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1 | /* -*-apcalc-*- |
2 | * |
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3 | * $Id: gfx.cal,v 1.2 2004/03/21 22:52:06 mdw Exp $ |
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4 | * |
5 | * Testbed for %$\gf{2}$% poltnomial arithmetic |
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: gfx.cal,v $ |
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33 | * Revision 1.2 2004/03/21 22:52:06 mdw |
34 | * Merge and close elliptic curve branch. |
35 | * |
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36 | * Revision 1.1.4.1 2004/03/21 22:39:46 mdw |
37 | * Elliptic curves on binary fields work. |
38 | * |
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39 | * Revision 1.1 2000/10/08 16:01:37 mdw |
40 | * Prototypes of various bits of code. |
41 | * |
42 | */ |
43 | |
44 | /*----- Object types ------------------------------------------------------*/ |
45 | |
46 | obj gf { x }; |
47 | |
48 | /*----- Static variables --------------------------------------------------*/ |
49 | |
50 | static obj gf example_gf_object; |
51 | |
52 | /*----- Main code ---------------------------------------------------------*/ |
53 | |
54 | dummy = config("lib_debug", -1); |
55 | |
56 | define gf(x) |
57 | { |
58 | local obj gf g; |
59 | g.x = x; |
60 | return (g); |
61 | } |
62 | |
63 | define gfint(x) |
64 | { |
65 | if (istype(x, example_gf_object)) |
66 | return (x.x); |
67 | else |
68 | return (x); |
69 | } |
70 | |
71 | define gf_add(x, y) = gf(xor(gfint(x), gfint(y))); |
72 | define gf_sub(x, y) = gf(xor(gfint(x), gfint(y))); |
73 | define gf_neg(x) = x; |
74 | |
75 | define gf_mul(x, y) |
76 | { |
77 | local a = gfint(x), b = gfint(y), z = 0, i, bits = highbit(a); |
78 | for (i = 0; i <= bits; i++) { |
79 | if (bit(a, i)) |
80 | z = xor(z, b << i); |
81 | } |
82 | return gf(z); |
83 | } |
84 | |
85 | define gfx_div(rx, dx) |
86 | { |
87 | local r = gfint(rx), d = gfint(dx), i; |
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88 | local q = 0, dbits, rbits; |
89 | dbits = highbit(d); |
90 | rbits = highbit(r); |
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91 | for (i = rbits - dbits; i >= 0; i--) { |
92 | if (bit(r, i + dbits)) { |
93 | r = xor(r, d << i); |
94 | q |= (1 << i); |
95 | } |
96 | } |
97 | return list(q, r); |
98 | } |
99 | |
100 | define gf_div(x, y) |
101 | { |
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102 | local l; |
103 | l = gfx_div(x, y); |
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104 | return gf(l[[0]]); |
105 | } |
106 | |
107 | define gf_mod(x, y) |
108 | { |
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109 | local l; |
110 | l = gfx_div(x, y); |
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111 | return gf(l[[1]]); |
112 | } |
113 | |
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114 | define gf_inv(a, b) |
115 | { |
116 | local g, x, y, X, Y, u, v, t, q, r; |
117 | x = gf(1); X = gf(0); |
118 | y = gf(0); Y = gf(1); |
119 | |
120 | if (b == gf(0)) { g = a; } else if (a == gf(0)) { g = b; } |
121 | else { |
122 | while (b != gf(0)) { |
123 | q = gf_div(b, a); r = gf_mod(b, a); |
124 | t = X * q + x; x = X; X = t; |
125 | t = Y * q + y; y = Y; Y = t; |
126 | b = a; a = r; |
127 | } |
128 | g = a; |
129 | } |
130 | if (g != gf(1)) quit "not coprime in gf_inv"; |
131 | return Y; |
132 | } |
133 | |
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134 | /*----- That's all, folks -------------------------------------------------*/ |