4885151bbcdf5d1815333c1f8de7a4362b45bf69
3 * $Id: mpmont.c,v 1.2 1999/11/19 13:17:26 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 1.2 1999/11/19 13:17:26 mdw
34 * Add extra interface to exponentiation which returns a Montgomerized
37 * Revision 1.1 1999/11/17 18:02:16 mdw
38 * New multiprecision integer arithmetic suite.
42 /*----- Header files ------------------------------------------------------*/
47 /*----- Main code ---------------------------------------------------------*/
49 /* --- @mpmont_create@ --- *
51 * Arguments: @mpmont *mm@ = pointer to Montgomery reduction context
52 * @mp *m@ = modulus to use
56 * Use: Initializes a Montgomery reduction context ready for use.
59 void mpmont_create(mpmont
*mm
, mp
*m
)
61 /* --- Take a copy of the modulus --- */
66 /* --- Find the magic value @mi@ --- *
68 * This is a slightly grungy way of solving the problem, but it does work.
77 mp_build(&a
, av
, av
+ 2);
78 mp_build(&b
, m
->v
, m
->v
+ 1);
79 mp_gcd(0, 0, &i
, &a
, &b
);
87 /* --- Discover the values %$R \bmod m$% and %$R^2 \bmod m$% --- */
91 mp
*r
= mp_create(l
+ 1);
93 mm
->shift
= l
* MPW_BITS
;
94 MPX_ZERO(r
->v
, r
->vl
- 1);
96 mm
->r
= mm
->r2
= MP_NEW
;
97 mp_div(0, &mm
->r
, r
, m
);
99 mp_div(0, &mm
->r2
, r
, m
);
104 /* --- @mpmont_destroy@ --- *
106 * Arguments: @mpmont *mm@ = pointer to a Montgomery reduction context
110 * Use: Disposes of a context when it's no longer of any use to
114 void mpmont_destroy(mpmont
*mm
)
121 /* --- @mpmont_reduce@ --- *
123 * Arguments: @mpmont *mm@ = pointer to Montgomery reduction context
124 * @mp *d@ = destination
125 * @const mp *a@ = source, assumed positive
127 * Returns: Result, %$a R^{-1} \bmod m$%.
130 mp
*mpmont_reduce(mpmont
*mm
, mp
*d
, const mp
*a
)
136 /* --- Initial conditioning of the arguments --- */
144 memcpy(d
->v
, a
->v
, MPWS(MP_LEN(a
)));
145 memset(d
->v
+ MP_LEN(a
), 0, MPWS(MP_LEN(d
) - MP_LEN(a
)));
148 dv
= d
->v
; dvl
= d
->vl
;
149 mv
= mm
->m
->v
; mvl
= mm
->m
->vl
;
151 /* --- Let's go to work --- */
154 mpw u
= MPW(*dv
* mm
->mi
);
155 MPX_UMLAN(dv
, dvl
, mv
, mvl
, u
);
161 memmove(d
->v
, dv
, MPWS(dvl
- dv
));
164 d
->f
= a
->f
& MP_BURN
;
165 if (MP_CMP(d
, >=, mm
->m
))
166 d
= mp_sub(d
, d
, mm
->m
);
170 /* --- @mpmont_mul@ --- *
172 * Arguments: @mpmont *mm@ = pointer to Montgomery reduction context
173 * @mp *d@ = destination
174 * @const mp *a, *b@ = sources, assumed positive
176 * Returns: Result, %$a b R^{-1} \bmod m$%.
179 mp
*mpmont_mul(mpmont
*mm
, mp
*d
, const mp
*a
, const mp
*b
)
188 /* --- Initial conditioning of the arguments --- */
190 if (MP_LEN(a
) > MP_LEN(b
)) {
191 const mp
*t
= a
; a
= b
; b
= t
;
195 MP_MODIFY(d
, 2 * n
+ 1);
196 dv
= d
->v
; dvl
= d
->vl
;
198 av
= a
->v
; avl
= a
->vl
;
199 bv
= b
->v
; bvl
= b
->vl
;
200 mv
= mm
->m
->v
; mvl
= mm
->m
->vl
;
203 /* --- Montgomery multiplication phase --- */
206 while (i
< n
&& av
< avl
) {
208 mpw u
= MPW((*dv
+ x
* y
) * mm
->mi
);
209 MPX_UMLAN(dv
, dvl
, bv
, bvl
, x
);
210 MPX_UMLAN(dv
, dvl
, mv
, mvl
, u
);
215 /* --- Simpler Montgomery reduction phase --- */
218 mpw u
= MPW(*dv
* mm
->mi
);
219 MPX_UMLAN(dv
, dvl
, mv
, mvl
, u
);
226 memmove(d
->v
, dv
, MPWS(dvl
- dv
));
229 d
->f
= (a
->f
| b
->f
) & MP_BURN
;
230 if (MP_CMP(d
, >=, mm
->m
))
231 d
= mp_sub(d
, d
, mm
->m
);
235 /* --- @mpmont_expr@ --- *
237 * Arguments: @mpmont *mm@ = pointer to Montgomery reduction context
238 * @const mp *a@ = base
239 * @const mp *e@ = exponent
241 * Returns: Result, %$a^e R \bmod m$%.
244 mp
*mpmont_expr(mpmont
*mm
, const mp
*a
, const mp
*e
)
247 mp
*ar
= mpmont_mul(mm
, MP_NEW
, a
, mm
->r2
);
248 mp
*d
= MP_COPY(mm
->r
);
259 dd
= mpmont_mul(mm
, spare
, ar
, ar
);
263 dd
= mpmont_mul(mm
, spare
, d
, ar
);
277 /* --- @mpmont_exp@ --- *
279 * Arguments: @mpmont *mm@ = pointer to Montgomery reduction context
280 * @const mp *a@ = base
281 * @const mp *e@ = exponent
283 * Returns: Result, %$a^e \bmod m$%.
