d3409d5e |
1 | /* -*-c-*- |
2 | * |
c3caa2fa |
3 | * $Id: mp-gcd.c,v 1.6 2004/03/21 22:52:06 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 $ |
c3caa2fa |
33 | * Revision 1.6 2004/03/21 22:52:06 mdw |
34 | * Merge and close elliptic curve branch. |
35 | * |
ceb3f0c0 |
36 | * Revision 1.5.4.1 2004/03/21 22:39:46 mdw |
37 | * Elliptic curves on binary fields work. |
38 | * |
b2253c70 |
39 | * Revision 1.5 2000/10/08 12:02:41 mdw |
40 | * Use Euclid's algorithm rather than the binary one. |
41 | * |
c9110b35 |
42 | * Revision 1.4 2000/06/17 11:34:46 mdw |
43 | * More hacking for the signs of the outputs. |
44 | * |
ef5f4810 |
45 | * Revision 1.3 1999/12/10 23:18:39 mdw |
46 | * Change interface for suggested destinations. |
47 | * |
da83a561 |
48 | * Revision 1.2 1999/11/22 20:49:56 mdw |
49 | * Fix bug which failed to favour `x' when `y' wasn't wanted and the two |
50 | * arguments needed swapping. |
51 | * |
d3409d5e |
52 | * Revision 1.1 1999/11/17 18:02:16 mdw |
53 | * New multiprecision integer arithmetic suite. |
54 | * |
55 | */ |
56 | |
57 | /*----- Header files ------------------------------------------------------*/ |
58 | |
59 | #include "mp.h" |
60 | |
61 | /*----- Main code ---------------------------------------------------------*/ |
62 | |
63 | /* --- @mp_gcd@ --- * |
64 | * |
65 | * Arguments: @mp **gcd, **xx, **yy@ = where to write the results |
66 | * @mp *a, *b@ = sources (must be nonzero) |
67 | * |
68 | * Returns: --- |
69 | * |
70 | * Use: Calculates @gcd(a, b)@, and two numbers @x@ and @y@ such that |
71 | * @ax + by = gcd(a, b)@. This is useful for computing modular |
ef5f4810 |
72 | * inverses. |
d3409d5e |
73 | */ |
74 | |
75 | void mp_gcd(mp **gcd, mp **xx, mp **yy, mp *a, mp *b) |
76 | { |
b2253c70 |
77 | mp *x = MP_ONE, *X = MP_ZERO; |
78 | mp *y = MP_ZERO, *Y = MP_ONE; |
d3409d5e |
79 | mp *u, *v; |
b2253c70 |
80 | mp *q = MP_NEW; |
ef5f4810 |
81 | unsigned f = 0; |
82 | |
ceb3f0c0 |
83 | #define f_swap 1u |
84 | #define f_aneg 2u |
85 | #define f_bneg 4u |
86 | #define f_ext 8u |
ef5f4810 |
87 | |
88 | /* --- Sort out some initial flags --- */ |
d3409d5e |
89 | |
ef5f4810 |
90 | if (xx || yy) |
91 | f |= f_ext; |
d3409d5e |
92 | |
ef5f4810 |
93 | if (a->f & MP_NEG) |
94 | f |= f_aneg; |
95 | if (b->f & MP_NEG) |
96 | f |= f_bneg; |
97 | |
98 | /* --- Ensure that @a@ is larger than @b@ --- * |
99 | * |
100 | * Use absolute values here! |
101 | */ |
102 | |
103 | if (MPX_UCMP(a->v, a->vl, <, b->v, b->vl)) { |
d3409d5e |
104 | { mp *t = a; a = b; b = t; } |
ef5f4810 |
105 | f |= f_swap; |
106 | } |
107 | |
108 | /* --- Check for zeroness --- */ |
109 | |
b2253c70 |
110 | if (MP_EQ(b, MP_ZERO)) { |
ef5f4810 |
111 | |
112 | /* --- Store %$|a|$% as the GCD --- */ |
113 | |
114 | if (gcd) { |
115 | if (*gcd) MP_DROP(*gcd); |
116 | a = MP_COPY(a); |
117 | if (a->f & MP_NEG) { |
118 | MP_SPLIT(a); |
119 | a->f &= ~MP_NEG; |
120 | f |= f_aneg; |
121 | } |
122 | *gcd = a; |
123 | } |
124 | |
125 | /* --- Store %$1$% and %$0$% in the appropriate bins --- */ |
126 | |
127 | if (f & f_ext) { |
