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