3 * $Id: mpmont.c,v 1.5 1999/11/22 13:58:40 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 1.5 1999/11/22 13:58:40 mdw
34 * Add an option to disable Montgomery reduction, so that performance
35 * comparisons can be done.
37 * Revision 1.4 1999/11/21 12:27:06 mdw
38 * Remove a division from the Montgomery setup by calculating
39 * %$R^2 \bmod m$% first and then %$R \bmod m$% by Montgomery reduction of
42 * Revision 1.3 1999/11/21 11:35:10 mdw
43 * Performance improvement: use @mp_sqr@ and @mpmont_reduce@ instead of
44 * @mpmont_mul@ for squaring in exponentiation.
46 * Revision 1.2 1999/11/19 13:17:26 mdw
47 * Add extra interface to exponentiation which returns a Montgomerized
50 * Revision 1.1 1999/11/17 18:02:16 mdw
51 * New multiprecision integer arithmetic suite.
55 /*----- Header files ------------------------------------------------------*/
60 /*----- Tweakables --------------------------------------------------------*/
62 /* --- @MPMONT_DISABLE@ --- *
64 * Replace all the clever Montgomery reduction with good old-fashioned long
68 /* #define MPMONT_DISABLE */
70 /*----- Main code ---------------------------------------------------------*/
72 /* --- @mpmont_create@ --- *
74 * Arguments: @mpmont *mm@ = pointer to Montgomery reduction context
75 * @mp *m@ = modulus to use
79 * Use: Initializes a Montgomery reduction context ready for use.
84 void mpmont_create(mpmont
*mm
, mp
*m
)
94 void mpmont_create(mpmont
*mm
, mp
*m
)
96 /* --- Take a copy of the modulus --- */
101 /* --- Find the magic value @mi@ --- *
103 * This is a slightly grungy way of solving the problem, but it does work.
107 mpw av
[2] = { 0, 1 };
112 mp_build(&a
, av
, av
+ 2);
113 mp_build(&b
, m
->v
, m
->v
+ 1);
114 mp_gcd(0, 0, &i
, &a
, &b
);
116 if (!(i
->f
& MP_NEG
))
122 /* --- Discover the values %$R \bmod m$% and %$R^2 \bmod m$% --- */
125 size_t l
= MP_LEN(m
);
126 mp
*r
= mp_create(2 * l
+ 1);
128 mm
->shift
= l
* MPW_BITS
;
129 MPX_ZERO(r
->v
, r
->vl
- 1);
132 mp_div(0, &mm
->r2
, r
, m
);
133 mm
->r
= mpmont_reduce(mm
, MP_NEW
, mm
->r2
);
140 /* --- @mpmont_destroy@ --- *
142 * Arguments: @mpmont *mm@ = pointer to a Montgomery reduction context
146 * Use: Disposes of a context when it's no longer of any use to
150 void mpmont_destroy(mpmont
*mm
)
157 /* --- @mpmont_reduce@ --- *
159 * Arguments: @mpmont *mm@ = pointer to Montgomery reduction context
160 * @mp *d@ = destination
161 * @const mp *a@ = source, assumed positive
163 * Returns: Result, %$a R^{-1} \bmod m$%.
166 #ifdef MPMONT_DISABLE
168 mp
*mpmont_reduce(mpmont
*mm
, mp
*d
, const mp
*a
)
170 mp_div(0, &d
, a
, mm
->m
);
176 mp
*mpmont_reduce(mpmont
*mm
, mp
*d
, const mp
*a
)
182 /* --- Initial conditioning of the arguments --- */
187 MP_MODIFY(d
, 2 * n
+ 1);
189 MP_MODIFY(d
, 2 * n
+ 1);
190 memcpy(d
->v
, a
->v
, MPWS(MP_LEN(a
)));
191 memset(d
->v
+ MP_LEN(a
), 0, MPWS(MP_LEN(d
) - MP_LEN(a
)));
194 dv
= d
->v
; dvl
= d
->vl
;
195 mv
= mm
->m
->v
; mvl
= mm
->m
->vl
;
197 /* --- Let's go to work --- */
200 mpw u
= MPW(*dv
* mm
->mi
);
201 MPX_UMLAN(dv
, dvl
, mv
, mvl
, u
);
207 memmove(d
->v
, dv
, MPWS(dvl
- dv
));
210 d
->f
= a
->f
& MP_BURN
;
211 if (MP_CMP(d
, >=, mm
->m
))
212 d
= mp_sub(d
, d
, mm
->m
);
218 /* --- @mpmont_mul@ --- *
220 * Arguments: @mpmont *mm@ = pointer to Montgomery reduction context
221 * @mp *d@ = destination
222 * @const mp *a, *b@ = sources, assumed positive
224 * Returns: Result, %$a b R^{-1} \bmod m$%.
