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1 | /* -*-apcalc-*- |
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2 | * |
3 | * Testbed for elliptic curve arithmetic over prime fields |
4 | * |
5 | * (c) 2000 Straylight/Edgeware |
6 | */ |
7 | |
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8 | /*----- Licensing notice --------------------------------------------------* |
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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. |
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16 | * |
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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. |
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21 | * |
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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 | |
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28 | /*----- Object types ------------------------------------------------------*/ |
29 | |
30 | obj ecp_curve { a, b, p }; |
31 | obj ecp_pt { x, y, e }; |
32 | |
33 | /*----- Main code ---------------------------------------------------------*/ |
34 | |
35 | define ecp_curve(a, b, p) |
36 | { |
37 | local obj ecp_curve e; |
38 | e.a = a; |
39 | e.b = b; |
40 | e.p = p; |
41 | return (e); |
42 | } |
43 | |
44 | define ecp_pt(x, y, e) |
45 | { |
46 | local obj ecp_pt p; |
47 | p.x = x % e.p; |
48 | p.y = y % e.p; |
49 | p.e = e; |
50 | return (p); |
51 | } |
52 | |
53 | define ecp_pt_print(a) |
54 | { |
55 | print "(" : a.x : ", " : a.y : ")" :; |
56 | } |
57 | |
58 | define ecp_pt_add(a, b) |
59 | { |
60 | local e, alpha; |
61 | local obj ecp_pt d; |
62 | |
63 | if (a == 0) |
64 | d = b; |
65 | else if (b == 0) |
66 | d = a; |
67 | else if (!istype(a, b)) |
68 | quit "bad type arguments to ecp_pt_add"; |
69 | else if (a.e != b.e) |
70 | quit "points from different curves in ecp_pt_add"; |
71 | else { |
72 | e = a.e; |
73 | if (a.x == b.x) { |
74 | if (a.y != b.y) { |
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75 | return (0); |
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76 | } |
77 | alpha = (3 * a.x^2 + e.a) * minv(2 * a.y, e.p) % e.p; |
78 | } else |
79 | alpha = (b.y - a.y) * minv(b.x - a.x, e.p) % e.p; |
80 | |
81 | d.x = (alpha^2 - a.x - b.x) % e.p; |
82 | d.y = (-a.y + alpha * (a.x - d.x)) % e.p; |
83 | d.e = e; |
84 | } |
85 | |
86 | return (d); |
87 | } |
88 | |
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89 | define ecp_pt_dbl(a) |
90 | { |
91 | local e, alpha; |
92 | local obj ecp_pt d; |
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93 | if (istype(a, 1)) |
94 | return (0); |
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95 | e = a.e; |
96 | alpha = (3 * a.x^2 + e.a) * minv(2 * a.y, e.p) % e.p; |
97 | d.x = (alpha^2 - 2 * a.x) % e.p; |
98 | d.y = (-a.y + alpha * (a.x - d.x)) % e.p; |
99 | d.e = e; |
100 | return (d); |
101 | } |
102 | |
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103 | define ecp_pt_neg(a) |
104 | { |
105 | local obj ecp_pt d; |
106 | d.x = a.x; |
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107 | d.y = a.e.p - a.y; |
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108 | d.e = a.e; |
109 | return (d); |
110 | } |
111 | |
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112 | define ecp_pt_check(a) |
113 | { |
114 | local e; |
115 | |
116 | e = a.e; |
117 | if (a.y^2 % e.p != (a.x^3 + e.a * a.x + e.b) % e.p) |
118 | quit "bad curve point"; |
119 | } |
120 | |
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121 | define ecp_pt_mul(a, b) |
122 | { |
123 | local p, n; |
124 | local d; |
125 | |
126 | if (istype(a, 1)) { |
127 | n = a; |
128 | p = b; |
129 | } else if (istype(b, 1)) { |
130 | n = b; |
131 | p = a; |
132 | } else |
133 | return (newerror("bad arguments to ecp_pt_mul")); |
134 | |
135 | d = 0; |
136 | while (n) { |
137 | if (n & 1) |
138 | d += p; |
139 | n >>= 1; |
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140 | p = ecp_pt_dbl(p); |
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141 | } |
142 | return (d); |
143 | } |
144 | |
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145 | /*----- FIPS186-2 standard curves -----------------------------------------*/ |
146 | |
147 | p192 = ecp_curve(-3, 0x64210519e59c80e70fa7e9ab72243049feb8deecc146b9b1, |
148 | 6277101735386680763835789423207666416083908700390324961279); |
149 | p192_r = 6277101735386680763835789423176059013767194773182842284081; |
150 | p192_g = ecp_pt(0x188da80eb03090f67cbf20eb43a18800f4ff0afd82ff1012, |
151 | 0x07192b95ffc8da78631011ed6b24cdd573f977a11e794811, p192); |
152 | |
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153 | /*----- That's all, folks -------------------------------------------------*/ |