5 * (c) 1999 Straylight/Edgeware
8 /*----- Licensing notice --------------------------------------------------*
10 * This file is part of Catacomb.
12 * Catacomb is free software; you can redistribute it and/or modify
13 * it under the terms of the GNU Library General Public License as
14 * published by the Free Software Foundation; either version 2 of the
15 * License, or (at your option) any later version.
17 * Catacomb is distributed in the hope that it will be useful,
18 * but WITHOUT ANY WARRANTY; without even the implied warranty of
19 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
20 * GNU Library General Public License for more details.
22 * You should have received a copy of the GNU Library General Public
23 * License along with Catacomb; if not, write to the Free
24 * Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
28 /*----- Header files ------------------------------------------------------*/
33 /*----- Tweakables --------------------------------------------------------*/
35 /* --- @MPMONT_DISABLE@ --- *
37 * Replace all the clever Montgomery reduction with good old-fashioned long
41 /* #define MPMONT_DISABLE */
43 /*----- Reduction and multiplication --------------------------------------*/
45 /* --- @mpmont_create@ --- *
47 * Arguments: @mpmont *mm@ = pointer to Montgomery reduction context
48 * @mp *m@ = modulus to use
50 * Returns: Zero on success, nonzero on error.
52 * Use: Initializes a Montgomery reduction context ready for use.
53 * The argument @m@ must be a positive odd integer.
58 int mpmont_create(mpmont
*mm
, mp
*m
)
70 int mpmont_create(mpmont
*mm
, mp
*m
)
73 mp
*r2
= mp_new(2 * n
+ 1, 0);
76 /* --- Take a copy of the modulus --- */
78 if (!MP_POSP(m
) || !MP_ODDP(m
))
82 /* --- Determine %$R^2$% --- */
85 MPX_ZERO(r2
->v
, r2
->vl
- 1);
88 /* --- Find the magic value @mi@ --- */
90 mp_build(&r
, r2
->v
+ n
, r2
->vl
);
91 mm
->mi
= mp_modinv(MP_NEW
, m
, &r
);
92 mm
->mi
= mp_sub(mm
->mi
, &r
, mm
->mi
);
94 /* --- Discover the values %$R \bmod m$% and %$R^2 \bmod m$% --- */
97 mp_div(0, &mm
->r2
, r2
, m
);
98 mm
->r
= mpmont_reduce(mm
, MP_NEW
, mm
->r2
);
105 /* --- @mpmont_destroy@ --- *
107 * Arguments: @mpmont *mm@ = pointer to a Montgomery reduction context
111 * Use: Disposes of a context when it's no longer of any use to
115 void mpmont_destroy(mpmont
*mm
)
123 /* --- @mpmont_reduce@ --- *
125 * Arguments: @mpmont *mm@ = pointer to Montgomery reduction context
126 * @mp *d@ = destination
127 * @mp *a@ = source, assumed positive
129 * Returns: Result, %$a R^{-1} \bmod m$%.
132 #ifdef MPMONT_DISABLE
134 mp
*mpmont_reduce(mpmont
*mm
, mp
*d
, mp
*a
)
136 mp_div(0, &d
, a
, mm
->m
);
142 mp
*mpmont_reduce(mpmont
*mm
, mp
*d
, mp
*a
)
146 /* --- Check for serious Karatsuba reduction --- */
148 if (n
> MPK_THRESH
* 3) {
157 mp_build(&al
, a
->v
, vl
);
158 u
= mp_mul(MP_NEW
, &al
, mm
->mi
);
161 u
= mp_mul(u
, u
, mm
->m
);
167 /* --- Otherwise do it the hard way --- */
175 /* --- Initial conditioning of the arguments --- */
181 MP_DEST(d
, 2 * n
+ 1, a
->f
);
183 dv
= d
->v
; dvl
= d
->vl
;
184 mv
= mm
->m
->v
; mvl
= mm
->m
->vl
;
186 /* --- Let's go to work --- */
190 mpw u
= MPW(*dv
* mi
);
191 MPX_UMLAN(dv
, dvl
, mv
, mvl
, u
);
196 /* --- Wrap everything up --- */
198 memmove(d
->v
, d
->v
+ n
, MPWS(MP_LEN(d
) - n
));
200 if (MPX_UCMP(d
->v
, d
->vl
, >=, mm
->m
->v
, mm
->m
->vl
))
201 mpx_usub(d
->v
, d
->vl
, d
->v
, d
->vl
, mm
->m
->v
, mm
->m
->vl
);
203 mpx_usub(d
->v
, d
->vl
, mm
->m
->v
, mm
->m
->vl
, d
->v
, d
->vl
);
212 /* --- @mpmont_mul@ --- *
214 * Arguments: @mpmont *mm@ = pointer to Montgomery reduction context
215 * @mp *d@ = destination
216 * @mp *a, *b@ = sources, assumed positive
218 * Returns: Result, %$a b R^{-1} \bmod m$%.
