3 * $Id: mpbarrett.c,v 1.9 2004/04/01 12:50:09 mdw Exp $
5 * Barrett modular reduction
7 * (c) 1999 Straylight/Edgeware
10 /*----- Licensing notice --------------------------------------------------*
12 * This file is part of Catacomb.
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.
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.
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,
30 /*----- Revision history --------------------------------------------------*
32 * $Log: mpbarrett.c,v $
33 * Revision 1.9 2004/04/01 12:50:09 mdw
34 * Add cyclic group abstraction, with test code. Separate off exponentation
35 * functions for better static linking. Fix a buttload of bugs on the way.
36 * Generally ensure that negative exponents do inversion correctly. Add
37 * table of standard prime-field subgroups. (Binary field subgroups are
38 * currently unimplemented but easy to add if anyone ever finds a good one.)
40 * Revision 1.8 2001/06/16 13:00:20 mdw
41 * Use the generic exponentiation functions.
43 * Revision 1.7 2001/04/19 18:25:26 mdw
44 * Use sliding-window exponentiation.
46 * Revision 1.6 2000/10/08 12:03:44 mdw
47 * (mpbarrett_reduce): Cope with negative numbers.
49 * Revision 1.5 2000/07/29 17:04:33 mdw
50 * Change to use left-to-right bitwise exponentiation. This will improve
51 * performance when the base is small.
53 * Revision 1.4 2000/06/17 11:45:09 mdw
54 * Major memory management overhaul. Added arena support. Use the secure
55 * arena for secret integers. Replace and improve the MP management macros
56 * (e.g., replace MP_MODIFY by MP_DEST).
58 * Revision 1.3 1999/12/12 15:08:52 mdw
59 * Don't bother shifting %$q$% in @mpbarrett_reduce@, just skip the least
62 * Revision 1.2 1999/12/11 01:50:56 mdw
63 * Improve initialization slightly.
65 * Revision 1.1 1999/12/10 23:21:59 mdw
66 * Barrett reduction support: works with even moduli.
70 /*----- Header files ------------------------------------------------------*/
73 #include "mpbarrett.h"
75 /*----- Main code ---------------------------------------------------------*/
77 /* --- @mpbarrett_create@ --- *
79 * Arguments: @mpbarrett *mb@ = pointer to Barrett reduction context
80 * @mp *m@ = modulus to work to
85 * Use: Initializes a Barrett reduction context ready for use.
88 void mpbarrett_create(mpbarrett *mb, mp *m)
92 /* --- Validate the arguments --- */
94 assert(((void)"Barrett modulus must be positive", (m->f & MP_NEG) == 0));
96 /* --- Compute %$\mu$% --- */
101 b = mp_new(2 * mb->k + 1, 0);
102 MPX_ZERO(b->v, b->vl - 1);
108 /* --- @mpbarrett_destroy@ --- *
110 * Arguments: @mpbarrett *mb@ = pointer to Barrett reduction context
114 * Use: Destroys a Barrett reduction context releasing any resources
118 void mpbarrett_destroy(mpbarrett *mb)
124 /* --- @mpbarrett_reduce@ --- *
126 * Arguments: @mpbarrett *mb@ = pointer to Barrett reduction context
127 * @mp *d@ = destination for result
128 * @mp *m@ = number to reduce
130 * Returns: The residue of @m@ modulo the number in the reduction
133 * Use: Performs an efficient modular reduction.
136 mp *mpbarrett_reduce(mpbarrett *mb, mp *d, mp *m)
141 /* --- Special case if @m@ is too small --- */
150 /* --- First stage --- */
154 mp_build(&qq, m->v + (k - 1), m->vl);
155 q = mp_mul(MP_NEW, &qq, mb->mu);
156 if (MP_LEN(q) <= k) {
164 /* --- Second stage --- */
171 if (MP_LEN(m) <= k + 1)
175 r = mp_new(k + 1, (q->f | mb->m->f) & MP_BURN);
176 mpx_umul(r->v, r->vl, q->v + k + 1, q->vl, mb->m->v, mb->m->vl);
177 MP_DEST(d, k + 1, r->f);
178 mpx_usub(d->v, d->vl, m->v, mvl, r->v, r->vl);
179 d->f = (m->f | r->f) & (MP_BURN | MP_NEG);
185 /* --- Final stage --- */
188 while (MPX_UCMP(d->v, d->vl, >=, mb->m->v, mb->m->vl))
189 mpx_usub(d->v, d->vl, d->v, d->vl, mb->m->v, mb->m->vl);
191 /* --- Fix up the sign --- */
194 mpx_usub(d->v, d->vl, mb->m->v, mb->m->vl, d->v, d->vl);
202 /*----- Test rig ----------------------------------------------------------*/
206 static int vmod(dstr *v)
208 mp *x = *(mp **)v[0].buf;
209 mp *n = *(mp **)v[1].buf;
210 mp *r = *(mp **)v[2].buf;
215 mpbarrett_create(&mb, n);
216 s = mpbarrett_reduce(&mb, MP_NEW, x);
219 fputs("\n*** barrett reduction failure\n", stderr);
220 fputs("x = ", stderr); mp_writefile(x, stderr, 10); fputc('\n', stderr);
221 fputs("n = ", stderr); mp_writefile(n, stderr, 10); fputc('\n', stderr);
222 fputs("r = ", stderr); mp_writefile(r, stderr, 10); fputc('\n', stderr);
223 fputs("s = ", stderr); mp_writefile(s, stderr, 10); fputc('\n', stderr);
227 mpbarrett_destroy(&mb);
232 assert(mparena_count(MPARENA_GLOBAL) == 0);
236 static test_chunk tests[] = {
237 { "mpbarrett-reduce", vmod, { &type_mp, &type_mp, &type_mp, 0 } },
241 int main(int argc, char *argv[])
244 test_run(argc, argv, tests, SRCDIR "/tests/mpbarrett");
250 /*----- That's all, folks -------------------------------------------------*/