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d3409d5e | 1 | /* -*-c-*- |
2 | * | |
a69a3efd | 3 | * $Id$ |
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 | ||
d3409d5e | 30 | /*----- Header files ------------------------------------------------------*/ |
31 | ||
32 | #include "mp.h" | |
33 | ||
34 | /*----- Main code ---------------------------------------------------------*/ | |
35 | ||
36 | /* --- @mp_gcd@ --- * | |
37 | * | |
38 | * Arguments: @mp **gcd, **xx, **yy@ = where to write the results | |
39 | * @mp *a, *b@ = sources (must be nonzero) | |
40 | * | |
41 | * Returns: --- | |
42 | * | |
43 | * Use: Calculates @gcd(a, b)@, and two numbers @x@ and @y@ such that | |
44 | * @ax + by = gcd(a, b)@. This is useful for computing modular | |
ef5f4810 | 45 | * inverses. |
d3409d5e | 46 | */ |
47 | ||
48 | void mp_gcd(mp **gcd, mp **xx, mp **yy, mp *a, mp *b) | |
49 | { | |
b2253c70 | 50 | mp *x = MP_ONE, *X = MP_ZERO; |
51 | mp *y = MP_ZERO, *Y = MP_ONE; | |
d3409d5e | 52 | mp *u, *v; |
b2253c70 | 53 | mp *q = MP_NEW; |
ef5f4810 | 54 | unsigned f = 0; |
55 | ||
ceb3f0c0 | 56 | #define f_swap 1u |
57 | #define f_aneg 2u | |
58 | #define f_bneg 4u | |
59 | #define f_ext 8u | |
ef5f4810 | 60 | |
61 | /* --- Sort out some initial flags --- */ | |
d3409d5e | 62 | |
ef5f4810 | 63 | if (xx || yy) |
64 | f |= f_ext; | |
d3409d5e | 65 | |
a69a3efd | 66 | if (MP_NEGP(a)) |
ef5f4810 | 67 | f |= f_aneg; |
a69a3efd | 68 | if (MP_NEGP(b)) |
ef5f4810 | 69 | f |= f_bneg; |
70 | ||
71 | /* --- Ensure that @a@ is larger than @b@ --- * | |
72 | * | |
73 | * Use absolute values here! | |
74 | */ | |
75 | ||
76 | if (MPX_UCMP(a->v, a->vl, <, b->v, b->vl)) { | |
d3409d5e | 77 | { mp *t = a; a = b; b = t; } |
ef5f4810 | 78 | f |= f_swap; |
79 | } | |
80 | ||
81 | /* --- Check for zeroness --- */ | |
82 | ||
b2253c70 | 83 | if (MP_EQ(b, MP_ZERO)) { |
ef5f4810 | 84 | |
85 | /* --- Store %$|a|$% as the GCD --- */ | |
86 | ||
87 | if (gcd) { | |
88 | if (*gcd) MP_DROP(*gcd); | |
89 | a = MP_COPY(a); | |
a69a3efd | 90 | if (MP_NEGP(a)) { |
ef5f4810 | 91 | MP_SPLIT(a); |
92 | a->f &= ~MP_NEG; | |
93 | f |= f_aneg; | |
94 | } | |
95 | *gcd = a; | |
96 | } | |
97 | ||
98 | /* --- Store %$1$% and %$0$% in the appropriate bins --- */ | |
99 | ||
100 | if (f & f_ext) { | |
101 | if (f & f_swap) { | |
102 | mp **t = xx; xx = yy; yy = t; | |
103 | } | |
104 | if (xx) { | |
105 | if (*xx) MP_DROP(*xx); | |
b2253c70 | 106 | if (MP_EQ(a, MP_ZERO)) |
ef5f4810 | 107 | *xx = MP_ZERO; |
108 | else if (f & f_aneg) | |
109 | *xx = MP_MONE; | |
110 | else | |
111 | *xx = MP_ONE; | |
112 | } | |
113 | if (yy) { | |
114 | if (*yy) MP_DROP(*yy); | |
115 | *yy = MP_ZERO; | |
116 | } | |
117 | } | |
118 | return; | |
d3409d5e | 119 | } |
120 | ||
121 | /* --- Take a reference to the arguments --- */ | |
122 | ||
123 | a = MP_COPY(a); | |
124 | b = MP_COPY(b); | |
125 | ||
126 | /* --- Make sure @a@ and @b@ are not both even --- */ | |
127 | ||
ef5f4810 | 128 | MP_SPLIT(a); a->f &= ~MP_NEG; |
129 | MP_SPLIT(b); b->f &= ~MP_NEG; | |
130 | ||
d3409d5e | 131 | u = MP_COPY(a); |
132 | v = MP_COPY(b); | |
133 | ||
a69a3efd | 134 | while (!MP_ZEROP(v)) { |
b2253c70 | 135 | mp *t; |
136 | mp_div(&q, &u, u, v); | |
137 | if (f & f_ext) { | |
138 | t = mp_mul(MP_NEW, X, q); | |
139 | t = mp_sub(t, x, t); | |
140 | MP_DROP(x); x = X; X = t; | |
141 | t = mp_mul(MP_NEW, Y, q); | |
