3 * Euclidian algorithm on binary polynomials
5 * (c) 2004 Straylight/Edgeware
8 /*----- Licensing notice --------------------------------------------------*
10 * This file is part of Catacomb.
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.
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.
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,
28 /*----- Header files ------------------------------------------------------*/
32 /*----- Main code ---------------------------------------------------------*/
36 * Arguments: @mp **gcd, **xx, **yy@ = where to write the results
37 * @mp *a, *b@ = sources (must be nonzero)
42 * Use: Calculates @gcd(a, b)@, and two numbers @x@ and @y@ such that
43 * @ax + by = gcd(a, b)@. This is useful for computing modular
47 void gf_gcd(mp
**gcd
, mp
**xx
, mp
**yy
, mp
*a
, mp
*b
)
49 mp
*x
= MP_ONE
, *X
= MP_ZERO
;
50 mp
*y
= MP_ZERO
, *Y
= MP_ONE
;
52 mp
*q
= MP_NEW
, *t
, *spare
= MP_NEW
;
58 /* --- Sort out some initial flags --- */
63 /* --- Ensure that @a@ is larger than @b@ --- *
65 * If they're the same length we don't care which order they're in, so this
66 * unsigned comparison is fine.
69 if (MPX_UCMP(a
->v
, a
->vl
, <, b
->v
, b
->vl
)) {
74 /* --- Check for zeroness --- */
76 if (MP_EQ(b
, MP_ZERO
)) {
78 /* --- Store %$|a|$% as the GCD --- */
81 if (*gcd
) MP_DROP(*gcd
);
86 /* --- Store %$1$% and %$0$% in the appropriate bins --- */
90 mp
**t
= xx
; xx
= yy
; yy
= t
;
93 if (*xx
) MP_DROP(*xx
);
94 if (MP_EQ(a
, MP_ZERO
))
100 if (*yy
) MP_DROP(*yy
);
107 /* --- Main extended Euclidean algorithm --- */
112 while (!MP_ZEROP(v
)) {
113 gf_div(&q
, &u
, u
, v
);
115 t
= gf_mul(spare
, X
, q
);
117 spare
= x
; x
= X
; X
= t
;
118 t
= gf_mul(spare
, Y
, q
);
120 spare
= y
; y
= Y
; Y
= t
;
125 MP_DROP(q
); if (spare
) MP_DROP(spare
);
129 if (*gcd
) MP_DROP(*gcd
);
134 /* --- Perform a little normalization --- */
138 /* --- If @a@ and @b@ got swapped, swap the coefficients back --- */
145 /* --- Store the results --- */
150 if (*xx
) MP_DROP(*xx
);
157 if (*yy
) MP_DROP(*yy
);
163 MP_DROP(X
); MP_DROP(Y
);
166 /* -- @gf_modinv@ --- *
168 * Arguments: @mp *d@ = destination
172 * Returns: The inverse %$x^{-1} \bmod p$%.
174 * Use: Computes a modular inverse, the catch being that the
175 * arguments and results are binary polynomials. An assertion
176 * fails if %$p$% has no inverse.
179 mp
*gf_modinv(mp
*d
, mp
*x
, mp
*p
)
182 gf_gcd(&g
, 0, &d
, p
, x
);
183 assert(MP_EQ(g
, MP_ONE
));
188 /*----- Test rig ----------------------------------------------------------*/
192 static int gcd(dstr
*v
)
195 mp
*a
= *(mp
**)v
[0].buf
;
196 mp
*b
= *(mp
**)v
[1].buf
;
197 mp
*g
= *(mp
**)v
[2].buf
;
198 mp
*x
= *(mp
**)v
[3].buf
;
199 mp
*y
= *(mp
**)v
[4].buf
;
201 mp
*gg
= MP_NEW
, *xx
= MP_NEW
, *yy
= MP_NEW
;
202 gf_gcd(&gg
, &xx
, &yy
, a
, b
);
204 fputs("\n*** gf_gcd(x) failed", stderr
);
205 fputs("\na = ", stderr
); mp_writefile(a
, stderr
, 16);
206 fputs("\nb = ", stderr
); mp_writefile(b
, stderr
, 16);
207 fputs("\nexpect = ", stderr
); mp_writefile(x
, stderr
, 16);
208 fputs("\nresult = ", stderr
); mp_writefile(xx
, stderr
, 16);
213 fputs("\n*** gf_gcd(y) failed", stderr
);
214 fputs("\na = ", stderr
); mp_writefile(a
, stderr
, 16);
215 fputs("\nb = ", stderr
); mp_writefile(b
, stderr
, 16);
216 fputs("\nexpect = ", stderr
); mp_writefile(y
, stderr
, 16);
217 fputs("\nresult = ", stderr
); mp_writefile(yy
, stderr
, 16);
223 mp
*ax
= gf_mul(MP_NEW
, a
, xx
);
224 mp
*by
= gf_mul(MP_NEW
, b
, yy
);
225 ax
= gf_add(ax
, ax
, by
);
227 fputs("\n*** (Alternative result found.)\n", stderr
);
233 fputs("\n*** gf_gcd(gcd) failed", stderr
);
234 fputs("\na = ", stderr
); mp_writefile(a
, stderr
, 16);
235 fputs("\nb = ", stderr
); mp_writefile(b
, stderr
, 16);
236 fputs("\nexpect = ", stderr
); mp_writefile(g
, stderr
, 16);
237 fputs("\nresult = ", stderr
); mp_writefile(gg
, stderr
, 16);
241 MP_DROP(a
); MP_DROP(b
); MP_DROP(g
); MP_DROP(x
); MP_DROP(y
);
242 MP_DROP(gg
); MP_DROP(xx
); MP_DROP(yy
);
243 assert(mparena_count(MPARENA_GLOBAL
) == 0);
247 static test_chunk tests
[] = {
248 { "gcd", gcd
, { &type_mp
, &type_mp
, &type_mp
, &type_mp
, &type_mp
, 0 } },
252 int main(int argc
, char *argv
[])
255 test_run(argc
, argv
, tests
, SRCDIR
"/t/gf");
261 /*----- That's all, folks -------------------------------------------------*/