3 * $Id: mpmont.c,v 1.8 1999/12/22 15:55:00 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 1.8 1999/12/22 15:55:00 mdw
34 * Adjust Karatsuba parameters.
36 * Revision 1.7 1999/12/11 01:51:14 mdw
37 * Use a Karatsuba-based reduction for large moduli.
39 * Revision 1.6 1999/12/10 23:18:39 mdw
40 * Change interface for suggested destinations.
42 * Revision 1.5 1999/11/22 13:58:40 mdw
43 * Add an option to disable Montgomery reduction, so that performance
44 * comparisons can be done.
46 * Revision 1.4 1999/11/21 12:27:06 mdw
47 * Remove a division from the Montgomery setup by calculating
48 * %$R^2 \bmod m$% first and then %$R \bmod m$% by Montgomery reduction of
51 * Revision 1.3 1999/11/21 11:35:10 mdw
52 * Performance improvement: use @mp_sqr@ and @mpmont_reduce@ instead of
53 * @mpmont_mul@ for squaring in exponentiation.
55 * Revision 1.2 1999/11/19 13:17:26 mdw
56 * Add extra interface to exponentiation which returns a Montgomerized
59 * Revision 1.1 1999/11/17 18:02:16 mdw
60 * New multiprecision integer arithmetic suite.
64 /*----- Header files ------------------------------------------------------*/
69 /*----- Tweakables --------------------------------------------------------*/
71 /* --- @MPMONT_DISABLE@ --- *
73 * Replace all the clever Montgomery reduction with good old-fashioned long
77 /* #define MPMONT_DISABLE */
79 /*----- Main code ---------------------------------------------------------*/
81 /* --- @mpmont_create@ --- *
83 * Arguments: @mpmont *mm@ = pointer to Montgomery reduction context
84 * @mp *m@ = modulus to use
88 * Use: Initializes a Montgomery reduction context ready for use.
89 * The argument @m@ must be a positive odd integer.
94 void mpmont_create(mpmont
*mm
, mp
*m
)
105 void mpmont_create(mpmont
*mm
, mp
*m
)
107 size_t n
= MP_LEN(m
);
108 mp
*r2
= mp_create(2 * n
+ 1);
111 /* --- Validate the arguments --- */
113 assert(((void)"Montgomery modulus must be positive",
114 (m
->f
& MP_NEG
) == 0));
115 assert(((void)"Montgomery modulus must be odd", m
->v
[0] & 1));
117 /* --- Take a copy of the modulus --- */
122 /* --- Determine %$R^2$% --- */
125 MPX_ZERO(r2
->v
, r2
->vl
- 1);
128 /* --- Find the magic value @mi@ --- */
130 mp_build(&r
, r2
->v
+ n
, r2
->vl
);
132 mp_gcd(0, 0, &mm
->mi
, &r
, m
);
133 mm
->mi
= mp_sub(mm
->mi
, &r
, mm
->mi
);
135 /* --- Discover the values %$R \bmod m$% and %$R^2 \bmod m$% --- */
138 mp_div(0, &mm
->r2
, r2
, m
);
139 mm
->r
= mpmont_reduce(mm
, MP_NEW
, mm
->r2
);
145 /* --- @mpmont_destroy@ --- *
147 * Arguments: @mpmont *mm@ = pointer to a Montgomery reduction context
151 * Use: Disposes of a context when it's no longer of any use to
155 void mpmont_destroy(mpmont
*mm
)
163 /* --- @mpmont_reduce@ --- *
165 * Arguments: @mpmont *mm@ = pointer to Montgomery reduction context
166 * @mp *d@ = destination
167 * @mp *a@ = source, assumed positive
169 * Returns: Result, %$a R^{-1} \bmod m$%.
172 #ifdef MPMONT_DISABLE
174 mp
*mpmont_reduce(mpmont
*mm
, mp
*d
, mp
*a
)
176 mp_div(0, &d
, a
, mm
->m
);
182 mp
*mpmont_reduce(mpmont
*mm
, mp
*d
, mp
*a
)
186 /* --- Check for serious Karatsuba reduction --- */
188 if (n
> KARATSUBA_CUTOFF
* 3) {
197 mp_build(&al
, a
->v
, vl
);
198 u
= mp_mul(MP_NEW
, &al
, mm
->mi
);
201 u
= mp_mul(u
, u
, mm
->m
);
206 /* --- Otherwise do it the hard way --- */
214 /* --- Initial conditioning of the arguments --- */
217 MP_MODIFY(d
, 2 * n
+ 1);
219 MP_MODIFY(d
, 2 * n
+ 1);
220 MPX_COPY(d
->v
, d
->vl
, a
->v
, a
->vl
);
223 dv
= d
->v
; dvl
= d
->vl
;
224 mv
= mm
->m
->v
; mvl
= mm
->m
->vl
;
226 /* --- Let's go to work --- */
230 mpw u
= MPW(*dv
* mi
);
231 MPX_UMLAN(dv
, dvl
, mv
, mvl
, u
);
236 /* --- Wrap everything up --- */
238 d
->f
= a
->f
& MP_BURN
;
239 memmove(d
->v
, d
->v
+ n
, MPWS(MP_LEN(d
) - n
));
241 if (MP_CMP(d
, >=, mm
->m
))
242 d
= mp_sub(d
, d
, mm
->m
);
249 /* --- @mpmont_mul@ --- *
251 * Arguments: @mpmont *mm@ = pointer to Montgomery reduction context
252 * @mp *d@ = destination
253 * @mp *a, *b@ = sources, assumed positive
255 * Returns: Result, %$a b R^{-1} \bmod m$%.
