3 * $Id: mpmont.c,v 1.4 1999/11/21 12:27:06 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 1.4 1999/11/21 12:27:06 mdw
34 * Remove a division from the Montgomery setup by calculating
35 * %$R^2 \bmod m$% first and then %$R \bmod m$% by Montgomery reduction of
38 * Revision 1.3 1999/11/21 11:35:10 mdw
39 * Performance improvement: use @mp_sqr@ and @mpmont_reduce@ instead of
40 * @mpmont_mul@ for squaring in exponentiation.
42 * Revision 1.2 1999/11/19 13:17:26 mdw
43 * Add extra interface to exponentiation which returns a Montgomerized
46 * Revision 1.1 1999/11/17 18:02:16 mdw
47 * New multiprecision integer arithmetic suite.
51 /*----- Header files ------------------------------------------------------*/
56 /*----- Main code ---------------------------------------------------------*/
58 /* --- @mpmont_create@ --- *
60 * Arguments: @mpmont *mm@ = pointer to Montgomery reduction context
61 * @mp *m@ = modulus to use
65 * Use: Initializes a Montgomery reduction context ready for use.
68 void mpmont_create(mpmont
*mm
, mp
*m
)
70 /* --- Take a copy of the modulus --- */
75 /* --- Find the magic value @mi@ --- *
77 * This is a slightly grungy way of solving the problem, but it does work.
86 mp_build(&a
, av
, av
+ 2);
87 mp_build(&b
, m
->v
, m
->v
+ 1);
88 mp_gcd(0, 0, &i
, &a
, &b
);
96 /* --- Discover the values %$R \bmod m$% and %$R^2 \bmod m$% --- */
100 mp
*r
= mp_create(2 * l
+ 1);
102 mm
->shift
= l
* MPW_BITS
;
103 MPX_ZERO(r
->v
, r
->vl
- 1);
106 mp_div(0, &mm
->r2
, r
, m
);
107 mm
->r
= mpmont_reduce(mm
, MP_NEW
, mm
->r2
);
112 /* --- @mpmont_destroy@ --- *
114 * Arguments: @mpmont *mm@ = pointer to a Montgomery reduction context
118 * Use: Disposes of a context when it's no longer of any use to
122 void mpmont_destroy(mpmont
*mm
)
129 /* --- @mpmont_reduce@ --- *
131 * Arguments: @mpmont *mm@ = pointer to Montgomery reduction context
132 * @mp *d@ = destination
133 * @const mp *a@ = source, assumed positive
135 * Returns: Result, %$a R^{-1} \bmod m$%.
138 mp
*mpmont_reduce(mpmont
*mm
, mp
*d
, const mp
*a
)
144 /* --- Initial conditioning of the arguments --- */
149 MP_MODIFY(d
, 2 * n
+ 1);
151 MP_MODIFY(d
, 2 * n
+ 1);
152 memcpy(d
->v
, a
->v
, MPWS(MP_LEN(a
)));
153 memset(d
->v
+ MP_LEN(a
), 0, MPWS(MP_LEN(d
) - MP_LEN(a
)));
156 dv
= d
->v
; dvl
= d
->vl
;
157 mv
= mm
->m
->v
; mvl
= mm
->m
->vl
;
159 /* --- Let's go to work --- */
162 mpw u
= MPW(*dv
* mm
->mi
);
163 MPX_UMLAN(dv
, dvl
, mv
, mvl
, u
);
169 memmove(d
->v
, dv
, MPWS(dvl
- dv
));
172 d
->f
= a
->f
& MP_BURN
;
173 if (MP_CMP(d
, >=, mm
->m
))
174 d
= mp_sub(d
, d
, mm
->m
);
178 /* --- @mpmont_mul@ --- *
180 * Arguments: @mpmont *mm@ = pointer to Montgomery reduction context
181 * @mp *d@ = destination
182 * @const mp *a, *b@ = sources, assumed positive
184 * Returns: Result, %$a b R^{-1} \bmod m$%.