227 #ifdef MPMONT_DISABLE
229 mp
*mpmont_mul(mpmont
*mm
, mp
*d
, const mp
*a
, const mp
*b
)
232 mp_div(0, &d
, d
, mm
->m
);
238 mp
*mpmont_mul(mpmont
*mm
, mp
*d
, const mp
*a
, const mp
*b
)
247 /* --- Initial conditioning of the arguments --- */
249 if (MP_LEN(a
) > MP_LEN(b
)) {
250 const mp
*t
= a
; a
= b
; b
= t
;
254 MP_MODIFY(d
, 2 * n
+ 1);
255 dv
= d
->v
; dvl
= d
->vl
;
257 av
= a
->v
; avl
= a
->vl
;
258 bv
= b
->v
; bvl
= b
->vl
;
259 mv
= mm
->m
->v
; mvl
= mm
->m
->vl
;
262 /* --- Montgomery multiplication phase --- */
265 while (i
< n
&& av
< avl
) {
267 mpw u
= MPW((*dv
+ x
* y
) * mm
->mi
);
268 MPX_UMLAN(dv
, dvl
, bv
, bvl
, x
);
269 MPX_UMLAN(dv
, dvl
, mv
, mvl
, u
);
274 /* --- Simpler Montgomery reduction phase --- */
277 mpw u
= MPW(*dv
* mm
->mi
);
278 MPX_UMLAN(dv
, dvl
, mv
, mvl
, u
);
285 memmove(d
->v
, dv
, MPWS(dvl
- dv
));
288 d
->f
= (a
->f
| b
->f
) & MP_BURN
;
289 if (MP_CMP(d
, >=, mm
->m
))
290 d
= mp_sub(d
, d
, mm
->m
);
296 /* --- @mpmont_expr@ --- *
298 * Arguments: @mpmont *mm@ = pointer to Montgomery reduction context
299 * @const mp *a@ = base
300 * @const mp *e@ = exponent
302 * Returns: Result, %$a^e R \bmod m$%.
305 mp
*mpmont_expr(mpmont
*mm
, const mp
*a
, const mp
*e
)
308 mp
*ar
= mpmont_mul(mm
, MP_NEW
, a
, mm
->r2
);
309 mp
*d
= MP_COPY(mm
->r
);
320 dd
= mp_sqr(spare
, ar
);
321 dd
= mpmont_reduce(mm
, dd
, dd
);
325 dd
= mpmont_mul(mm
, spare
, d
, ar
);
339 /* --- @mpmont_exp@ --- *
341 * Arguments: @mpmont *mm@ = pointer to Montgomery reduction context
342 * @const mp *a@ = base
343 * @const mp *e@ = exponent
345 * Returns: Result, %$a^e \bmod m$%.
