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d3409d5e | 1 | /* -*-c-*- |
d3409d5e | 2 | * |
3 | * Extended GCD calculation | |
4 | * | |
5 | * (c) 1999 Straylight/Edgeware | |
6 | */ | |
7 | ||
45c0fd36 | 8 | /*----- Licensing notice --------------------------------------------------* |
d3409d5e | 9 | * |
10 | * This file is part of Catacomb. | |
11 | * | |
12 | * Catacomb is free software; you can redistribute it and/or modify | |
13 | * it under the terms of the GNU Library General Public License as | |
14 | * published by the Free Software Foundation; either version 2 of the | |
15 | * License, or (at your option) any later version. | |
45c0fd36 | 16 | * |
d3409d5e | 17 | * Catacomb is distributed in the hope that it will be useful, |
18 | * but WITHOUT ANY WARRANTY; without even the implied warranty of | |
19 | * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the | |
20 | * GNU Library General Public License for more details. | |
45c0fd36 | 21 | * |
d3409d5e | 22 | * You should have received a copy of the GNU Library General Public |
23 | * License along with Catacomb; if not, write to the Free | |
24 | * Software Foundation, Inc., 59 Temple Place - Suite 330, Boston, | |
25 | * MA 02111-1307, USA. | |
26 | */ | |
27 | ||
d3409d5e | 28 | /*----- Header files ------------------------------------------------------*/ |
29 | ||
30 | #include "mp.h" | |
31 | ||
32 | /*----- Main code ---------------------------------------------------------*/ | |
33 | ||
34 | /* --- @mp_gcd@ --- * | |
35 | * | |
36 | * Arguments: @mp **gcd, **xx, **yy@ = where to write the results | |
37 | * @mp *a, *b@ = sources (must be nonzero) | |
38 | * | |
39 | * Returns: --- | |
40 | * | |
41 | * Use: Calculates @gcd(a, b)@, and two numbers @x@ and @y@ such that | |
42 | * @ax + by = gcd(a, b)@. This is useful for computing modular | |
ef5f4810 | 43 | * inverses. |
d3409d5e | 44 | */ |
45 | ||
46 | void mp_gcd(mp **gcd, mp **xx, mp **yy, mp *a, mp *b) | |
47 | { | |
b2253c70 | 48 | mp *x = MP_ONE, *X = MP_ZERO; |
49 | mp *y = MP_ZERO, *Y = MP_ONE; | |
d3409d5e | 50 | mp *u, *v; |
3d6115d1 | 51 | mp *q = MP_NEW, *t, *spare = MP_NEW; |
ef5f4810 | 52 | unsigned f = 0; |
53 | ||
ceb3f0c0 | 54 | #define f_swap 1u |
55 | #define f_aneg 2u | |
56 | #define f_bneg 4u | |
57 | #define f_ext 8u | |
ef5f4810 | 58 | |
59 | /* --- Sort out some initial flags --- */ | |
d3409d5e | 60 | |
a7b6288f | 61 | if (xx || yy) f |= f_ext; |
d3409d5e | 62 | |
a7b6288f MW |
63 | if (MP_NEGP(a)) f |= f_aneg; |
64 | if (MP_NEGP(b)) f |= f_bneg; | |
ef5f4810 | 65 | |
66 | /* --- Ensure that @a@ is larger than @b@ --- * | |
67 | * | |
68 | * Use absolute values here! | |
69 | */ | |
70 | ||
71 | if (MPX_UCMP(a->v, a->vl, <, b->v, b->vl)) { | |
3d6115d1 | 72 | t = a; a = b; b = t; |
ef5f4810 | 73 | f |= f_swap; |
74 | } | |
75 | ||
76 | /* --- Check for zeroness --- */ | |
77 | ||
3d6115d1 | 78 | if (MP_ZEROP(b)) { |
ef5f4810 | 79 | |
80 | /* --- Store %$|a|$% as the GCD --- */ | |
81 | ||
82 | if (gcd) { | |
83 | if (*gcd) MP_DROP(*gcd); | |
84 | a = MP_COPY(a); | |
a69a3efd | 85 | if (MP_NEGP(a)) { |
ef5f4810 | 86 | MP_SPLIT(a); |
87 | a->f &= ~MP_NEG; | |
88 | f |= f_aneg; | |
89 | } | |
90 | *gcd = a; | |
91 | } | |
92 | ||
