3 * $Id: mpbarrett.c,v 1.6 2000/10/08 12:03:44 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 1.6 2000/10/08 12:03:44 mdw
34 * (mpbarrett_reduce): Cope with negative numbers.
36 * Revision 1.5 2000/07/29 17:04:33 mdw
37 * Change to use left-to-right bitwise exponentiation. This will improve
38 * performance when the base is small.
40 * Revision 1.4 2000/06/17 11:45:09 mdw
41 * Major memory management overhaul. Added arena support. Use the secure
42 * arena for secret integers. Replace and improve the MP management macros
43 * (e.g., replace MP_MODIFY by MP_DEST).
45 * Revision 1.3 1999/12/12 15:08:52 mdw
46 * Don't bother shifting %$q$% in @mpbarrett_reduce@, just skip the least
49 * Revision 1.2 1999/12/11 01:50:56 mdw
50 * Improve initialization slightly.
52 * Revision 1.1 1999/12/10 23:21:59 mdw
53 * Barrett reduction support: works with even moduli.
57 /*----- Header files ------------------------------------------------------*/
60 #include "mpbarrett.h"
62 /*----- Main code ---------------------------------------------------------*/
64 /* --- @mpbarrett_create@ --- *
66 * Arguments: @mpbarrett *mb@ = pointer to Barrett reduction context
67 * @mp *m@ = modulus to work to
72 * Use: Initializes a Barrett reduction context ready for use.
75 void mpbarrett_create(mpbarrett
*mb
, mp
*m
)
79 /* --- Validate the arguments --- */
81 assert(((void)"Barrett modulus must be positive", (m
->f
& MP_NEG
) == 0));
83 /* --- Compute %$\mu$% --- */
88 b
= mp_new(2 * mb
->k
+ 1, 0);
89 MPX_ZERO(b
->v
, b
->vl
- 1);
95 /* --- @mpbarrett_destroy@ --- *
97 * Arguments: @mpbarrett *mb@ = pointer to Barrett reduction context
101 * Use: Destroys a Barrett reduction context releasing any resources
105 void mpbarrett_destroy(mpbarrett
*mb
)
111 /* --- @mpbarrett_reduce@ --- *
113 * Arguments: @mpbarrett *mb@ = pointer to Barrett reduction context
114 * @mp *d@ = destination for result
115 * @mp *m@ = number to reduce
117 * Returns: The residue of @m@ modulo the number in the reduction
120 * Use: Performs an efficient modular reduction.
123 mp
*mpbarrett_reduce(mpbarrett
*mb
, mp
*d
, mp
*m
)
128 /* --- Special case if @m@ is too small --- */
137 /* --- First stage --- */
141 mp_build(&qq
, m
->v
+ (k
- 1), m
->vl
);
142 q
= mp_mul(MP_NEW
, &qq
, mb
->mu
);
143 if (MP_LEN(q
) <= k
) {
151 /* --- Second stage --- */
158 if (MP_LEN(m
) <= k
+ 1)
162 r
= mp_new(k
+ 1, (q
->f
| mb
->m
->f
) & MP_BURN
);
163 mpx_umul(r
->v
, r
->vl
, q
->v
+ k
+ 1, q
->vl
, mb
->m
->v
, mb
->m
->vl
);
164 MP_DEST(d
, k
+ 1, r
->f
);
165 mpx_usub(d
->v
, d
->vl
, m
->v
, mvl
, r
->v
, r
->vl
);
166 d
->f
= (m
->f
| r
->f
) & (MP_BURN
| MP_NEG
);
172 /* --- Final stage --- */
175 while (MPX_UCMP(d
->v
, d
->vl
, >=, mb
->m
->v
, mb
->m
->vl
))
176 mpx_usub(d
->v
, d
->vl
, d
->v
, d
->vl
, mb
->m
->v
, mb
->m
->vl
);
178 /* --- Fix up the sign --- */
181 mpx_usub(d
->v
, d
->vl
, mb
->m
->v
, mb
->m
->vl
, d
->v
, d
->vl
);
189 /* --- @mpbarrett_exp@ --- *
191 * Arguments: @mpbarrett *mb@ = pointer to Barrett reduction context
192 * @mp *d@ = fake destination
196 * Returns: Result, %$a^e \bmod m$%.
199 mp
*mpbarrett_exp(mpbarrett
*mb
, mp
*d
, mp
*a
, mp
*e
)
203 mp
*spare
= (e
->f
& MP_BURN
) ? MP_NEWSEC
: MP_NEW
;
210 while (!MP_RBIT(&sc
))
213 /* --- Do the main body of the work --- */
219 y
= mp_sqr(spare
, x
);
220 y
= mpbarrett_reduce(mb
, y
, y
);
225 mp
*y
= mp_mul(spare
, x
, a
);
226 y
= mpbarrett_reduce(mb
, y
, y
);
238 /* --- Do a final round of squaring --- */
243 y
= mp_sqr(spare
, x
);
244 y
= mpbarrett_reduce(mb
, y
, y
);
258 /*----- Test rig ----------------------------------------------------------*/
262 static int vmod(dstr
*v
)
264 mp
*x
= *(mp
**)v
[0].buf
;
265 mp
*n
= *(mp
**)v
[1].buf
;
266 mp
*r
= *(mp
**)v
[2].buf
;
271 mpbarrett_create(&mb
, n
);
272 s
= mpbarrett_reduce(&mb
, MP_NEW
, x
);
275 fputs("\n*** barrett reduction failure\n", stderr
);
276 fputs("x = ", stderr
); mp_writefile(x
, stderr
, 10); fputc('\n', stderr
);
277 fputs("n = ", stderr
); mp_writefile(n
, stderr
, 10); fputc('\n', stderr
);
278 fputs("r = ", stderr
); mp_writefile(r
, stderr
, 10); fputc('\n', stderr
);
279 fputs("s = ", stderr
); mp_writefile(s
, stderr
, 10); fputc('\n', stderr
);
283 mpbarrett_destroy(&mb
);
288 assert(mparena_count(MPARENA_GLOBAL
) == 0);
292 static int vexp(dstr
*v
)
294 mp
*m
= *(mp
**)v
[0].buf
;
295 mp
*a
= *(mp
**)v
[1].buf
;
296 mp
*b
= *(mp
**)v
[2].buf
;
297 mp
*r
= *(mp
**)v
[3].buf
;
302 mpbarrett_create(&mb
, m
);
304 mr
= mpbarrett_exp(&mb
, MP_NEW
, a
, b
);
307 fputs("\n*** barrett modexp failed", stderr
);
308 fputs("\n m = ", stderr
); mp_writefile(m
, stderr
, 10);
309 fputs("\n a = ", stderr
); mp_writefile(a
, stderr
, 10);
310 fputs("\n e = ", stderr
); mp_writefile(b
, stderr
, 10);
311 fputs("\n r = ", stderr
); mp_writefile(r
, stderr
, 10);
312 fputs("\nmr = ", stderr
); mp_writefile(mr
, stderr
, 10);
322 mpbarrett_destroy(&mb
);
323 assert(mparena_count(MPARENA_GLOBAL
) == 0);
327 static test_chunk tests
[] = {
328 { "mpbarrett-reduce", vmod
, { &type_mp
, &type_mp
, &type_mp
, 0 } },
329 { "mpbarrett-exp", vexp
, { &type_mp
, &type_mp
, &type_mp
, &type_mp
, 0 } },
333 int main(int argc
, char *argv
[])
336 test_run(argc
, argv
, tests
, SRCDIR
"/tests/mpbarrett");
342 /*----- That's all, folks -------------------------------------------------*/