3 * $Id: mpmont.c,v 1.7 1999/12/11 01:51:14 mdw Exp $
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 --------------------------------------------------*
33 * Revision 1.7 1999/12/11 01:51:14 mdw
34 * Use a Karatsuba-based reduction for large moduli.
36 * Revision 1.6 1999/12/10 23:18:39 mdw
37 * Change interface for suggested destinations.
39 * Revision 1.5 1999/11/22 13:58:40 mdw
40 * Add an option to disable Montgomery reduction, so that performance
41 * comparisons can be done.
43 * Revision 1.4 1999/11/21 12:27:06 mdw
44 * Remove a division from the Montgomery setup by calculating
45 * %$R^2 \bmod m$% first and then %$R \bmod m$% by Montgomery reduction of
48 * Revision 1.3 1999/11/21 11:35:10 mdw
49 * Performance improvement: use @mp_sqr@ and @mpmont_reduce@ instead of
50 * @mpmont_mul@ for squaring in exponentiation.
52 * Revision 1.2 1999/11/19 13:17:26 mdw
53 * Add extra interface to exponentiation which returns a Montgomerized
56 * Revision 1.1 1999/11/17 18:02:16 mdw
57 * New multiprecision integer arithmetic suite.
61 /*----- Header files ------------------------------------------------------*/
66 /*----- Tweakables --------------------------------------------------------*/
68 /* --- @MPMONT_DISABLE@ --- *
70 * Replace all the clever Montgomery reduction with good old-fashioned long
74 /* #define MPMONT_DISABLE */
76 /*----- Main code ---------------------------------------------------------*/
78 /* --- @mpmont_create@ --- *
80 * Arguments: @mpmont *mm@ = pointer to Montgomery reduction context
81 * @mp *m@ = modulus to use
85 * Use: Initializes a Montgomery reduction context ready for use.
86 * The argument @m@ must be a positive odd integer.
91 void mpmont_create(mpmont
*mm
, mp
*m
)
102 void mpmont_create(mpmont
*mm
, mp
*m
)
104 size_t n
= MP_LEN(m
);
105 mp
*r2
= mp_create(2 * n
+ 1);
108 /* --- Validate the arguments --- */
110 assert(((void)"Montgomery modulus must be positive",
111 (m
->f
& MP_NEG
) == 0));
112 assert(((void)"Montgomery modulus must be odd", m
->v
[0] & 1));
114 /* --- Take a copy of the modulus --- */
119 /* --- Determine %$R^2$% --- */
122 MPX_ZERO(r2
->v
, r2
->vl
- 1);
125 /* --- Find the magic value @mi@ --- */
127 mp_build(&r
, r2
->v
+ n
, r2
->vl
);
129 mp_gcd(0, 0, &mm
->mi
, &r
, m
);
130 mm
->mi
= mp_sub(mm
->mi
, &r
, mm
->mi
);
132 /* --- Discover the values %$R \bmod m$% and %$R^2 \bmod m$% --- */
135 mp_div(0, &mm
->r2
, r2
, m
);
136 mm
->r
= mpmont_reduce(mm
, MP_NEW
, mm
->r2
);
142 /* --- @mpmont_destroy@ --- *
144 * Arguments: @mpmont *mm@ = pointer to a Montgomery reduction context
148 * Use: Disposes of a context when it's no longer of any use to
152 void mpmont_destroy(mpmont
*mm
)
160 /* --- @mpmont_reduce@ --- *
162 * Arguments: @mpmont *mm@ = pointer to Montgomery reduction context
163 * @mp *d@ = destination
164 * @mp *a@ = source, assumed positive
166 * Returns: Result, %$a R^{-1} \bmod m$%.
169 #ifdef MPMONT_DISABLE
171 mp
*mpmont_reduce(mpmont
*mm
, mp
*d
, mp
*a
)
173 mp_div(0, &d
, a
, mm
->m
);
179 mp
*mpmont_reduce(mpmont
*mm
, mp
*d
, mp
*a
)
183 /* --- Check for serious Karatsuba reduction --- */
185 if (n
> KARATSUBA_CUTOFF
* 2) {
194 mp_build(&al
, a
->v
, vl
);
195 u
= mp_mul(MP_NEW
, &al
, mm
->mi
);
198 u
= mp_mul(u
, u
, mm
->m
);
203 /* --- Otherwise do it the hard way --- */
211 /* --- Initial conditioning of the arguments --- */
214 MP_MODIFY(d
, 2 * n
+ 1);
216 MP_MODIFY(d
, 2 * n
+ 1);
217 MPX_COPY(d
->v
, d
->vl
, a
->v
, a
->vl
);
220 dv
= d
->v
; dvl
= d
->vl
;
221 mv
= mm
->m
->v
; mvl
= mm
->m
->vl
;
223 /* --- Let's go to work --- */
227 mpw u
= MPW(*dv
* mi
);
228 MPX_UMLAN(dv
, dvl
, mv
, mvl
, u
);
233 /* --- Wrap everything up --- */
235 d
->f
= a
->f
& MP_BURN
;
236 memmove(d
->v
, d
->v
+ n
, MPWS(MP_LEN(d
) - n
));
238 if (MP_CMP(d
, >=, mm
->m
))
239 d
= mp_sub(d
, d
, mm
->m
);
246 /* --- @mpmont_mul@ --- *
248 * Arguments: @mpmont *mm@ = pointer to Montgomery reduction context
249 * @mp *d@ = destination
250 * @mp *a, *b@ = sources, assumed positive
252 * Returns: Result, %$a b R^{-1} \bmod m$%.