128 | if (f & f_swap) { |
129 | mp **t = xx; xx = yy; yy = t; |
130 | } |
131 | if (xx) { |
132 | if (*xx) MP_DROP(*xx); |
b2253c70 |
133 | if (MP_EQ(a, MP_ZERO)) |
ef5f4810 |
134 | *xx = MP_ZERO; |
135 | else if (f & f_aneg) |
136 | *xx = MP_MONE; |
137 | else |
138 | *xx = MP_ONE; |
139 | } |
140 | if (yy) { |
141 | if (*yy) MP_DROP(*yy); |
142 | *yy = MP_ZERO; |
143 | } |
144 | } |
145 | return; |
d3409d5e |
146 | } |
147 | |
148 | /* --- Take a reference to the arguments --- */ |
149 | |
150 | a = MP_COPY(a); |
151 | b = MP_COPY(b); |
152 | |
153 | /* --- Make sure @a@ and @b@ are not both even --- */ |
154 | |
ef5f4810 |
155 | MP_SPLIT(a); a->f &= ~MP_NEG; |
156 | MP_SPLIT(b); b->f &= ~MP_NEG; |
157 | |
d3409d5e |
158 | u = MP_COPY(a); |
159 | v = MP_COPY(b); |
160 | |
b2253c70 |
161 | while (MP_LEN(v)) { |
162 | mp *t; |
163 | mp_div(&q, &u, u, v); |
164 | if (f & f_ext) { |
165 | t = mp_mul(MP_NEW, X, q); |
166 | t = mp_sub(t, x, t); |
167 | MP_DROP(x); x = X; X = t; |
168 | t = mp_mul(MP_NEW, Y, q); |
169 | t = mp_sub(t, y, t); |
170 | MP_DROP(y); y = Y; Y = t; |
d3409d5e |
171 | } |
b2253c70 |
172 | t = u; u = v; v = t; |
d3409d5e |
173 | } |
174 | |
b2253c70 |
175 | MP_DROP(q); |
ef5f4810 |
176 | if (!gcd) |
b2253c70 |
177 | MP_DROP(u); |
ef5f4810 |
178 | else { |
179 | if (*gcd) MP_DROP(*gcd); |
b2253c70 |
180 | u->f &= ~MP_NEG; |
181 | *gcd = u; |
ef5f4810 |
182 | } |
d3409d5e |
183 | |
184 | /* --- Perform a little normalization --- * |
185 | * |
186 | * Ensure that the coefficient returned is positive, if there is only one. |
ef5f4810 |
187 | * If there are two, favour @y@. Of course, if the original arguments were |
188 | * negative then I'll need to twiddle their signs as well. |
d3409d5e |
189 | */ |
190 | |
ef5f4810 |
191 | if (f & f_ext) { |
192 | |
193 | /* --- If @a@ and @b@ got swapped, swap the coefficients back --- */ |
194 | |
195 | if (f & f_swap) { |
d3409d5e |
196 | mp *t = x; x = y; y = t; |
da83a561 |
197 | t = a; a = b; b = t; |
d3409d5e |
198 | } |
ef5f4810 |
199 | |
200 | /* --- Sort out the signs --- * |
201 | * |
202 | * Note that %$ax + by = a(x - b) + b(y + a)$%. |
c9110b35 |
203 | * |
204 | * This is currently bodgy. It needs sorting out at some time. |
ef5f4810 |
205 | */ |
206 | |
d3409d5e |
207 | if (yy) { |
208 | if (y->f & MP_NEG) { |
c9110b35 |
209 | do { |
210 | y = mp_add(y, y, a); |
211 | x = mp_sub(x, x, b); |
212 | } while (y->f & MP_NEG); |
213 | } else { |
214 | while (MP_CMP(y, >=, a)) { |
215 | y = mp_sub(y, y, a); |
216 | x = mp_add(x, x, b); |
217 | } |
d3409d5e |
218 | } |
c9110b35 |
219 | } else { |
220 | if (x->f & MP_NEG) { |
221 | do |
222 | x = mp_add(x, x, b); |
223 | while (x->f & MP_NEG); |
224 | } else { |
225 | while (MP_CMP(x, >=, b)) |
226 | x = mp_sub(x, x, b); |
227 | } |
228 | } |
d3409d5e |
229 | |
ef5f4810 |
230 | /* --- Twiddle the signs --- */ |
231 | |
232 | if (f & f_aneg) |
233 | x->f ^= MP_NEG; |
234 | if (f & f_bneg) |
235 | y->f ^= MP_NEG; |
236 | |
237 | /* --- Store the results --- */ |
238 | |
239 | if (!xx) |
