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1 | /* -*-apcalc-*- |
2 | * |
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3 | * $Id: ec2.cal,v 1.4 2004/04/08 01:36:15 mdw Exp $ |
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4 | * |
5 | * Testbed for elliptic curve arithmetic over binary fields |
6 | * |
7 | * (c) 2004 Straylight/Edgeware |
8 | */ |
9 | |
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10 | /*----- Licensing notice --------------------------------------------------* |
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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. |
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18 | * |
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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. |
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23 | * |
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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 ec2_curve { a, b, p }; |
33 | obj ec2_pt { x, y, e }; |
34 | obj ecpp_pt { x, y, z, e }; |
35 | |
36 | /*----- Main code ---------------------------------------------------------*/ |
37 | |
38 | define ec2_curve(a, b, p) |
39 | { |
40 | local obj ec2_curve e; |
41 | e.a = a; |
42 | e.b = b; |
43 | e.p = p; |
44 | return (e); |
45 | } |
46 | |
47 | define ec2_pt(x, y, e) |
48 | { |
49 | local obj ec2_pt p; |
50 | p.x = x % e.p; |
51 | p.y = y % e.p; |
52 | p.e = e; |
53 | return (p); |
54 | } |
55 | |
56 | define ec2_pt_print(a) |
57 | { |
58 | print "(" : a.x : ", " : a.y : ")" :; |
59 | } |
60 | |
61 | define ec2_pt_add(a, b) |
62 | { |
63 | local e, alpha; |
64 | local obj ec2_pt d; |
65 | |
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66 | if (a == 0) |
67 | d = b; |
68 | else if (b == 0) |
69 | d = a; |
70 | else if (!istype(a, b)) |
71 | quit "bad type arguments to ec2_pt_add"; |
72 | else if (a.e != b.e) |
73 | quit "points from different curves in ec2_pt_add"; |
74 | else { |
75 | e = a.e; |
76 | if (a.x != b.x) { |
77 | alpha = ((a.y + b.y) * gf_inv(a.x + b.x, e.p)) % e.p; |
78 | d.x = (e.a + alpha^2 + alpha + a.x + b.x) % e.p; |
79 | } else if (a.y != b.y || a.x == gf(0)) |
80 | return 0; |
81 | else { |
82 | alpha = a.x + a.y * gf_inv(a.x, e.p) % e.p; |
83 | d.x = (e.a + alpha^2 + alpha) % e.p; |
84 | } |
85 | d.y = ((a.x + d.x) * alpha + d.x + a.y) % e.p; |
86 | d.e = e; |
87 | } |
88 | |
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89 | return (d); |
90 | } |
91 | |
92 | define ec2_pt_dbl(a) |
93 | { |
94 | local e, alpha; |
95 | local obj ec2_pt d; |
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96 | if (istype(a, 1)) |
97 | return (0); |
98 | e = a.e; |
99 | alpha = a.x + a.y * gf_inv(a.x, e.p) % e.p; |
100 | d.x = (e.a + alpha^2 + alpha) % e.p; |
101 | d.y = ((a.x + d.x) * alpha + d.x + a.y) % e.p; |
102 | d.e = e; |
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103 | return (d); |
104 | } |
105 | |
106 | define ec2_pt_sub(a, b) { return ec2_pt_add(a, ec2_pt_neg(b)); } |
107 | |
108 | define ec2_pt_neg(a) |
109 | { |
110 | local obj ec2_pt d; |
111 | d.x = a.x; |
112 | d.y = a.x + a.y; |
113 | d.e = a.e; |
114 | return (d); |
115 | } |
116 | |
117 | define ec2_pt_check(a) |
118 | { |
119 | local e; |
120 | |
121 | e = a.e; |
122 | if ((a.y^2 + a.x * a.y) % e.p != (a.x^3 + e.a * a.x^2 + e.b) % e.p) |
123 | quit "bad curve point"; |
124 | } |
125 | |
126 | define ec2_pt_mul(a, b) |
127 | { |
128 | local p, n; |
129 | local d; |
130 | |
131 | if (istype(a, 1)) { |
132 | n = a; |
133 | p = b; |
134 | } else if (istype(b, 1)) { |
135 | n = b; |
136 | p = a; |
137 | } else |
138 | return (newerror("bad arguments to ec2_pt_mul")); |
139 | |
140 | d = 0; |
141 | while (n) { |
142 | if (n & 1) |
143 | d += p; |
144 | n >>= 1; |
145 | p = ec2_pt_dbl(p); |
146 | } |
147 | return (d); |
148 | } |
149 | |
150 | /*----- FIPS186-2 standard curves -----------------------------------------*/ |
151 | |
152 | b163 = ec2_curve(gf(1),gf(0x20a601907b8c953ca1481eb10512f78744a3205fd), |
153 | gf(0x800000000000000000000000000000000000000c9)); |
154 | b163_r = 5846006549323611672814742442876390689256843201587; |
155 | b163_g = ec2_pt(0x3f0eba16286a2d57ea0991168d4994637e8343e36, |
156 | 0x0d51fbc6c71a0094fa2cdd545b11c5c0c797324f1, b163); |
157 | |
158 | /*----- That's all, folks -------------------------------------------------*/ |
159 | |