255 #ifdef MPMONT_DISABLE
257 mp
*mpmont_mul(mpmont
*mm
, mp
*d
, mp
*a
, mp
*b
)
260 mp_div(0, &d
, d
, mm
->m
);
266 mp
*mpmont_mul(mpmont
*mm
, mp
*d
, mp
*a
, mp
*b
)
268 if (mm
->n
> KARATSUBA_CUTOFF
* 2) {
270 d
= mpmont_reduce(mm
, d
, d
);
280 /* --- Initial conditioning of the arguments --- */
282 if (MP_LEN(a
) > MP_LEN(b
)) {
283 mp
*t
= a
; a
= b
; b
= t
;
289 MP_MODIFY(d
, 2 * n
+ 1);
290 dv
= d
->v
; dvl
= d
->vl
;
292 av
= a
->v
; avl
= a
->vl
;
293 bv
= b
->v
; bvl
= b
->vl
;
294 mv
= mm
->m
->v
; mvl
= mm
->m
->vl
;
297 /* --- Montgomery multiplication phase --- */
301 while (i
< n
&& av
< avl
) {
303 mpw u
= MPW((*dv
+ x
* y
) * mi
);
304 MPX_UMLAN(dv
, dvl
, bv
, bvl
, x
);
305 MPX_UMLAN(dv
, dvl
, mv
, mvl
, u
);
310 /* --- Simpler Montgomery reduction phase --- */
313 mpw u
= MPW(*dv
* mi
);
314 MPX_UMLAN(dv
, dvl
, mv
, mvl
, u
);
321 memmove(d
->v
, dv
, MPWS(dvl
- dv
));
324 d
->f
= (a
->f
| b
->f
) & MP_BURN
;
325 if (MP_CMP(d
, >=, mm
->m
))
326 d
= mp_sub(d
, d
, mm
->m
);
336 /* --- @mpmont_expr@ --- *
338 * Arguments: @mpmont *mm@ = pointer to Montgomery reduction context
339 * @mp *d@ = fake destination
343 * Returns: Result, %$a^e R \bmod m$%.
346 mp
*mpmont_expr(mpmont
*mm
, mp
*d
, mp
*a
, mp
*e
)
349 mp
*ar
= mpmont_mul(mm
, MP_NEW
, a
, mm
->r2
);
350 mp
*x
= MP_COPY(mm
->r
);
361 dd
= mp_sqr(spare
, ar
);
362 dd
= mpmont_reduce(mm
, dd
, dd
);
366 dd
= mpmont_mul(mm
, spare
, x
, ar
);
382 /* --- @mpmont_exp@ --- *
384 * Arguments: @mpmont *mm@ = pointer to Montgomery reduction context
385 * @mp *d@ = fake destination
389 * Returns: Result, %$a^e \bmod m$%.
