3 * $Id: mpmont.c,v 1.1 1999/11/17 18:02:16 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 1.1 1999/11/17 18:02:16 mdw
34 * New multiprecision integer arithmetic suite.
38 /*----- Header files ------------------------------------------------------*/
43 /*----- Main code ---------------------------------------------------------*/
45 /* --- @mpmont_create@ --- *
47 * Arguments: @mpmont *mm@ = pointer to Montgomery reduction context
48 * @mp *m@ = modulus to use
52 * Use: Initializes a Montgomery reduction context ready for use.
55 void mpmont_create(mpmont
*mm
, mp
*m
)
57 /* --- Take a copy of the modulus --- */
62 /* --- Find the magic value @mi@ --- *
64 * This is a slightly grungy way of solving the problem, but it does work.
73 mp_build(&a
, av
, av
+ 2);
74 mp_build(&b
, m
->v
, m
->v
+ 1);
75 mp_gcd(0, 0, &i
, &a
, &b
);
83 /* --- Discover the values %$R \bmod m$% and %$R^2 \bmod m$% --- */
87 mp
*r
= mp_create(l
+ 1);
89 mm
->shift
= l
* MPW_BITS
;
90 MPX_ZERO(r
->v
, r
->vl
- 1);
92 mm
->r
= mm
->r2
= MP_NEW
;
93 mp_div(0, &mm
->r
, r
, m
);
95 mp_div(0, &mm
->r2
, r
, m
);
100 /* --- @mpmont_destroy@ --- *
102 * Arguments: @mpmont *mm@ = pointer to a Montgomery reduction context
106 * Use: Disposes of a context when it's no longer of any use to
110 void mpmont_destroy(mpmont
*mm
)
117 /* --- @mpmont_reduce@ --- *
119 * Arguments: @mpmont *mm@ = pointer to Montgomery reduction context
120 * @mp *d@ = destination
121 * @const mp *a@ = source, assumed positive
123 * Returns: Result, %$a R^{-1} \bmod m$%.
126 mp
*mpmont_reduce(mpmont
*mm
, mp
*d
, const mp
*a
)
132 /* --- Initial conditioning of the arguments --- */
140 memcpy(d
->v
, a
->v
, MPWS(MP_LEN(a
)));
141 memset(d
->v
+ MP_LEN(a
), 0, MPWS(MP_LEN(d
) - MP_LEN(a
)));
144 dv
= d
->v
; dvl
= d
->vl
;
145 mv
= mm
->m
->v
; mvl
= mm
->m
->vl
;
147 /* --- Let's go to work --- */
150 mpw u
= MPW(*dv
* mm
->mi
);
151 MPX_UMLAN(dv
, dvl
, mv
, mvl
, u
);
157 memmove(d
->v
, dv
, MPWS(dvl
- dv
));
160 d
->f
= a
->f
& MP_BURN
;
164 /* --- @mpmont_mul@ --- *
166 * Arguments: @mpmont *mm@ = pointer to Montgomery reduction context
167 * @mp *d@ = destination
168 * @const mp *a, *b@ = sources, assumed positive
170 * Returns: Result, %$a b R^{-1} \bmod m$%.
173 mp
*mpmont_mul(mpmont
*mm
, mp
*d
, const mp
*a
, const mp
*b
)
182 /* --- Initial conditioning of the arguments --- */
184 if (MP_LEN(a
) > MP_LEN(b
)) {
185 const mp
*t
= a
; a
= b
; b
= t
;
189 MP_MODIFY(d
, 2 * n
+ 1);
190 dv
= d
->v
; dvl
= d
->vl
;
192 av
= a
->v
; avl
= a
->vl
;
193 bv
= b
->v
; bvl
= b
->vl
;
194 mv
= mm
->m
->v
; mvl
= mm
->m
->vl
;
197 /* --- Montgomery multiplication phase --- */
200 while (i
< n
&& av
< avl
) {
202 mpw u
= MPW((*dv
+ x
* y
) * mm
->mi
);
203 MPX_UMLAN(dv
, dvl
, bv
, bvl
, x
);
204 MPX_UMLAN(dv
, dvl
, mv
, mvl
, u
);
209 /* --- Simpler Montgomery reduction phase --- */
212 mpw u
= MPW(*dv
* mm
->mi
);
213 MPX_UMLAN(dv
, dvl
, mv
, mvl
, u
);
220 memmove(d
->v
, dv
, MPWS(dvl
- dv
));
223 d
->f
= (a
->f
| b
->f
) & MP_BURN
;
227 /* --- @mpmont_exp@ --- *
229 * Arguments: @mpmont *mm@ = pointer to Montgomery reduction context
230 * @const mp *a@ = base
231 * @const mp *e@ = exponent
233 * Returns: Result, %$a^e \bmod m$%.