187 mp
*mpmont_mul(mpmont
*mm
, mp
*d
, const mp
*a
, const mp
*b
)
196 /* --- Initial conditioning of the arguments --- */
198 if (MP_LEN(a
) > MP_LEN(b
)) {
199 const mp
*t
= a
; a
= b
; b
= t
;
203 MP_MODIFY(d
, 2 * n
+ 1);
204 dv
= d
->v
; dvl
= d
->vl
;
206 av
= a
->v
; avl
= a
->vl
;
207 bv
= b
->v
; bvl
= b
->vl
;
208 mv
= mm
->m
->v
; mvl
= mm
->m
->vl
;
211 /* --- Montgomery multiplication phase --- */
214 while (i
< n
&& av
< avl
) {
216 mpw u
= MPW((*dv
+ x
* y
) * mm
->mi
);
217 MPX_UMLAN(dv
, dvl
, bv
, bvl
, x
);
218 MPX_UMLAN(dv
, dvl
, mv
, mvl
, u
);
223 /* --- Simpler Montgomery reduction phase --- */
226 mpw u
= MPW(*dv
* mm
->mi
);
227 MPX_UMLAN(dv
, dvl
, mv
, mvl
, u
);
234 memmove(d
->v
, dv
, MPWS(dvl
- dv
));
237 d
->f
= (a
->f
| b
->f
) & MP_BURN
;
238 if (MP_CMP(d
, >=, mm
->m
))
239 d
= mp_sub(d
, d
, mm
->m
);
243 /* --- @mpmont_expr@ --- *
245 * Arguments: @mpmont *mm@ = pointer to Montgomery reduction context
246 * @const mp *a@ = base
247 * @const mp *e@ = exponent
249 * Returns: Result, %$a^e R \bmod m$%.
252 mp
*mpmont_expr(mpmont
*mm
, const mp
*a
, const mp
*e
)
255 mp
*ar
= mpmont_mul(mm
, MP_NEW
, a
, mm
->r2
);
256 mp
*d
= MP_COPY(mm
->r
);
267 dd
= mp_sqr(spare
, ar
);
268 dd
= mpmont_reduce(mm
, dd
, dd
);
272 dd
= mpmont_mul(mm
, spare
, d
, ar
);
286 /* --- @mpmont_exp@ --- *
288 * Arguments: @mpmont *mm@ = pointer to Montgomery reduction context
289 * @const mp *a@ = base
290 * @const mp *e@ = exponent
292 * Returns: Result, %$a^e \bmod m$%.
295 mp
*mpmont_exp(mpmont
*mm
, const mp
*a
, const mp
*e
)
297 mp
*d
= mpmont_expr(mm
, a
, e
);
298 d
= mpmont_reduce(mm
, d
, d
);
302 /*----- Test rig ----------------------------------------------------------*/
306 static int tcreate(dstr
*v
)
308 mp
*m
= *(mp
**)v
[0].buf
;
309 mp
*mi
= *(mp
**)v
[1].buf
;
310 mp
*r
= *(mp
**)v
[2].buf
;
311 mp
*r2
= *(mp
**)v
[3].buf
;
316 mpmont_create(&mm
, m
);
318 if (mm
.mi
!= mi
->v
[0]) {
319 fprintf(stderr
, "\n*** bad mi: found %lu, expected %lu",
320 (unsigned long)mm
.mi
, (unsigned long)mi
->v
[0]);
321 fputs("\nm = ", stderr
); mp_writefile(m
, stderr
, 10);
326 if (MP_CMP(mm
.r
, !=, r
)) {
327 fputs("\n*** bad r", stderr
);
328 fputs("\nm = ", stderr
); mp_writefile(m
, stderr
, 10);
329 fputs("\nexpected ", stderr
); mp_writefile(r
, stderr
, 10);
330 fputs("\n found ", stderr
); mp_writefile(mm
.r
, stderr
, 10);
335 if (MP_CMP(mm
.r2
, !=, r2
)) {
336 fputs("\n*** bad r2", stderr
);
337 fputs("\nm = ", stderr