240 | MP_DROP(x); |
241 | else { |
242 | if (*xx) MP_DROP(*xx); |
243 | *xx = x; |
244 | } |
245 | |
246 | if (!yy) |
247 | MP_DROP(y); |
248 | else { |
249 | if (*yy) MP_DROP(*yy); |
250 | *yy = y; |
251 | } |
d3409d5e |
252 | } |
253 | |
b2253c70 |
254 | MP_DROP(v); |
d3409d5e |
255 | MP_DROP(X); MP_DROP(Y); |
256 | MP_DROP(a); MP_DROP(b); |
257 | } |
258 | |
259 | /*----- Test rig ----------------------------------------------------------*/ |
260 | |
261 | #ifdef TEST_RIG |
262 | |
263 | static int gcd(dstr *v) |
264 | { |
265 | int ok = 1; |
266 | mp *a = *(mp **)v[0].buf; |
267 | mp *b = *(mp **)v[1].buf; |
268 | mp *g = *(mp **)v[2].buf; |
269 | mp *x = *(mp **)v[3].buf; |
270 | mp *y = *(mp **)v[4].buf; |
271 | |
ef5f4810 |
272 | mp *gg = MP_NEW, *xx = MP_NEW, *yy = MP_NEW; |
d3409d5e |
273 | mp_gcd(&gg, &xx, &yy, a, b); |
b2253c70 |
274 | if (!MP_EQ(x, xx)) { |
d3409d5e |
275 | fputs("\n*** mp_gcd(x) failed", stderr); |
276 | fputs("\na = ", stderr); mp_writefile(a, stderr, 10); |
277 | fputs("\nb = ", stderr); mp_writefile(b, stderr, 10); |
278 | fputs("\nexpect = ", stderr); mp_writefile(x, stderr, 10); |
279 | fputs("\nresult = ", stderr); mp_writefile(xx, stderr, 10); |
280 | fputc('\n', stderr); |
281 | ok = 0; |
282 | } |
b2253c70 |
283 | if (!MP_EQ(y, yy)) { |
d3409d5e |
284 | fputs("\n*** mp_gcd(y) failed", stderr); |
285 | fputs("\na = ", stderr); mp_writefile(a, stderr, 10); |
286 | fputs("\nb = ", stderr); mp_writefile(b, stderr, 10); |
287 | fputs("\nexpect = ", stderr); mp_writefile(y, stderr, 10); |
288 | fputs("\nresult = ", stderr); mp_writefile(yy, stderr, 10); |
289 | fputc('\n', stderr); |
290 | ok = 0; |
291 | } |
292 | |
293 | if (!ok) { |
294 | mp *ax = mp_mul(MP_NEW, a, xx); |
295 | mp *by = mp_mul(MP_NEW, b, yy); |
296 | ax = mp_add(ax, ax, by); |
b2253c70 |
297 | if (MP_EQ(ax, gg)) |
d3409d5e |
298 | fputs("\n*** (Alternative result found.)\n", stderr); |
299 | MP_DROP(ax); |
300 | MP_DROP(by); |
301 | } |
302 | |
b2253c70 |
303 | if (!MP_EQ(g, gg)) { |
d3409d5e |
304 | fputs("\n*** mp_gcd(gcd) failed", stderr); |
305 | fputs("\na = ", stderr); mp_writefile(a, stderr, 10); |
306 | fputs("\nb = ", stderr); mp_writefile(b, stderr, 10); |
307 | fputs("\nexpect = ", stderr); mp_writefile(g, stderr, 10); |
308 | fputs("\nresult = ", stderr); mp_writefile(gg, stderr, 10); |
309 | fputc('\n', stderr); |
310 | ok = 0; |
311 | } |
312 | MP_DROP(a); MP_DROP(b); MP_DROP(g); MP_DROP(x); MP_DROP(y); |
313 | MP_DROP(gg); MP_DROP(xx); MP_DROP(yy); |
ef5f4810 |
314 | assert(mparena_count(MPARENA_GLOBAL) == 0); |
d3409d5e |
315 | return (ok); |
316 | } |
317 | |
318 | static test_chunk tests[] = { |
319 | { "gcd", gcd, { &type_mp, &type_mp, &type_mp, &type_mp, &type_mp, 0 } }, |
320 | { 0, 0, { 0 } } |
321 | }; |
322 | |
323 | int main(int argc, char *argv[]) |
324 | { |
325 | sub_init(); |
326 | test_run(argc, argv, tests, SRCDIR "/tests/mp"); |
327 | return (0); |
328 | } |
329 | |
330 | #endif |
331 | |
332 | /*----- That's all, folks -------------------------------------------------*/ |