236 mp
*mpmont_exp(mpmont
*mm
, const mp
*a
, const mp
*e
)
239 mp
*ar
= mpmont_mul(mm
, MP_NEW
, a
, mm
->r2
);
240 mp
*d
= MP_COPY(mm
->r
);
248 dd
= mpmont_mul(mm
, MP_NEW
, d
, ar
);
254 dd
= mpmont_mul(mm
, MP_NEW
, ar
, ar
);
260 return (mpmont_reduce(mm
, d
, d
));
263 /*----- Test rig ----------------------------------------------------------*/
267 static int tcreate(dstr
*v
)
269 mp
*m
= *(mp
**)v
[0].buf
;
270 mp
*mi
= *(mp
**)v
[1].buf
;
271 mp
*r
= *(mp
**)v
[2].buf
;
272 mp
*r2
= *(mp
**)v
[3].buf
;
277 mpmont_create(&mm
, m
);
279 if (mm
.mi
!= mi
->v
[0]) {
280 fprintf(stderr
, "\n*** bad mi: found %lu, expected %lu",
281 (unsigned long)mm
.mi
, (unsigned long)mi
->v
[0]);
282 fputs("\nm = ", stderr
); mp_writefile(m
, stderr
, 10);
287 if (MP_CMP(mm
.r
, !=, r
)) {
288 fputs("\n*** bad r", stderr
);
289 fputs("\nm = ", stderr
); mp_writefile(m
, stderr
, 10);
290 fputs("\nexpected ", stderr
); mp_writefile(r
, stderr
, 10);
291 fputs("\n found ", stderr
); mp_writefile(r
, stderr
, 10);
296 if (MP_CMP(mm
.r2
, !=, r2
)) {
297 fputs("\n*** bad r2", stderr
);
298 fputs("\nm = ", stderr
); mp_writefile(m
, stderr
, 10);
299 fputs("\nexpected ", stderr
); mp_writefile(r2
, stderr
, 10);
300 fputs("\n found ", stderr
); mp_writefile(r2
, stderr
, 10);
313 static int tmul(dstr
*v
)
315 mp
*m
= *(mp
**)v
[0].buf
;
316 mp
*a
= *(mp
**)v
[1].buf
;
317 mp
*b
= *(mp
**)v
[2].buf
;
318 mp
*r
= *(mp
**)v
[3].buf
;
323 mpmont_create(&mm
, m
);
326 mp
*ar
= mpmont_mul(&mm
, MP_NEW
, a
, mm
.r2
);
327 mp
*br
= mpmont_mul(&mm
, MP_NEW
, b
, mm
.r2
);
328 mr
= mpmont_mul(&mm
, MP_NEW
, ar
, br
);
329 mr
= mpmont_reduce(&mm
, mr
, mr
);
330 MP_DROP(ar
); MP_DROP(br
);
333 qr
= mp_mul(MP_NEW
, a
, b
);
334 mp_div(0, &qr
, qr
, m
);
336 if (MP_CMP(qr
, !=, r
)) {
337 fputs("\n*** classical modmul failed", stderr
);
338 fputs("\n m = ", stderr
); mp_writefile(m
, stderr
, 10);
339 fputs("\n a = ", stderr
); mp_writefile(a
, stderr
, 10);
340 fputs("\n b = ", stderr
); mp_writefile(b
, stderr
, 10);
341 fputs("\n r = ", stderr
); mp_writefile(r
, stderr
, 10);
342 fputs("\nqr = ", stderr
); mp_writefile(qr
, stderr
, 10);
347 if (MP_CMP(mr
, !=, r
)) {
348 fputs("\n*** montgomery modmul failed", stderr
);
349 fputs("\n m = ", stderr
); mp_writefile(m
, stderr
, 10);
350 fputs("\n a = ", stderr
); mp_writefile(a
, stderr
, 10);
351 fputs("\n b = ", stderr
); mp_writefile(b
, stderr
, 10);
352 fputs("\n r = ", stderr
); mp_writefile(r
, stderr
, 10);
353 fputs("\nmr = ", stderr
); mp_writefile(mr
, stderr
, 10);
368 static int texp(dstr
*v
)
370 mp
*m
= *(mp
**)v
[0].buf
;
371 mp
*a
= *(mp
**)v
[1].buf
;
372 mp
*b
= *(mp
**)v
[2].buf
;
373 mp
*r
= *(mp
**)v
[3].buf
;
378 mpmont_create(&mm
, m
);
380 mr
= mpmont_exp(&mm
, a
, b
);
382 if (MP_CMP(mr
, !=, r
)) {
383 fputs("\n*** montgomery modexp failed", stderr
);
384 fputs("\n m = ", stderr
); mp_writefile(m
, stderr
, 10);
385 fputs("\n a = ", stderr
); mp_writefile(a
, stderr
, 10);
386 fputs("\n e = ", stderr
); mp_writefile(b
, stderr
, 10);
387 fputs("\n r = ", stderr
); mp_writefile(r
, stderr
, 10);
388 fputs("\nmr = ", stderr
); mp_writefile(mr
, stderr
, 10);
403 static test_chunk tests
[] = {
404 { "create", tcreate
, { &type_mp
, &type_mp
, &type_mp
, &type_mp
} },
405 { "mul", tmul
, { &type_mp
, &type_mp
, &type_mp
, &type_mp
} },
406 { "exp", texp
, { &type_mp
, &type_mp
, &type_mp
, &type_mp
} },
410 int main(int argc
, char *argv
[])
413 test_run(argc
, argv
, tests
, SRCDIR
"/tests/mpmont");
419 /*----- That's all, folks -------------------------------------------------*/