ceb3f0c0 |
1 | /* -*-c-*- |
2 | * |
3 | * $Id: gf-gcd.c,v 1.1.2.1 2004/03/21 22:39:46 mdw Exp $ |
4 | * |
5 | * Euclidian algorithm on binary polynomials |
6 | * |
7 | * (c) 2004 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: gf-gcd.c,v $ |
33 | * Revision 1.1.2.1 2004/03/21 22:39:46 mdw |
34 | * Elliptic curves on binary fields work. |
35 | * |
36 | */ |
37 | |
38 | /*----- Header files ------------------------------------------------------*/ |
39 | |
40 | #include "gf.h" |
41 | |
42 | /*----- Main code ---------------------------------------------------------*/ |
43 | |
44 | /* --- @gf_gcd@ --- * |
45 | * |
46 | * Arguments: @mp **gcd, **xx, **yy@ = where to write the results |
47 | * @mp *a, *b@ = sources (must be nonzero) |
48 | * |
49 | * |
50 | * Returns: --- |
51 | * |
52 | * Use: Calculates @gcd(a, b)@, and two numbers @x@ and @y@ such that |
53 | * @ax + by = gcd(a, b)@. This is useful for computing modular |
54 | * inverses. |
55 | */ |
56 | |
57 | void gf_gcd(mp **gcd, mp **xx, mp **yy, mp *a, mp *b) |
58 | { |
59 | mp *x = MP_ONE, *X = MP_ZERO; |
60 | mp *y = MP_ZERO, *Y = MP_ONE; |
61 | mp *u, *v; |
62 | mp *q = MP_NEW; |
63 | unsigned f = 0; |
64 | |
65 | #define f_swap 1u |
66 | #define f_ext 2u |
67 | |
68 | /* --- Sort out some initial flags --- */ |
69 | |
70 | if (xx || yy) |
71 | f |= f_ext; |
72 | |
73 | /* --- Ensure that @a@ is larger than @b@ --- * |
74 | * |
75 | * If they're the same length we don't care which order they're in, so this |
76 | * unsigned comparison is fine. |
77 | */ |
78 | |
79 | if (MPX_UCMP(a->v, a->vl, <, b->v, b->vl)) { |
80 | { mp *t = a; a = b; b = t; } |
81 | f |= f_swap; |
82 | } |
83 | |
84 | /* --- Check for zeroness --- */ |
85 | |
86 | if (MP_EQ(b, MP_ZERO)) { |
87 | |
88 | /* --- Store %$|a|$% as the GCD --- */ |
89 | |
90 | if (gcd) { |
91 | if (*gcd) MP_DROP(*gcd); |
92 | a = MP_COPY(a); |
93 | *gcd = a; |
94 | } |
95 | |
96 | /* --- Store %$1$% and %$0$% in the appropriate bins --- */ |
97 | |
98 | if (f & f_ext) { |
99 | if (f & f_swap) { |
100 | mp **t = xx; xx = yy; yy = t; |
101 | } |
102 | if (xx) { |
103 | if (*xx) MP_DROP(*xx); |
104 | if (MP_EQ(a, MP_ZERO)) |
105 | *xx = MP_ZERO; |
106 | else |
107 | *xx = MP_ONE; |
108 | } |
109 | if (yy) { |
110 | if (*yy) MP_DROP(*yy); |
111 | *yy = MP_ZERO; |
112 | } |
113 | } |
114 | return; |
115 | } |
116 | |
117 | /* --- Take a reference to the arguments --- */ |
118 | |
119 | a = MP_COPY(a); |
120 | b = MP_COPY(b); |
121 | |
122 | /* --- Make sure @a@ and @b@ are not both even --- */ |
123 | |
124 | MP_SPLIT(a); a->f &= ~MP_NEG; |
125 | MP_SPLIT(b); b->f &= ~MP_NEG; |
126 | |
127 | u = MP_COPY(a); |
128 | v = MP_COPY(b); |
129 | |
130 | while (MP_LEN(v)) { |
131 | mp *t; |
132 | gf_div(&q, &u, u, v); |
133 | if (f & f_ext) { |
134 | t = gf_mul(MP_NEW, X, q); |
135 | t = gf_add(t, x, t); |
136 | MP_DROP(x); x = X; X = t; |
137 | t = gf_mul(MP_NEW, Y, q); |
138 | t = gf_add(t, y, t); |
139 | MP_DROP(y); y = Y; Y = t; |
140 | } |
141 | t = u; u = v; v = t; |
142 | } |
143 | |
144 | MP_DROP(q); |
145 | if (!gcd) |
146 | MP_DROP(u); |
147 | else { |
148 | if (*gcd) MP_DROP(*gcd); |
149 | u->f &= ~MP_NEG; |
150 | *gcd = u; |
151 | } |
152 | |