392 mp
*mpmont_exp(mpmont
*mm
, mp
*d
, mp
*a
, mp
*e
)
394 d
= mpmont_expr(mm
, d
, a
, e
);
395 d
= mpmont_reduce(mm
, d
, d
);
399 /*----- Test rig ----------------------------------------------------------*/
403 static int tcreate(dstr
*v
)
405 mp
*m
= *(mp
**)v
[0].buf
;
406 mp
*mi
= *(mp
**)v
[1].buf
;
407 mp
*r
= *(mp
**)v
[2].buf
;
408 mp
*r2
= *(mp
**)v
[3].buf
;
413 mpmont_create(&mm
, m
);
415 if (mm
.mi
->v
[0] != mi
->v
[0]) {
416 fprintf(stderr
, "\n*** bad mi: found %lu, expected %lu",
417 (unsigned long)mm
.mi
->v
[0], (unsigned long)mi
->v
[0]);
418 fputs("\nm = ", stderr
); mp_writefile(m
, stderr
, 10);
423 if (MP_CMP(mm
.r
, !=, r
)) {
424 fputs("\n*** bad r", stderr
);
425 fputs("\nm = ", stderr
); mp_writefile(m
, stderr
, 10);
426 fputs("\nexpected ", stderr
); mp_writefile(r
, stderr
, 10);
427 fputs("\n found ", stderr
); mp_writefile(mm
.r
, stderr
, 10);
432 if (MP_CMP(mm
.r2
, !=, r2
)) {
433 fputs("\n*** bad r2", stderr
);
434 fputs("\nm = ", stderr
); mp_writefile(m
, stderr
, 10);
435 fputs("\nexpected ", stderr
); mp_writefile(r2
, stderr
, 10);
436 fputs("\n found ", stderr
); mp_writefile(mm
.r2
, stderr
, 10);
446 assert(mparena_count(MPARENA_GLOBAL
) == 0);
450 static int tmul(dstr
*v
)
452 mp
*m
= *(mp
**)v
[0].buf
;
453 mp
*a
= *(mp
**)v
[1].buf
;
454 mp
*b
= *(mp
**)v
[2].buf
;
455 mp
*r
= *(mp
**)v
[3].buf
;
459 mpmont_create(&mm
, m
);
462 mp
*qr
= mp_mul(MP_NEW
, a
, b
);
463 mp_div(0, &qr
, qr
, m
);
465 if (MP_CMP(qr
, !=, r
)) {
466 fputs("\n*** classical modmul failed", stderr
);
467 fputs("\n m = ", stderr
); mp_writefile(m
, stderr
, 10);
468 fputs("\n a = ", stderr
); mp_writefile(a
, stderr
, 10);
469 fputs("\n b = ", stderr
); mp_writefile(b
, stderr
, 10);
470 fputs("\n r = ", stderr
); mp_writefile(r
, stderr
, 10);
471 fputs("\nqr = ", stderr
); mp_writefile(qr
, stderr
, 10);
480 mp
*ar
= mpmont_mul(&mm
, MP_NEW
, a
, mm
.r2
);
481 mp
*br
= mpmont_mul(&mm
, MP_NEW
, b
, mm
.r2
);
482 mp
*mr
= mpmont_mul(&mm
, MP_NEW
, ar
, br
);
483 mr
= mpmont_reduce(&mm
, mr
, mr
);
484 if (MP_CMP(mr
, !=, r
)) {
485 fputs("\n*** montgomery modmul failed", stderr
);
486 fputs("\n m = ", stderr
); mp_writefile(m
, stderr
, 10);
487 fputs("\n a = ", stderr
); mp_writefile(a
, stderr
, 10);
488 fputs("\n b = ", stderr
); mp_writefile(b
, stderr
, 10);
489 fputs("\n r = ", stderr
); mp_writefile(r
, stderr
, 10);
490 fputs("\nmr = ", stderr
); mp_writefile(mr
, stderr
, 10);
494 MP_DROP(ar
); MP_DROP(br
);
504 assert(mparena_count(MPARENA_GLOBAL
) == 0);
508 static int texp(dstr
*v
)
510 mp
*m
= *(mp
**)v
[0].buf
;
511 mp
*a
= *(mp
**)v
[1].buf
;
512 mp
*b
= *(mp
**)v
[2].buf
;
513 mp
*r
= *(mp
**)v
[3].buf
;
518 mpmont_create(&mm
, m
);
520 mr
= mpmont_exp(&mm
, MP_NEW
, a
, b
);
522 if (MP_CMP(mr
, !=, r
)) {
523 fputs("\n*** montgomery modexp failed", stderr
);
524 fputs("\n m = ", stderr
); mp_writefile(m
, stderr
, 10);
525 fputs("\n a = ", stderr
); mp_writefile(a
, stderr
, 10);
526 fputs("\n e = ", stderr
); mp_writefile(b
, stderr
, 10);
527 fputs("\n r = ", stderr
); mp_writefile(r
, stderr
, 10);
528 fputs("\nmr = ", stderr
); mp_writefile(mr
, stderr
, 10);
539 assert(mparena_count(MPARENA_GLOBAL
) == 0);
544 static test_chunk tests
[] = {
545 { "create", tcreate
, { &type_mp
, &type_mp
, &type_mp
, &type_mp
, 0 } },
546 { "mul", tmul
, { &type_mp
, &type_mp
, &type_mp
, &type_mp
, 0 } },
547 { "exp", texp
, { &type_mp
, &type_mp
, &type_mp
, &type_mp
, 0 } },
551 int main(int argc
, char *argv
[])
554 test_run(argc
, argv
, tests
, SRCDIR
"/tests/mpmont");
560 /*----- That's all, folks -------------------------------------------------*/