d3409d5e |
1 | /* -*-c-*- |
2 | * |
ceb3f0c0 |
3 | * $Id: mp-gcd.c,v 1.5.4.1 2004/03/21 22:39:46 mdw Exp $ |
d3409d5e |
4 | * |
5 | * Extended GCD calculation |
6 | * |
7 | * (c) 1999 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: mp-gcd.c,v $ |
ceb3f0c0 |
33 | * Revision 1.5.4.1 2004/03/21 22:39:46 mdw |
34 | * Elliptic curves on binary fields work. |
35 | * |
b2253c70 |
36 | * Revision 1.5 2000/10/08 12:02:41 mdw |
37 | * Use Euclid's algorithm rather than the binary one. |
38 | * |
c9110b35 |
39 | * Revision 1.4 2000/06/17 11:34:46 mdw |
40 | * More hacking for the signs of the outputs. |
41 | * |
ef5f4810 |
42 | * Revision 1.3 1999/12/10 23:18:39 mdw |
43 | * Change interface for suggested destinations. |
44 | * |
da83a561 |
45 | * Revision 1.2 1999/11/22 20:49:56 mdw |
46 | * Fix bug which failed to favour `x' when `y' wasn't wanted and the two |
47 | * arguments needed swapping. |
48 | * |
d3409d5e |
49 | * Revision 1.1 1999/11/17 18:02:16 mdw |
50 | * New multiprecision integer arithmetic suite. |
51 | * |
52 | */ |
53 | |
54 | /*----- Header files ------------------------------------------------------*/ |
55 | |
56 | #include "mp.h" |
57 | |
58 | /*----- Main code ---------------------------------------------------------*/ |
59 | |
60 | /* --- @mp_gcd@ --- * |
61 | * |
62 | * Arguments: @mp **gcd, **xx, **yy@ = where to write the results |
63 | * @mp *a, *b@ = sources (must be nonzero) |
64 | * |
65 | * Returns: --- |
66 | * |
67 | * Use: Calculates @gcd(a, b)@, and two numbers @x@ and @y@ such that |
68 | * @ax + by = gcd(a, b)@. This is useful for computing modular |
ef5f4810 |
69 | * inverses. |
d3409d5e |
70 | */ |
71 | |
72 | void mp_gcd(mp **gcd, mp **xx, mp **yy, mp *a, mp *b) |
73 | { |
b2253c70 |
74 | mp *x = MP_ONE, *X = MP_ZERO; |
75 | mp *y = MP_ZERO, *Y = MP_ONE; |
d3409d5e |
76 | mp *u, *v; |
b2253c70 |
77 | mp *q = MP_NEW; |
ef5f4810 |
78 | unsigned f = 0; |
79 | |
ceb3f0c0 |
80 | #define f_swap 1u |
81 | #define f_aneg 2u |
82 | #define f_bneg 4u |
83 | #define f_ext 8u |
ef5f4810 |
84 | |
85 | /* --- Sort out some initial flags --- */ |
d3409d5e |
86 | |
ef5f4810 |
87 | if (xx || yy) |
88 | f |= f_ext; |
d3409d5e |
89 | |
ef5f4810 |
90 | if (a->f & MP_NEG) |
91 | f |= f_aneg; |
92 | if (b->f & MP_NEG) |
93 | f |= f_bneg; |
94 | |
95 | /* --- Ensure that @a@ is larger than @b@ --- * |
96 | * |
97 | * Use absolute values here! |
98 | */ |
99 | |
100 | if (MPX_UCMP(a->v, a->vl, <, b->v, b->vl)) { |
d3409d5e |
101 | { mp *t = a; a = b; b = t; } |
ef5f4810 |
102 | f |= f_swap; |
103 | } |
104 | |
105 | /* --- Check for zeroness --- */ |
106 | |
b2253c70 |
107 | if (MP_EQ(b, MP_ZERO)) { |
ef5f4810 |
108 | |
109 | /* --- Store %$|a|$% as the GCD --- */ |
110 | |
111 | if (gcd) { |
112 | if (*gcd) MP_DROP(*gcd); |
113 | a = MP_COPY(a); |
114 | if (a->f & MP_NEG) { |
115 | MP_SPLIT(a); |
116 | a->f &= ~MP_NEG; |
117 | f |= f_aneg; |
118 | } |
119 | *gcd = a; |
120 | } |
121 | |
122 | /* --- Store %$1$% and %$0$% in the appropriate bins --- */ |
123 | |
124 | if (f & f_ext) { |