93 | /* --- Store %$1$% and %$0$% in the appropriate bins --- */ | |
94 | ||
95 | if (f & f_ext) { | |
96 | if (f & f_swap) { | |
3d6115d1 | 97 | mp **tt = xx; xx = yy; yy = tt; |
ef5f4810 | 98 | } |
99 | if (xx) { | |
100 | if (*xx) MP_DROP(*xx); | |
a7b6288f MW |
101 | if (MP_EQ(a, MP_ZERO)) *xx = MP_ZERO; |
102 | else if (f & f_aneg) *xx = MP_MONE; | |
103 | else *xx = MP_ONE; | |
ef5f4810 | 104 | } |
105 | if (yy) { | |
106 | if (*yy) MP_DROP(*yy); | |
107 | *yy = MP_ZERO; | |
108 | } | |
109 | } | |
110 | return; | |
d3409d5e | 111 | } |
112 | ||
cf76bcbb | 113 | /* --- Force the signs on the arguments and take copies --- */ |
d3409d5e | 114 | |
115 | a = MP_COPY(a); | |
116 | b = MP_COPY(b); | |
117 | ||
ef5f4810 | 118 | MP_SPLIT(a); a->f &= ~MP_NEG; |
119 | MP_SPLIT(b); b->f &= ~MP_NEG; | |
120 | ||
d3409d5e | 121 | u = MP_COPY(a); |
122 | v = MP_COPY(b); | |
123 | ||
cf76bcbb MW |
124 | /* --- Main extended Euclidean algorithm --- */ |
125 | ||
a69a3efd | 126 | while (!MP_ZEROP(v)) { |
b2253c70 | 127 | mp_div(&q, &u, u, v); |
128 | if (f & f_ext) { | |
3d6115d1 | 129 | t = mp_mul(spare, X, q); |
b2253c70 | 130 | t = mp_sub(t, x, t); |
3d6115d1 MW |
131 | spare = x; x = X; X = t; |
132 | t = mp_mul(spare, Y, q); | |
b2253c70 | 133 | t = mp_sub(t, y, t); |
3d6115d1 | 134 | spare = y; y = Y; Y = t; |
d3409d5e | 135 | } |
b2253c70 | 136 | t = u; u = v; v = t; |
d3409d5e | 137 | } |
138 | ||
3d6115d1 | 139 | MP_DROP(q); if (spare) MP_DROP(spare); |
ef5f4810 | 140 | if (!gcd) |
b2253c70 | 141 | MP_DROP(u); |
ef5f4810 | 142 | else { |
143 | if (*gcd) MP_DROP(*gcd); | |
b2253c70 | 144 | u->f &= ~MP_NEG; |
145 | *gcd = u; | |
ef5f4810 | 146 | } |
d3409d5e | 147 | |
148 | /* --- Perform a little normalization --- * | |
149 | * | |
150 | * Ensure that the coefficient returned is positive, if there is only one. | |
ef5f4810 | 151 | * If there are two, favour @y@. Of course, if the original arguments were |
152 | * negative then I'll need to twiddle their signs as well. | |
d3409d5e | 153 | */ |
154 | ||
ef5f4810 | 155 | if (f & f_ext) { |
156 | ||
157 | /* --- If @a@ and @b@ got swapped, swap the coefficients back --- */ | |
158 | ||
159 | if (f & f_swap) { | |
3d6115d1 | 160 | t = x; x = y; y = t; |
da83a561 | 161 | t = a; a = b; b = t; |
d3409d5e | 162 | } |
ef5f4810 | 163 | |
164 | /* --- Sort out the signs --- * | |
165 | * | |
166 | * Note that %$ax + by = a(x - b) + b(y + a)$%. | |
c9110b35 | 167 | * |
168 | * This is currently bodgy. It needs sorting out at some time. | |
ef5f4810 | 169 | */ |
170 | ||
d3409d5e | 171 | if (yy) { |
a69a3efd | 172 | if (MP_NEGP(y)) { |
c9110b35 | 173 | do { |
174 | y = mp_add(y, y, a); | |
175 | x = mp_sub(x, x, b); | |
a69a3efd | 176 | } while (MP_NEGP(y)); |
c9110b35 | 177 | } else { |
178 | while (MP_CMP(y, >=, a)) { | |
179 | y = mp_sub(y, y, a); | |
180 | x = mp_add(x, x, b); | |
181 | } | |
d3409d5e | 182 | } |
c9110b35 | 183 | } else { |
a7b6288f MW |
184 | if (MP_NEGP(x)) |
185 | do x = mp_add(x, x, b); while (MP_NEGP(x)); | |
186 | else | |
187 | while (MP_CMP(x, >=, b)) x = mp_sub(x, x, b); | |
c9110b35 | 188 | } |
d3409d5e | 189 | |
ef5f4810 | 190 | /* --- Twiddle the signs --- */ |
191 | ||
9b8ff1cf MW |
192 | if (f & f_aneg) { MP_SPLIT(x); x->f ^= MP_NEG; } |