348 mp
*mpmont_exp(mpmont
*mm
, const mp
*a
, const mp
*e
)
350 mp
*d
= mpmont_expr(mm
, a
, e
);
351 d
= mpmont_reduce(mm
, d
, d
);
355 /*----- Test rig ----------------------------------------------------------*/
359 static int tcreate(dstr
*v
)
361 mp
*m
= *(mp
**)v
[0].buf
;
362 mp
*mi
= *(mp
**)v
[1].buf
;
363 mp
*r
= *(mp
**)v
[2].buf
;
364 mp
*r2
= *(mp
**)v
[3].buf
;
369 mpmont_create(&mm
, m
);
371 if (mm
.mi
!= mi
->v
[0]) {
372 fprintf(stderr
, "\n*** bad mi: found %lu, expected %lu",
373 (unsigned long)mm
.mi
, (unsigned long)mi
->v
[0]);
374 fputs("\nm = ", stderr
); mp_writefile(m
, stderr
, 10);
379 if (MP_CMP(mm
.r
, !=, r
)) {
380 fputs("\n*** bad r", stderr
);
381 fputs("\nm = ", stderr
); mp_writefile(m
, stderr
, 10);
382 fputs("\nexpected ", stderr
); mp_writefile(r
, stderr
, 10);
383 fputs("\n found ", stderr
); mp_writefile(mm
.r
, stderr
, 10);
388 if (MP_CMP(mm
.r2
, !=, r2
)) {
389 fputs("\n*** bad r2", stderr
);
390 fputs("\nm = ", stderr
); mp_writefile(m
, stderr
, 10);
391 fputs("\nexpected ", stderr
); mp_writefile(r2
, stderr
, 10);
392 fputs("\n found ", stderr
); mp_writefile(mm
.r2
, stderr
, 10);
405 static int tmul(dstr
*v
)
407 mp
*m
= *(mp
**)v
[0].buf
;
408 mp
*a
= *(mp
**)v
[1].buf
;
409 mp
*b
= *(mp
**)v
[2].buf
;
410 mp
*r
= *(mp
**)v
[3].buf
;
414 mpmont_create(&mm
, m
);
417 mp
*qr
= mp_mul(MP_NEW
, a
, b
);
418 mp_div(0, &qr
, qr
, m
);
420 if (MP_CMP(qr
, !=, r
)) {
421 fputs("\n*** classical modmul failed", stderr
);
422 fputs("\n m = ", stderr
); mp_writefile(m
, stderr
, 10);
423 fputs("\n a = ", stderr
); mp_writefile(a
, stderr
, 10);
424 fputs("\n b = ", stderr
); mp_writefile(b
, stderr
, 10);
425 fputs("\n r = ", stderr
); mp_writefile(r
, stderr
, 10);
426 fputs("\nqr = ", stderr
); mp_writefile(qr
, stderr
, 10);
435 mp
*ar
= mpmont_mul(&mm
, MP_NEW
, a
, mm
.r2
);
436 mp
*br
= mpmont_mul(&mm
, MP_NEW
, b
, mm
.r2
);
437 mp
*mr
= mpmont_mul(&mm
, MP_NEW
, ar
, br
);
438 mr
= mpmont_reduce(&mm
, mr
, mr
);
439 if (MP_CMP(mr
, !=, r
)) {
440 fputs("\n*** montgomery modmul failed", stderr
);
441 fputs("\n m = ", stderr
); mp_writefile(m
, stderr
, 10);
442 fputs("\n a = ", stderr
); mp_writefile(a
, stderr
, 10);
443 fputs("\n b = ", stderr
); mp_writefile(b
, stderr
, 10);
444 fputs("\n r = ", stderr
); mp_writefile(r
, stderr
, 10);
445 fputs("\nmr = ", stderr
); mp_writefile(mr
, stderr
, 10);
449 MP_DROP(ar
); MP_DROP(br
);
462 static int texp(dstr
*v
)
464 mp
*m
= *(mp
**)v
[0].buf
;
465 mp
*a
= *(mp
**)v
[1].buf
;
466 mp
*b
= *(mp
**)v
[2].buf
;
467 mp
*r
= *(mp
**)v
[3].buf
;
472 mpmont_create(&mm
, m
);
474 mr
= mpmont_exp(&mm
, a
, b
);
476 if (MP_CMP(mr
, !=, r
)) {
477 fputs("\n*** montgomery modexp failed", stderr
);
478 fputs("\n m = ", stderr
); mp_writefile(m
, stderr
, 10);
479 fputs("\n a = ", stderr
); mp_writefile(a
, stderr
, 10);
480 fputs("\n e = ", stderr
); mp_writefile(b
, stderr
, 10);
481 fputs("\n r = ", stderr
); mp_writefile(r
, stderr
, 10);
482 fputs("\nmr = ", stderr
); mp_writefile(mr
, stderr
, 10);
497 static test_chunk tests
[] = {
498 { "create", tcreate
, { &type_mp
, &type_mp
, &type_mp
, &type_mp
} },
499 { "mul", tmul
, { &type_mp
, &type_mp
, &type_mp
, &type_mp
} },
500 { "exp", texp
, { &type_mp
, &type_mp
, &type_mp
, &type_mp
} },
504 int main(int argc
, char *argv
[])
507 test_run(argc
, argv
, tests
, SRCDIR
"/tests/mpmont");
513 /*----- That's all, folks -------------------------------------------------*/