) * minv(2 * a.y, e.p) % e.p; |
99 | d.x = (alpha^2 - 2 * a.x) % e.p; |
100 | d.y = (-a.y + alpha * (a.x - d.x)) % e.p; |
101 | d.e = e; |
102 | return (d); |
103 | } |
104 | |
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105 | define ecp_pt_neg(a) |
106 | { |
107 | local obj ecp_pt d; |
108 | d.x = a.x; |
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109 | d.y = a.e.p - a.y; |
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110 | d.e = a.e; |
111 | return (d); |
112 | } |
113 | |
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114 | define ecp_pt_check(a) |
115 | { |
116 | local e; |
117 | |
118 | e = a.e; |
119 | if (a.y^2 % e.p != (a.x^3 + e.a * a.x + e.b) % e.p) |
120 | quit "bad curve point"; |
121 | } |
122 | |
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123 | define ecp_pt_mul(a, b) |
124 | { |
125 | local p, n; |
126 | local d; |
127 | |
128 | if (istype(a, 1)) { |
129 | n = a; |
130 | p = b; |
131 | } else if (istype(b, 1)) { |
132 | n = b; |
133 | p = a; |
134 | } else |
135 | return (newerror("bad arguments to ecp_pt_mul")); |
136 | |
137 | d = 0; |
138 | while (n) { |
139 | if (n & 1) |
140 | d += p; |
141 | n >>= 1; |
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142 | p = ecp_pt_dbl(p); |
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143 | } |
144 | return (d); |
145 | } |
146 | |
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147 | /*----- FIPS186-2 standard curves -----------------------------------------*/ |
148 | |
149 | p192 = ecp_curve(-3, 0x64210519e59c80e70fa7e9ab72243049feb8deecc146b9b1, |
150 | 6277101735386680763835789423207666416083908700390324961279); |
151 | p192_r = 6277101735386680763835789423176059013767194773182842284081; |
152 | p192_g = ecp_pt(0x188da80eb03090f67cbf20eb43a18800f4ff0afd82ff1012, |
153 | 0x07192b95ffc8da78631011ed6b24cdd573f977a11e794811, p192); |
154 | |
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155 | /*----- That's all, folks -------------------------------------------------*/ |
156 | |