221 #ifdef MPMONT_DISABLE
223 mp
*mpmont_mul(mpmont
*mm
, mp
*d
, mp
*a
, mp
*b
)
226 mp_div(0, &d
, d
, mm
->m
);
232 mp
*mpmont_mul(mpmont
*mm
, mp
*d
, mp
*a
, mp
*b
)
234 if (mm
->n
> MPK_THRESH
* 3) {
236 d
= mpmont_reduce(mm
, d
, d
);
246 /* --- Initial conditioning of the arguments --- */
248 if (MP_LEN(a
) > MP_LEN(b
)) {
249 mp
*t
= a
; a
= b
; b
= t
;
255 MP_DEST(d
, 2 * n
+ 1, a
->f
| b
->f
| MP_UNDEF
);
256 dv
= d
->v
; dvl
= d
->vl
;
258 av
= a
->v
; avl
= a
->vl
;
259 bv
= b
->v
; bvl
= b
->vl
;
260 mv
= mm
->m
->v
; mvl
= mm
->m
->vl
;
263 /* --- Montgomery multiplication phase --- */
267 while (i
< n
&& av
< avl
) {
269 mpw u
= MPW((*dv
+ x
* y
) * mi
);
270 MPX_UMLAN(dv
, dvl
, bv
, bvl
, x
);
271 MPX_UMLAN(dv
, dvl
, mv
, mvl
, u
);
276 /* --- Simpler Montgomery reduction phase --- */
279 mpw u
= MPW(*dv
* mi
);
280 MPX_UMLAN(dv
, dvl
, mv
, mvl
, u
);
287 memmove(d
->v
, dv
, MPWS(dvl
- dv
));
289 if (MPX_UCMP(d
->v
, d
->vl
, >=, mm
->m
->v
, mm
->m
->vl
))
290 mpx_usub(d
->v
, d
->vl
, d
->v
, d
->vl
, mm
->m
->v
, mm
->m
->vl
);
291 if ((a
->f
^ b
->f
) & MP_NEG
)
292 mpx_usub(d
->v
, d
->vl
, mm
->m
->v
, mm
->m
->vl
, d
->v
, d
->vl
);
294 d
->f
= (a
->f
| b
->f
) & MP_BURN
;
304 /*----- Test rig ----------------------------------------------------------*/
308 static int tcreate(dstr
*v
)
310 mp
*m
= *(mp
**)v
[0].buf
;
311 mp
*mi
= *(mp
**)v
[1].buf
;
312 mp
*r
= *(mp
**)v
[2].buf
;
313 mp
*r2
= *(mp
**)v
[3].buf
;
318 mpmont_create(&mm
, m
);
320 if (mm
.mi
->v
[0] != mi
->v
[0]) {
321 fprintf(stderr
, "\n*** bad mi: found %lu, expected %lu",
322 (unsigned long)mm
.mi
->v
[0], (unsigned long)mi
->v
[0]);
323 fputs("\nm = ", stderr
); mp_writefile(m
, stderr
, 10);
328 if (!MP_EQ(mm
.r
, r
)) {
329 fputs("\n*** bad r", stderr
);
330 fputs("\nm = ", stderr
); mp_writefile(m
, stderr
, 10);
331 fputs("\nexpected ", stderr
); mp_writefile(r
, stderr
, 10);
332 fputs("\n found ", stderr
); mp_writefile(mm
.r
, stderr
, 10);
337 if (!MP_EQ(mm
.r2
, r2
)) {
338 fputs("\n*** bad r2", stderr
);
339 fputs("\nm = ", stderr
); mp_writefile(m
, stderr
, 10);
340 fputs("\nexpected ", stderr
); mp_writefile(r2
, stderr
, 10);
341 fputs("\n found ", stderr
); mp_writefile(mm
.r2
, stderr
, 10);
351 assert(mparena_count(MPARENA_GLOBAL
) == 0);
355 static int tmul(dstr
*v
)
357 mp
*m
= *(mp
**)v
[0].buf
;
358 mp
*a
= *(mp
**)v
[1].buf
;
359 mp
*b
= *(mp
**)v
[2].buf
;
360 mp
*r
= *(mp
**)v
[3].buf
;
364 mpmont_create(&mm
, m
);
367 mp
*qr
= mp_mul(MP_NEW
, a
, b
);
368 mp_div(0, &qr
, qr
, m
);
371 fputs("\n*** classical modmul failed", stderr
);
372 fputs("\n m = ", stderr
); mp_writefile(m
, stderr
, 10);
373 fputs("\n a = ", stderr
); mp_writefile(a
, stderr
, 10);
374 fputs("\n b = ", stderr
); mp_writefile(b
, stderr
, 10);
375 fputs("\n r = ", stderr
); mp_writefile(r
, stderr
, 10);
376 fputs("\nqr = ", stderr
); mp_writefile(qr
, stderr
, 10);
385 mp
*ar
= mpmont_mul(&mm
, MP_NEW
, a
, mm
.r2
);
386 mp
*br
= mpmont_mul(&mm
, MP_NEW
, b
, mm
.r2
);
387 mp
*mr
= mpmont_mul(&mm
, MP_NEW
, ar
, br
);
388 mr
= mpmont_reduce(&mm
, mr
, mr
);
390 fputs("\n*** montgomery modmul failed", stderr
);
391 fputs("\n m = ", stderr
); mp_writefile(m
, stderr
, 10);
392 fputs("\n a = ", stderr
); mp_writefile(a
, stderr
, 10);
393 fputs("\n b = ", stderr
); mp_writefile(b
, stderr
, 10);
394 fputs("\n r = ", stderr
); mp_writefile(r
, stderr
, 10);
395 fputs("\nmr = ", stderr
); mp_writefile(mr
, stderr
, 10);
399 MP_DROP(ar
); MP_DROP(br
);
409 assert(mparena_count(MPARENA_GLOBAL
) == 0);
413 static test_chunk tests
[] = {
414 { "create", tcreate
, { &type_mp
, &type_mp
, &type_mp
, &type_mp
, 0 } },
415 { "mul", tmul
, { &type_mp
, &type_mp
, &type_mp
, &type_mp
, 0 } },
419 int main(int argc
, char *argv
[])
422 test_run(argc
, argv
, tests
, SRCDIR
"/t/mpmont");
428 /*----- That's all, folks -------------------------------------------------*/