); mp_writefile(m
, stderr
, 10);
338 fputs("\nexpected ", stderr
); mp_writefile(r2
, stderr
, 10);
339 fputs("\n found ", stderr
); mp_writefile(mm
.r2
, stderr
, 10);
352 static int tmul(dstr
*v
)
354 mp
*m
= *(mp
**)v
[0].buf
;
355 mp
*a
= *(mp
**)v
[1].buf
;
356 mp
*b
= *(mp
**)v
[2].buf
;
357 mp
*r
= *(mp
**)v
[3].buf
;
361 mpmont_create(&mm
, m
);
364 mp
*qr
= mp_mul(MP_NEW
, a
, b
);
365 mp_div(0, &qr
, qr
, m
);
367 if (MP_CMP(qr
, !=, r
)) {
368 fputs("\n*** classical modmul failed", stderr
);
369 fputs("\n m = ", stderr
); mp_writefile(m
, stderr
, 10);
370 fputs("\n a = ", stderr
); mp_writefile(a
, stderr
, 10);
371 fputs("\n b = ", stderr
); mp_writefile(b
, stderr
, 10);
372 fputs("\n r = ", stderr
); mp_writefile(r
, stderr
, 10);
373 fputs("\nqr = ", stderr
); mp_writefile(qr
, stderr
, 10);
382 mp
*ar
= mpmont_mul(&mm
, MP_NEW
, a
, mm
.r2
);
383 mp
*br
= mpmont_mul(&mm
, MP_NEW
, b
, mm
.r2
);
384 mp
*mr
= mpmont_mul(&mm
, MP_NEW
, ar
, br
);
385 mr
= mpmont_reduce(&mm
, mr
, mr
);
386 if (MP_CMP(mr
, !=, r
)) {
387 fputs("\n*** montgomery modmul failed", stderr
);
388 fputs("\n m = ", stderr
); mp_writefile(m
, stderr
, 10);
389 fputs("\n a = ", stderr
); mp_writefile(a
, stderr
, 10);
390 fputs("\n b = ", stderr
); mp_writefile(b
, stderr
, 10);
391 fputs("\n r = ", stderr
); mp_writefile(r
, stderr
, 10);
392 fputs("\nmr = ", stderr
); mp_writefile(mr
, stderr
, 10);
396 MP_DROP(ar
); MP_DROP(br
);
409 static int texp(dstr
*v
)
411 mp
*m
= *(mp
**)v
[0].buf
;
412 mp
*a
= *(mp
**)v
[1].buf
;
413 mp
*b
= *(mp
**)v
[2].buf
;
414 mp
*r
= *(mp
**)v
[3].buf
;
419 mpmont_create(&mm
, m
);
421 mr
= mpmont_exp(&mm
, a
, b
);
423 if (MP_CMP(mr
, !=, r
)) {
424 fputs("\n*** montgomery modexp failed", stderr
);
425 fputs("\n m = ", stderr
); mp_writefile(m
, stderr
, 10);
426 fputs("\n a = ", stderr
); mp_writefile(a
, stderr
, 10);
427 fputs("\n e = ", stderr
); mp_writefile(b
, stderr
, 10);
428 fputs("\n r = ", stderr
); mp_writefile(r
, stderr
, 10);
429 fputs("\nmr = ", stderr
); mp_writefile(mr
, stderr
, 10);
444 static test_chunk tests
[] = {
445 { "create", tcreate
, { &type_mp
, &type_mp
, &type_mp
, &type_mp
} },
446 { "mul", tmul
, { &type_mp
, &type_mp
, &type_mp
, &type_mp
} },
447 { "exp", texp
, { &type_mp
, &type_mp
, &type_mp
, &type_mp
} },
451 int main(int argc
, char *argv
[])
454 test_run(argc
, argv
, tests
, SRCDIR
"/tests/mpmont");
460 /*----- That's all, folks -------------------------------------------------*/