125 | if (f & f_swap) { |
126 | mp **t = xx; xx = yy; yy = t; |
127 | } |
128 | if (xx) { |
129 | if (*xx) MP_DROP(*xx); |
b2253c70 |
130 | if (MP_EQ(a, MP_ZERO)) |
ef5f4810 |
131 | *xx = MP_ZERO; |
132 | else if (f & f_aneg) |
133 | *xx = MP_MONE; |
134 | else |
135 | *xx = MP_ONE; |
136 | } |
137 | if (yy) { |
138 | if (*yy) MP_DROP(*yy); |
139 | *yy = MP_ZERO; |
140 | } |
141 | } |
142 | return; |
d3409d5e |
143 | } |
144 | |
145 | /* --- Take a reference to the arguments --- */ |
146 | |
147 | a = MP_COPY(a); |
148 | b = MP_COPY(b); |
149 | |
150 | /* --- Make sure @a@ and @b@ are not both even --- */ |
151 | |
ef5f4810 |
152 | MP_SPLIT(a); a->f &= ~MP_NEG; |
153 | MP_SPLIT(b); b->f &= ~MP_NEG; |
154 | |
d3409d5e |
155 | u = MP_COPY(a); |
156 | v = MP_COPY(b); |
157 | |
b2253c70 |
158 | while (MP_LEN(v)) { |
159 | mp *t; |
160 | mp_div(&q, &u, u, v); |
161 | if (f & f_ext) { |
162 | t = mp_mul(MP_NEW, X, q); |
163 | t = mp_sub(t, x, t); |
164 | MP_DROP(x); x = X; X = t; |
165 | t = mp_mul(MP_NEW, Y, q); |
166 | t = mp_sub(t, y, t); |
167 | MP_DROP(y); y = Y; Y = t; |
d3409d5e |
168 | } |
b2253c70 |
169 | t = u; u = v; v = t; |
d3409d5e |
170 | } |
171 | |
b2253c70 |
172 | MP_DROP(q); |
ef5f4810 |
173 | if (!gcd) |
b2253c70 |
174 | MP_DROP(u); |
ef5f4810 |
175 | else { |
176 | if (*gcd) MP_DROP(*gcd); |
b2253c70 |
177 | u->f &= ~MP_NEG; |
178 | *gcd = u; |
ef5f4810 |
179 | } |
d3409d5e |
180 | |
181 | /* --- Perform a little normalization --- * |
182 | * |
183 | * Ensure that the coefficient returned is positive, if there is only one. |
ef5f4810 |
184 | * If there are two, favour @y@. Of course, if the original arguments were |
185 | * negative then I'll need to twiddle their signs as well. |
d3409d5e |
186 | */ |
187 | |
ef5f4810 |
188 | if (f & f_ext) { |
189 | |
190 | /* --- If @a@ and @b@ got swapped, swap the coefficients back --- */ |
191 | |
192 | if (f & f_swap) { |
d3409d5e |
193 | mp *t = x; x = y; y = t; |
da83a561 |
194 | t = a; a = b; b = t; |
d3409d5e |
195 | } |
ef5f4810 |
196 | |
197 | /* --- Sort out the signs --- * |
198 | * |
199 | * Note that %$ax + by = a(x - b) + b(y + a)$%. |
c9110b35 |
200 | * |
201 | * This is currently bodgy. It needs sorting out at some time. |
ef5f4810 |
202 | */ |
203 | |
d3409d5e |
204 | if (yy) { |
205 | if (y->f & MP_NEG) { |
c9110b35 |
206 | do { |
207 | y = mp_add(y, y, a); |
208 | x = mp_sub(x, x, b); |
209 | } while (y->f & MP_NEG); |
210 | } else { |
211 | while (MP_CMP(y, >=, a)) { |
212 | y = mp_sub(y, y, a); |
213 | x = mp_add(x, x, b); |
214 | } |
d3409d5e |
215 | } |
c9110b35 |
216 | } else { |
217 | if (x->f & MP_NEG) { |
218 | do |
219 | x = mp_add(x, x, b); |
220 | while (x->f & MP_NEG); |
221 | } else { |
222 | while (MP_CMP(x, >=, b)) |
223 | x = mp_sub(x, x, b); |
224 | } |
225 | } |
d3409d5e |
226 | |
ef5f4810 |
227 | /* --- Twiddle the signs --- */ |
228 | |
229 | if (f & f_aneg) |
230 | x->f ^= MP_NEG; |
231 | if (f & f_bneg) |
232 | y->f ^= MP_NEG; |
233 | |
234 | /* --- Store the results --- */ |
235 | |
236 | if (!xx) |