258 #ifdef MPMONT_DISABLE
260 mp
*mpmont_mul(mpmont
*mm
, mp
*d
, mp
*a
, mp
*b
)
263 mp_div(0, &d
, d
, mm
->m
);
269 mp
*mpmont_mul(mpmont
*mm
, mp
*d
, mp
*a
, mp
*b
)
271 if (mm
->n
> KARATSUBA_CUTOFF
* 3) {
273 d
= mpmont_reduce(mm
, d
, d
);
283 /* --- Initial conditioning of the arguments --- */
285 if (MP_LEN(a
) > MP_LEN(b
)) {
286 mp
*t
= a
; a
= b
; b
= t
;
292 MP_MODIFY(d
, 2 * n
+ 1);
293 dv
= d
->v
; dvl
= d
->vl
;
295 av
= a
->v
; avl
= a
->vl
;
296 bv
= b
->v
; bvl
= b
->vl
;
297 mv
= mm
->m
->v
; mvl
= mm
->m
->vl
;
300 /* --- Montgomery multiplication phase --- */
304 while (i
< n
&& av
< avl
) {
306 mpw u
= MPW((*dv
+ x
* y
) * mi
);
307 MPX_UMLAN(dv
, dvl
, bv
, bvl
, x
);
308 MPX_UMLAN(dv
, dvl
, mv
, mvl
, u
);
313 /* --- Simpler Montgomery reduction phase --- */
316 mpw u
= MPW(*dv
* mi
);
317 MPX_UMLAN(dv
, dvl
, mv
, mvl
, u
);
324 memmove(d
->v
, dv
, MPWS(dvl
- dv
));
327 d
->f
= (a
->f
| b
->f
) & MP_BURN
;
328 if (MP_CMP(d
, >=, mm
->m
))
329 d
= mp_sub(d
, d
, mm
->m
);
339 /* --- @mpmont_expr@ --- *
341 * Arguments: @mpmont *mm@ = pointer to Montgomery reduction context
342 * @mp *d@ = fake destination
346 * Returns: Result, %$a^e R \bmod m$%.
349 mp
*mpmont_expr(mpmont
*mm
, mp
*d
, mp
*a
, mp
*e
)
352 mp
*ar
= mpmont_mul(mm
, MP_NEW
, a
, mm
->r2
);
353 mp
*x
= MP_COPY(mm
->r
);
364 dd
= mp_sqr(spare
, ar
);
365 dd
= mpmont_reduce(mm
, dd
, dd
);
369 dd
= mpmont_mul(mm
, spare
, x
, ar
);
385 /* --- @mpmont_exp@ --- *
387 * Arguments: @mpmont *mm@ = pointer to Montgomery reduction context
388 * @mp *d@ = fake destination
392 * Returns: Result, %$a^e \bmod m$%.