286 mp
*mpmont_exp(mpmont
*mm
, const mp
*a
, const mp
*e
)
288 mp
*d
= mpmont_expr(mm
, a
, e
);
289 d
= mpmont_reduce(mm
, d
, d
);
293 /*----- Test rig ----------------------------------------------------------*/
297 static int tcreate(dstr
*v
)
299 mp
*m
= *(mp
**)v
[0].buf
;
300 mp
*mi
= *(mp
**)v
[1].buf
;
301 mp
*r
= *(mp
**)v
[2].buf
;
302 mp
*r2
= *(mp
**)v
[3].buf
;
307 mpmont_create(&mm
, m
);
309 if (mm
.mi
!= mi
->v
[0]) {
310 fprintf(stderr
, "\n*** bad mi: found %lu, expected %lu",
311 (unsigned long)mm
.mi
, (unsigned long)mi
->v
[0]);
312 fputs("\nm = ", stderr
); mp_writefile(m
, stderr
, 10);
317 if (MP_CMP(mm
.r
, !=, r
)) {
318 fputs("\n*** bad r", stderr
);
319 fputs("\nm = ", stderr
); mp_writefile(m
, stderr
, 10);
320 fputs("\nexpected ", stderr
); mp_writefile(r
, stderr
, 10);
321 fputs("\n found ", stderr
); mp_writefile(mm
.r
, stderr
, 10);
326 if (MP_CMP(mm
.r2
, !=, r2
)) {
327 fputs("\n*** bad r2", stderr
);
328 fputs("\nm = ", stderr
); mp_writefile(m
, stderr
, 10);
329 fputs("\nexpected ", stderr
); mp_writefile(r2
, stderr
, 10);
330 fputs("\n found ", stderr
); mp_writefile(mm
.r2
, stderr
, 10);
343 static int tmul(dstr
*v
)
345 mp
*m
= *(mp
**)v
[0].buf
;
346 mp
*a
= *(mp
**)v
[1].buf
;
347 mp
*b
= *(mp
**)v
[2].buf
;
348 mp
*r
= *(mp
**)v
[3].buf
;
353 mpmont_create(&mm
, m
);
356 mp
*ar
= mpmont_mul(&mm
, MP_NEW
, a
, mm
.r2
);
357 mp
*br
= mpmont_mul(&mm
, MP_NEW
, b
, mm
.r2
);
358 mr
= mpmont_mul(&mm
, MP_NEW
, ar
, br
);
359 mr
= mpmont_reduce(&mm
, mr
, mr
);
360 MP_DROP(ar
); MP_DROP(br
);
363 qr
= mp_mul(MP_NEW
, a
, b
);
364 mp_div(0, &qr
, qr
, m
);
366 if (MP_CMP(qr
, !=, r
)) {
367 fputs("\n*** classical modmul failed", stderr
);
368 fputs("\n m = ", stderr
); mp_writefile(m
, stderr
, 10);
369 fputs("\n a = ", stderr
); mp_writefile(a
, stderr
, 10);
370 fputs("\n b = ", stderr
); mp_writefile(b
, stderr
, 10);
371 fputs("\n r = ", stderr
); mp_writefile(r
, stderr
, 10);
372 fputs("\nqr = ", stderr
); mp_writefile(qr
, stderr
, 10);
377 if (MP_CMP(mr
, !=, r
)) {
378 fputs("\n*** montgomery modmul failed", stderr
);
379 fputs("\n m = ", stderr
); mp_writefile(m
, stderr
, 10);
380 fputs("\n a = ", stderr
); mp_writefile(a
, stderr
, 10);
381 fputs("\n b = ", stderr
); mp_writefile(b
, stderr
, 10);
382 fputs("\n r = ", stderr
); mp_writefile(r
, stderr
, 10);
383 fputs("\nmr = ", stderr
); mp_writefile(mr
, stderr
, 10);
398 static int texp(dstr
*v
)
400 mp
*m
= *(mp
**)v
[0].buf
;
401 mp
*a
= *(mp
**)v
[1].buf
;
402 mp
*b
= *(mp
**)v
[2].buf
;
403 mp
*r
= *(mp
**)v
[3].buf
;
408 mpmont_create(&mm
, m
);
410 mr
= mpmont_exp(&mm
, a
, b
);
412 if (MP_CMP(mr
, !=, r
)) {
413 fputs("\n*** montgomery modexp failed", stderr
);
414 fputs("\n m = ", stderr
); mp_writefile(m
, stderr
, 10);
415 fputs("\n a = ", stderr
); mp_writefile(a
, stderr
, 10);
416 fputs("\n e = ", stderr
); mp_writefile(b
, stderr
, 10);
417 fputs("\n r = ", stderr
); mp_writefile(r
, stderr
, 10);
418 fputs("\nmr = ", stderr
); mp_writefile(mr
, stderr
, 10);
433 static test_chunk tests
[] = {
434 { "create", tcreate
, { &type_mp
, &type_mp
, &type_mp
, &type_mp
} },
435 { "mul", tmul
, { &type_mp
, &type_mp
, &type_mp
, &type_mp
} },
436 { "exp", texp
, { &type_mp
, &type_mp
, &type_mp
, &type_mp
} },
440 int main(int argc
, char *argv
[])
443 test_run(argc
, argv
, tests
, SRCDIR
"/tests/mpmont");
449 /*----- That's all, folks -------------------------------------------------*/