237 | MP_DROP(x); |
238 | else { |
239 | if (*xx) MP_DROP(*xx); |
240 | *xx = x; |
241 | } |
242 | |
243 | if (!yy) |
244 | MP_DROP(y); |
245 | else { |
246 | if (*yy) MP_DROP(*yy); |
247 | *yy = y; |
248 | } |
d3409d5e |
249 | } |
250 | |
b2253c70 |
251 | MP_DROP(v); |
d3409d5e |
252 | MP_DROP(X); MP_DROP(Y); |
253 | MP_DROP(a); MP_DROP(b); |
254 | } |
255 | |
256 | /*----- Test rig ----------------------------------------------------------*/ |
257 | |
258 | #ifdef TEST_RIG |
259 | |
260 | static int gcd(dstr *v) |
261 | { |
262 | int ok = 1; |
263 | mp *a = *(mp **)v[0].buf; |
264 | mp *b = *(mp **)v[1].buf; |
265 | mp *g = *(mp **)v[2].buf; |
266 | mp *x = *(mp **)v[3].buf; |
267 | mp *y = *(mp **)v[4].buf; |
268 | |
ef5f4810 |
269 | mp *gg = MP_NEW, *xx = MP_NEW, *yy = MP_NEW; |
d3409d5e |
270 | mp_gcd(&gg, &xx, &yy, a, b); |
b2253c70 |
271 | if (!MP_EQ(x, xx)) { |
d3409d5e |
272 | fputs("\n*** mp_gcd(x) failed", stderr); |
273 | fputs("\na = ", stderr); mp_writefile(a, stderr, 10); |
274 | fputs("\nb = ", stderr); mp_writefile(b, stderr, 10); |
275 | fputs("\nexpect = ", stderr); mp_writefile(x, stderr, 10); |
276 | fputs("\nresult = ", stderr); mp_writefile(xx, stderr, 10); |
277 | fputc('\n', stderr); |
278 | ok = 0; |
279 | } |
b2253c70 |
280 | if (!MP_EQ(y, yy)) { |
d3409d5e |
281 | fputs("\n*** mp_gcd(y) failed", stderr); |
282 | fputs("\na = ", stderr); mp_writefile(a, stderr, 10); |
283 | fputs("\nb = ", stderr); mp_writefile(b, stderr, 10); |
284 | fputs("\nexpect = ", stderr); mp_writefile(y, stderr, 10); |
285 | fputs("\nresult = ", stderr); mp_writefile(yy, stderr, 10); |
286 | fputc('\n', stderr); |
287 | ok = 0; |
288 | } |
289 | |
290 | if (!ok) { |
291 | mp *ax = mp_mul(MP_NEW, a, xx); |
292 | mp *by = mp_mul(MP_NEW, b, yy); |
293 | ax = mp_add(ax, ax, by); |
b2253c70 |
294 | if (MP_EQ(ax, gg)) |
d3409d5e |
295 | fputs("\n*** (Alternative result found.)\n", stderr); |
296 | MP_DROP(ax); |
297 | MP_DROP(by); |
298 | } |
299 | |
b2253c70 |
300 | if (!MP_EQ(g, gg)) { |
d3409d5e |
301 | fputs("\n*** mp_gcd(gcd) failed", stderr); |
302 | fputs("\na = ", stderr); mp_writefile(a, stderr, 10); |
303 | fputs("\nb = ", stderr); mp_writefile(b, stderr, 10); |
304 | fputs("\nexpect = ", stderr); mp_writefile(g, stderr, 10); |
305 | fputs("\nresult = ", stderr); mp_writefile(gg, stderr, 10); |
306 | fputc('\n', stderr); |
307 | ok = 0; |
308 | } |
309 | MP_DROP(a); MP_DROP(b); MP_DROP(g); MP_DROP(x); MP_DROP(y); |
310 | MP_DROP(gg); MP_DROP(xx); MP_DROP(yy); |
ef5f4810 |
311 | assert(mparena_count(MPARENA_GLOBAL) == 0); |
d3409d5e |
312 | return (ok); |
313 | } |
314 | |
315 | static test_chunk tests[] = { |
316 | { "gcd", gcd, { &type_mp, &type_mp, &type_mp, &type_mp, &type_mp, 0 } }, |
317 | { 0, 0, { 0 } } |
318 | }; |
319 | |
320 | int main(int argc, char *argv[]) |
321 | { |
322 | sub_init(); |
323 | test_run(argc, argv, tests, SRCDIR "/tests/mp"); |
324 | return (0); |
325 | } |
326 | |
327 | #endif |
328 | |
329 | /*----- That's all, folks -------------------------------------------------*/ |