395 mp
*mpmont_exp(mpmont
*mm
, mp
*d
, mp
*a
, mp
*e
)
397 d
= mpmont_expr(mm
, d
, a
, e
);
398 d
= mpmont_reduce(mm
, d
, d
);
402 /*----- Test rig ----------------------------------------------------------*/
406 static int tcreate(dstr
*v
)
408 mp
*m
= *(mp
**)v
[0].buf
;
409 mp
*mi
= *(mp
**)v
[1].buf
;
410 mp
*r
= *(mp
**)v
[2].buf
;
411 mp
*r2
= *(mp
**)v
[3].buf
;
416 mpmont_create(&mm
, m
);
418 if (mm
.mi
->v
[0] != mi
->v
[0]) {
419 fprintf(stderr
, "\n*** bad mi: found %lu, expected %lu",
420 (unsigned long)mm
.mi
->v
[0], (unsigned long)mi
->v
[0]);
421 fputs("\nm = ", stderr
); mp_writefile(m
, stderr
, 10);
426 if (MP_CMP(mm
.r
, !=, r
)) {
427 fputs("\n*** bad r", stderr
);
428 fputs("\nm = ", stderr
); mp_writefile(m
, stderr
, 10);
429 fputs("\nexpected ", stderr
); mp_writefile(r
, stderr
, 10);
430 fputs("\n found ", stderr
); mp_writefile(mm
.r
, stderr
, 10);
435 if (MP_CMP(mm
.r2
, !=, r2
)) {
436 fputs("\n*** bad r2", stderr
);
437 fputs("\nm = ", stderr
); mp_writefile(m
, stderr
, 10);
438 fputs("\nexpected ", stderr
); mp_writefile(r2
, stderr
, 10);
439 fputs("\n found ", stderr
); mp_writefile(mm
.r2
, stderr
, 10);
449 assert(mparena_count(MPARENA_GLOBAL
) == 0);
453 static int tmul(dstr
*v
)
455 mp
*m
= *(mp
**)v
[0].buf
;
456 mp
*a
= *(mp
**)v
[1].buf
;
457 mp
*b
= *(mp
**)v
[2].buf
;
458 mp
*r
= *(mp
**)v
[3].buf
;
462 mpmont_create(&mm
, m
);
465 mp
*qr
= mp_mul(MP_NEW
, a
, b
);
466 mp_div(0, &qr
, qr
, m
);
468 if (MP_CMP(qr
, !=, r
)) {
469 fputs("\n*** classical modmul failed", stderr
);
470 fputs("\n m = ", stderr
); mp_writefile(m
, stderr
, 10);
471 fputs("\n a = ", stderr
); mp_writefile(a
, stderr
, 10);
472 fputs("\n b = ", stderr
); mp_writefile(b
, stderr
, 10);
473 fputs("\n r = ", stderr
); mp_writefile(r
, stderr
, 10);
474 fputs("\nqr = ", stderr
); mp_writefile(qr
, stderr
, 10);
483 mp
*ar
= mpmont_mul(&mm
, MP_NEW
, a
, mm
.r2
);
484 mp
*br
= mpmont_mul(&mm
, MP_NEW
, b
, mm
.r2
);
485 mp
*mr
= mpmont_mul(&mm
, MP_NEW
, ar
, br
);
486 mr
= mpmont_reduce(&mm
, mr
, mr
);
487 if (MP_CMP(mr
, !=, r
)) {
488 fputs("\n*** montgomery modmul failed", stderr
);
489 fputs("\n m = ", stderr
); mp_writefile(m
, stderr
, 10);
490 fputs("\n a = ", stderr
); mp_writefile(a
, stderr
, 10);
491 fputs("\n b = ", stderr
); mp_writefile(b
, stderr
, 10);
492 fputs("\n r = ", stderr
); mp_writefile(r
, stderr
, 10);
493 fputs("\nmr = ", stderr
); mp_writefile(mr
, stderr
, 10);
497 MP_DROP(ar
); MP_DROP(br
);
507 assert(mparena_count(MPARENA_GLOBAL
) == 0);
511 static int texp(dstr
*v
)
513 mp
*m
= *(mp
**)v
[0].buf
;
514 mp
*a
= *(mp
**)v
[1].buf
;
515 mp
*b
= *(mp
**)v
[2].buf
;
516 mp
*r
= *(mp
**)v
[3].buf
;
521 mpmont_create(&mm
, m
);
523 mr
= mpmont_exp(&mm
, MP_NEW
, a
, b
);
525 if (MP_CMP(mr
, !=, r
)) {
526 fputs("\n*** montgomery modexp failed", stderr
);
527 fputs("\n m = ", stderr
); mp_writefile(m
, stderr
, 10);
528 fputs("\n a = ", stderr
); mp_writefile(a
, stderr
, 10);
529 fputs("\n e = ", stderr
); mp_writefile(b
, stderr
, 10);
530 fputs("\n r = ", stderr
); mp_writefile(r
, stderr
, 10);
531 fputs("\nmr = ", stderr
); mp_writefile(mr
, stderr
, 10);
542 assert(mparena_count(MPARENA_GLOBAL
) == 0);
547 static test_chunk tests
[] = {
548 { "create", tcreate
, { &type_mp
, &type_mp
, &type_mp
, &type_mp
, 0 } },
549 { "mul", tmul
, { &type_mp
, &type_mp
, &type_mp
, &type_mp
, 0 } },
550 { "exp", texp
, { &type_mp
, &type_mp
, &type_mp
, &type_mp
, 0 } },
554 int main(int argc
, char *argv
[])
557 test_run(argc
, argv
, tests
, SRCDIR
"/tests/mpmont");
563 /*----- That's all, folks -------------------------------------------------*/