142 | t = mp_sub(t, y, t); | |
143 | MP_DROP(y); y = Y; Y = t; | |
d3409d5e | 144 | } |
b2253c70 | 145 | t = u; u = v; v = t; |
d3409d5e | 146 | } |
147 | ||
b2253c70 | 148 | MP_DROP(q); |
ef5f4810 | 149 | if (!gcd) |
b2253c70 | 150 | MP_DROP(u); |
ef5f4810 | 151 | else { |
152 | if (*gcd) MP_DROP(*gcd); | |
b2253c70 | 153 | u->f &= ~MP_NEG; |
154 | *gcd = u; | |
ef5f4810 | 155 | } |
d3409d5e | 156 | |
157 | /* --- Perform a little normalization --- * | |
158 | * | |
159 | * Ensure that the coefficient returned is positive, if there is only one. | |
ef5f4810 | 160 | * If there are two, favour @y@. Of course, if the original arguments were |
161 | * negative then I'll need to twiddle their signs as well. | |
d3409d5e | 162 | */ |
163 | ||
ef5f4810 | 164 | if (f & f_ext) { |
165 | ||
166 | /* --- If @a@ and @b@ got swapped, swap the coefficients back --- */ | |
167 | ||
168 | if (f & f_swap) { | |
d3409d5e | 169 | mp *t = x; x = y; y = t; |
da83a561 | 170 | t = a; a = b; b = t; |
d3409d5e | 171 | } |
ef5f4810 | 172 | |
173 | /* --- Sort out the signs --- * | |
174 | * | |
175 | * Note that %$ax + by = a(x - b) + b(y + a)$%. | |
c9110b35 | 176 | * |
177 | * This is currently bodgy. It needs sorting out at some time. | |
ef5f4810 | 178 | */ |
179 | ||
d3409d5e | 180 | if (yy) { |
a69a3efd | 181 | if (MP_NEGP(y)) { |
c9110b35 | 182 | do { |
183 | y = mp_add(y, y, a); | |
184 | x = mp_sub(x, x, b); | |
a69a3efd | 185 | } while (MP_NEGP(y)); |
c9110b35 | 186 | } else { |
187 | while (MP_CMP(y, >=, a)) { | |
188 | y = mp_sub(y, y, a); | |
189 | x = mp_add(x, x, b); | |
190 | } | |
d3409d5e | 191 | } |
c9110b35 | 192 | } else { |
a69a3efd | 193 | if (MP_NEGP(x)) { |
c9110b35 | 194 | do |
195 | x = mp_add(x, x, b); | |
a69a3efd | 196 | while (MP_NEGP(x)); |
c9110b35 | 197 | } else { |
198 | while (MP_CMP(x, >=, b)) | |
199 | x = mp_sub(x, x, b); | |
200 | } | |
201 | } | |
d3409d5e | 202 | |
ef5f4810 | 203 | /* --- Twiddle the signs --- */ |
204 | ||
205 | if (f & f_aneg) | |
206 | x->f ^= MP_NEG; | |
207 | if (f & f_bneg) | |
208 | y->f ^= MP_NEG; | |
209 | ||
210 | /* --- Store the results --- */ | |
211 | ||
212 | if (!xx) | |
213 | MP_DROP(x); | |
214 | else { | |
215 | if (*xx) MP_DROP(*xx); | |
216 | *xx = x; | |
217 | } | |
218 | ||
219 | if (!yy) | |
220 | MP_DROP(y); | |
221 | else { | |
222 | if (*yy) MP_DROP(*yy); | |
223 | *yy = y; | |
224 | } | |
d3409d5e | 225 | } |
226 | ||
b2253c70 | 227 | MP_DROP(v); |
d3409d5e | 228 | MP_DROP(X); MP_DROP(Y); |
229 | MP_DROP(a); MP_DROP(b); | |
230 | } | |
231 | ||
b817bfc6 | 232 | /* -- @mp_modinv@ --- * |
233 | * | |
234 | * Arguments: @mp *d@ = destination | |
235 | * @mp *x@ = argument | |
236 | * @mp *p@ = modulus | |
237 | * | |
238 | * Returns: The inverse %$x^{-1} \bmod p$%. | |
239 | * | |
240 | * Use: Computes a modular inverse. An assertion fails if %$p$% | |
241 | * has no inverse. | |
242 | */ | |
243 | ||
244 | mp *mp_modinv(mp *d, mp *x, mp *p) | |
245 | { | |
246 | mp *g = MP_NEW; | |
247 | mp_gcd(&g, 0, &d, p, x); | |
248 | assert(MP_EQ(g, MP_ONE)); | |
249 | mp_drop(g); | |
250 | return (d); | |
251 | } | |
252 | ||
d3409d5e | 253 | /*----- Test rig ----------------------------------------------------------*/ |
254 | ||
255 | #ifdef TEST_RIG | |
256 | ||
7c404803 MW |
257 | static int modinv(dstr *v) |
258 | { | |
259 | int ok = 1; | |
260 | mp *x = *(mp **)v[0].buf; | |
261 | mp *m = *(mp **)v[1].buf; | |