193 | if (f & f_bneg) { MP_SPLIT(y); y->f ^= MP_NEG; } | |
ef5f4810 | 194 | |
195 | /* --- Store the results --- */ | |
196 | ||
197 | if (!xx) | |
198 | MP_DROP(x); | |
199 | else { | |
200 | if (*xx) MP_DROP(*xx); | |
201 | *xx = x; | |
202 | } | |
203 | ||
204 | if (!yy) | |
205 | MP_DROP(y); | |
206 | else { | |
207 | if (*yy) MP_DROP(*yy); | |
208 | *yy = y; | |
209 | } | |
d3409d5e | 210 | } |
211 | ||
b2253c70 | 212 | MP_DROP(v); |
d3409d5e | 213 | MP_DROP(X); MP_DROP(Y); |
214 | MP_DROP(a); MP_DROP(b); | |
215 | } | |
216 | ||
b817bfc6 | 217 | /* -- @mp_modinv@ --- * |
218 | * | |
219 | * Arguments: @mp *d@ = destination | |
220 | * @mp *x@ = argument | |
221 | * @mp *p@ = modulus | |
222 | * | |
223 | * Returns: The inverse %$x^{-1} \bmod p$%. | |
224 | * | |
225 | * Use: Computes a modular inverse. An assertion fails if %$p$% | |
226 | * has no inverse. | |
227 | */ | |
228 | ||
229 | mp *mp_modinv(mp *d, mp *x, mp *p) | |
230 | { | |
231 | mp *g = MP_NEW; | |
232 | mp_gcd(&g, 0, &d, p, x); | |
233 | assert(MP_EQ(g, MP_ONE)); | |
234 | mp_drop(g); | |
235 | return (d); | |
236 | } | |
237 | ||
d3409d5e | 238 | /*----- Test rig ----------------------------------------------------------*/ |
239 | ||
240 | #ifdef TEST_RIG | |
241 | ||
7c404803 MW |
242 | static int modinv(dstr *v) |
243 | { | |
244 | int ok = 1; | |
245 | mp *x = *(mp **)v[0].buf; | |
246 | mp *m = *(mp **)v[1].buf; | |
247 | mp *r = *(mp **)v[2].buf; | |
248 | ||
249 | mp *y = mp_modinv(MP_NEW, x, m); | |
250 | if (!MP_EQ(y, r)) { | |
251 | fputs("\n*** mp_modinv failed", stderr); | |
45c0fd36 MW |
252 | fputs("\nx = ", stderr); mp_writefile(x, stderr, 10); |
253 | fputs("\nm = ", stderr); mp_writefile(m, stderr, 10); | |
7c404803 MW |
254 | fputs("\nexpect = ", stderr); mp_writefile(r, stderr, 10); |
255 | fputs("\nresult = ", stderr); mp_writefile(y, stderr, 10); | |
256 | ok = 0; | |
257 | } | |
258 | MP_DROP(x); MP_DROP(m); MP_DROP(r); MP_DROP(y); | |
259 | assert(mparena_count(MPARENA_GLOBAL) == 0); | |
45c0fd36 | 260 | return (ok); |
7c404803 MW |
261 | } |
262 | ||
d3409d5e | 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); |
45c0fd36 MW |
276 | fputs("\na = ", stderr); mp_writefile(a, stderr, 10); |
277 | fputs("\nb = ", stderr); mp_writefile(b, stderr, 10); | |
d3409d5e | 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); |
45c0fd36 MW |
285 | fputs("\na = ", stderr); mp_writefile(a, stderr, 10); |
286 | fputs("\nb = ", stderr); mp_writefile(b, stderr, 10); | |
d3409d5e | 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); |
45c0fd36 MW |
305 | fputs("\na = ", stderr); mp_writefile(a, stderr, 10); |
306 | fputs("\nb = ", stderr); mp_writefile(b, stderr, 10); | |
d3409d5e | 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 } }, | |
7c404803 | 320 | { "modinv", modinv, { &type_mp, &type_mp, &type_mp, 0 } }, |
d3409d5e | 321 | { 0, 0, { 0 } } |
322 | }; | |
323 | ||
324 | int main(int argc, char *argv[]) | |
325 | { | |
326 | sub_init(); | |
0f00dc4c | 327 | test_run(argc, argv, tests, SRCDIR "/t/mp"); |
d3409d5e | 328 | return (0); |
329 | } | |
330 | ||
331 | #endif | |
332 | ||
333 | /*----- That's all, folks -------------------------------------------------*/ |