153 | /* --- Perform a little normalization --- */ |
154 | |
155 | if (f & f_ext) { |
156 | |
157 | /* --- If @a@ and @b@ got swapped, swap the coefficients back --- */ |
158 | |
159 | if (f & f_swap) { |
160 | mp *t = x; x = y; y = t; |
161 | t = a; a = b; b = t; |
162 | } |
163 | |
164 | /* --- Store the results --- */ |
165 | |
166 | if (!xx) |
167 | MP_DROP(x); |
168 | else { |
169 | if (*xx) MP_DROP(*xx); |
170 | *xx = x; |
171 | } |
172 | |
173 | if (!yy) |
174 | MP_DROP(y); |
175 | else { |
176 | if (*yy) MP_DROP(*yy); |
177 | *yy = y; |
178 | } |
179 | } |
180 | |
181 | MP_DROP(v); |
182 | MP_DROP(X); MP_DROP(Y); |
183 | MP_DROP(a); MP_DROP(b); |
184 | } |
185 | |
186 | /*----- Test rig ----------------------------------------------------------*/ |
187 | |
188 | #ifdef TEST_RIG |
189 | |
190 | static int gcd(dstr *v) |
191 | { |
192 | int ok = 1; |
193 | mp *a = *(mp **)v[0].buf; |
194 | mp *b = *(mp **)v[1].buf; |
195 | mp *g = *(mp **)v[2].buf; |
196 | mp *x = *(mp **)v[3].buf; |
197 | mp *y = *(mp **)v[4].buf; |
198 | |
199 | mp *gg = MP_NEW, *xx = MP_NEW, *yy = MP_NEW; |
200 | gf_gcd(&gg, &xx, &yy, a, b); |
201 | if (!MP_EQ(x, xx)) { |
202 | fputs("\n*** mp_gcd(x) failed", stderr); |
203 | fputs("\na = ", stderr); mp_writefile(a, stderr, 16); |
204 | fputs("\nb = ", stderr); mp_writefile(b, stderr, 16); |
205 | fputs("\nexpect = ", stderr); mp_writefile(x, stderr, 16); |
206 | fputs("\nresult = ", stderr); mp_writefile(xx, stderr, 16); |
207 | fputc('\n', stderr); |
208 | ok = 0; |
209 | } |
210 | if (!MP_EQ(y, yy)) { |
211 | fputs("\n*** mp_gcd(y) failed", stderr); |
212 | fputs("\na = ", stderr); mp_writefile(a, stderr, 16); |
213 | fputs("\nb = ", stderr); mp_writefile(b, stderr, 16); |
214 | fputs("\nexpect = ", stderr); mp_writefile(y, stderr, 16); |
215 | fputs("\nresult = ", stderr); mp_writefile(yy, stderr, 16); |
216 | fputc('\n', stderr); |
217 | ok = 0; |
218 | } |
219 | |
220 | if (!ok) { |
221 | mp *ax = gf_mul(MP_NEW, a, xx); |
222 | mp *by = gf_mul(MP_NEW, b, yy); |
223 | ax = gf_add(ax, ax, by); |
224 | if (MP_EQ(ax, gg)) |
225 | fputs("\n*** (Alternative result found.)\n", stderr); |
226 | MP_DROP(ax); |
227 | MP_DROP(by); |
228 | } |
229 | |
230 | if (!MP_EQ(g, gg)) { |
231 | fputs("\n*** mp_gcd(gcd) failed", stderr); |
232 | fputs("\na = ", stderr); mp_writefile(a, stderr, 16); |
233 | fputs("\nb = ", stderr); mp_writefile(b, stderr, 16); |
234 | fputs("\nexpect = ", stderr); mp_writefile(g, stderr, 16); |
235 | fputs("\nresult = ", stderr); mp_writefile(gg, stderr, 16); |
236 | fputc('\n', stderr); |
237 | ok = 0; |
238 | } |
239 | MP_DROP(a); MP_DROP(b); MP_DROP(g); MP_DROP(x); MP_DROP(y); |
240 | MP_DROP(gg); MP_DROP(xx); MP_DROP(yy); |
241 | assert(mparena_count(MPARENA_GLOBAL) == 0); |
242 | return (ok); |
243 | } |
244 | |
245 | static test_chunk tests[] = { |
246 | { "gcd", gcd, { &type_mp, &type_mp, &type_mp, &type_mp, &type_mp, 0 } }, |
247 | { 0, 0, { 0 } } |
248 | }; |
249 | |
250 | int main(int argc, char *argv[]) |
251 | { |
252 | sub_init(); |
253 | test_run(argc, argv, tests, SRCDIR "/tests/gf"); |
254 | return (0); |
255 | } |
256 | |
257 | #endif |
258 | |
259 | /*----- That's all, folks -------------------------------------------------*/ |