262 | mp *r = *(mp **)v[2].buf; | |
263 | ||
264 | mp *y = mp_modinv(MP_NEW, x, m); | |
265 | if (!MP_EQ(y, r)) { | |
266 | fputs("\n*** mp_modinv failed", stderr); | |
267 | fputs("\nx = ", stderr); mp_writefile(x, stderr, 10); | |
268 | fputs("\nm = ", stderr); mp_writefile(m, stderr, 10); | |
269 | fputs("\nexpect = ", stderr); mp_writefile(r, stderr, 10); | |
270 | fputs("\nresult = ", stderr); mp_writefile(y, stderr, 10); | |
271 | ok = 0; | |
272 | } | |
273 | MP_DROP(x); MP_DROP(m); MP_DROP(r); MP_DROP(y); | |
274 | assert(mparena_count(MPARENA_GLOBAL) == 0); | |
275 | return (ok); | |
276 | } | |
277 | ||
d3409d5e | 278 | static int gcd(dstr *v) |
279 | { | |
280 | int ok = 1; | |
281 | mp *a = *(mp **)v[0].buf; | |
282 | mp *b = *(mp **)v[1].buf; | |
283 | mp *g = *(mp **)v[2].buf; | |
284 | mp *x = *(mp **)v[3].buf; | |
285 | mp *y = *(mp **)v[4].buf; | |
286 | ||
ef5f4810 | 287 | mp *gg = MP_NEW, *xx = MP_NEW, *yy = MP_NEW; |
d3409d5e | 288 | mp_gcd(&gg, &xx, &yy, a, b); |
b2253c70 | 289 | if (!MP_EQ(x, xx)) { |
d3409d5e | 290 | fputs("\n*** mp_gcd(x) failed", stderr); |
291 | fputs("\na = ", stderr); mp_writefile(a, stderr, 10); | |
292 | fputs("\nb = ", stderr); mp_writefile(b, stderr, 10); | |
293 | fputs("\nexpect = ", stderr); mp_writefile(x, stderr, 10); | |
294 | fputs("\nresult = ", stderr); mp_writefile(xx, stderr, 10); | |
295 | fputc('\n', stderr); | |
296 | ok = 0; | |
297 | } | |
b2253c70 | 298 | if (!MP_EQ(y, yy)) { |
d3409d5e | 299 | fputs("\n*** mp_gcd(y) failed", stderr); |
300 | fputs("\na = ", stderr); mp_writefile(a, stderr, 10); | |
301 | fputs("\nb = ", stderr); mp_writefile(b, stderr, 10); | |
302 | fputs("\nexpect = ", stderr); mp_writefile(y, stderr, 10); | |
303 | fputs("\nresult = ", stderr); mp_writefile(yy, stderr, 10); | |
304 | fputc('\n', stderr); | |
305 | ok = 0; | |
306 | } | |
307 | ||
308 | if (!ok) { | |
309 | mp *ax = mp_mul(MP_NEW, a, xx); | |
310 | mp *by = mp_mul(MP_NEW, b, yy); | |
311 | ax = mp_add(ax, ax, by); | |
b2253c70 | 312 | if (MP_EQ(ax, gg)) |
d3409d5e | 313 | fputs("\n*** (Alternative result found.)\n", stderr); |
314 | MP_DROP(ax); | |
315 | MP_DROP(by); | |
316 | } | |
317 | ||
b2253c70 | 318 | if (!MP_EQ(g, gg)) { |
d3409d5e | 319 | fputs("\n*** mp_gcd(gcd) failed", stderr); |
320 | fputs("\na = ", stderr); mp_writefile(a, stderr, 10); | |
321 | fputs("\nb = ", stderr); mp_writefile(b, stderr, 10); | |
322 | fputs("\nexpect = ", stderr); mp_writefile(g, stderr, 10); | |
323 | fputs("\nresult = ", stderr); mp_writefile(gg, stderr, 10); | |
324 | fputc('\n', stderr); | |
325 | ok = 0; | |
326 | } | |
327 | MP_DROP(a); MP_DROP(b); MP_DROP(g); MP_DROP(x); MP_DROP(y); | |
328 | MP_DROP(gg); MP_DROP(xx); MP_DROP(yy); | |
ef5f4810 | 329 | assert(mparena_count(MPARENA_GLOBAL) == 0); |
d3409d5e | 330 | return (ok); |
331 | } | |
332 | ||
333 | static test_chunk tests[] = { | |
334 | { "gcd", gcd, { &type_mp, &type_mp, &type_mp, &type_mp, &type_mp, 0 } }, | |
7c404803 | 335 | { "modinv", modinv, { &type_mp, &type_mp, &type_mp, 0 } }, |
d3409d5e | 336 | { 0, 0, { 0 } } |
337 | }; | |
338 | ||
339 | int main(int argc, char *argv[]) | |
340 | { | |
341 | sub_init(); | |
342 | test_run(argc, argv, tests, SRCDIR "/tests/mp"); | |
343 | return (0); | |
344 | } | |
345 | ||
346 | #endif | |
347 | ||
348 | /*----- That's all, folks -------------------------------------------------*/ |