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 -------------------------------------------------*/