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 ------------------------------------------------------*/
35 /*----- Tweakables --------------------------------------------------------*/
37 /* --- @MPMONT_DISABLE@ --- *
39 * Replace all the clever Montgomery reduction with good old-fashioned long
43 /* #define MPMONT_DISABLE */
45 #define MPMONT_KTHRESH (16*MPK_THRESH)
47 /*----- Low-level implementation ------------------------------------------*/
49 #ifndef MPMONT_DISABLE
51 /* --- @redccore@ --- *
53 * Arguments: @mpw *dv, *dvl@ = base and limit of source/destination
54 * @const mpw *mv@ = base of modulus %$m$%
55 * @size_t n@ = length of modulus
56 * @const mpw *mi@ = base of REDC coefficient %$m'$%
60 * Use: Let %$a$% be the input operand. Store in %$d$% the value
61 * %$a + (m' a \bmod R) m$%. The destination has space for at
62 * least %$2 n + 1$% words of result.
65 CPU_DISPATCH(static, (void), void, redccore
,
66 (mpw
*dv
, mpw
*dvl
, const mpw
*mv
, size_t n
, const mpw
*mi
),
67 (dv
, dvl
, mv
, n
, mi
), pick_redccore
, simple_redccore
);
69 static void simple_redccore(mpw
*dv
, mpw
*dvl
, const mpw
*mv
,
70 size_t n
, const mpw
*mi
)
75 for (i
= 0; i
< n
; i
++) {
76 MPX_UMLAN(dv
, dvl
, mv
, mv
+ n
, MPW(*dv
*mi0
));
81 #define MAYBE_REDC4(impl) \
82 extern void mpxmont_redc4_##impl(mpw *dv, mpw *dvl, const mpw *mv, \
83 size_t n, const mpw *mi); \
84 static void maybe_redc4_##impl(mpw *dv, mpw *dvl, const mpw *mv, \
85 size_t n, const mpw *mi) \
87 if (n%4) simple_redccore(dv, dvl, mv, n, mi); \
88 else mpxmont_redc4_##impl(dv, dvl, mv, n, mi); \
96 MAYBE_REDC4(amd64_sse2
)
99 static redccore__functype
*pick_redccore(void)
102 DISPATCH_PICK_COND(mpmont_reduce
, maybe_redc4_x86_sse2
,
103 cpu_feature_p(CPUFEAT_X86_SSE2
));
106 DISPATCH_PICK_COND(mpmont_reduce
, maybe_redc4_amd64_sse2
,
107 cpu_feature_p(CPUFEAT_X86_SSE2
));
109 DISPATCH_PICK_FALLBACK(mpmont_reduce
, simple_redccore
);
112 /* --- @redccore@ --- *
114 * Arguments: @mpw *dv, *dvl@ = base and limit of source/destination
115 * @const mpw *av, *avl@ = base and limit of first multiplicand
116 * @const mpw *bv, *bvl@ = base and limit of second multiplicand
117 * @const mpw *mv@ = base of modulus %$m$%
118 * @size_t n@ = length of modulus
119 * @const mpw *mi@ = base of REDC coefficient %$m'$%
123 * Use: Let %$a$% and %$b$% be the multiplicands. Let %$w = a b$%.
124 * Store in %$d$% the value %$a b + (m' a b \bmod R) m$%.
127 CPU_DISPATCH(static, (void), void, mulcore
,
128 (mpw
*dv
, mpw
*dvl
, const mpw
*av
, const mpw
*avl
,
129 const mpw
*bv
, const mpw
*bvl
, const mpw
*mv
,
130 size_t n
, const mpw
*mi
),
131 (dv
, dvl
, av
, avl
, bv
, bvl
, mv
, n
, mi
),
132 pick_mulcore
, simple_mulcore
);
134 static void simple_mulcore(mpw
*dv
, mpw
*dvl
,
135 const mpw
*av
, const mpw
*avl
,
136 const mpw
*bv
, const mpw
*bvl
,
137 const mpw
*mv
, size_t n
, const mpw
*mi
)
139 mpw ai
, b0
, y
, mi0
= *mi
;
141 const mpw
*mvl
= mv
+ n
;
144 /* --- Initial setup --- */
147 if (avl
- av
> bvl
- bv
) {
148 tv
= av
; av
= bv
; bv
= tv
;
149 tvl
= avl
; avl
= bvl
; bvl
= tvl
;
153 /* --- Multiply, until we run out of multiplicand --- */
155 while (i
< n
&& av
< avl
) {
157 y
= MPW((*dv
+ ai
*b0
)*mi0
);
158 MPX_UMLAN(dv
, dvl
, bv
, bvl
, ai
);
159 MPX_UMLAN(dv
, dvl
, mv
, mvl
, y
);
163 /* --- Continue reducing until we run out of modulus --- */
167 MPX_UMLAN(dv
, dvl
, mv
, mvl
, y
);
172 #define MAYBE_MUL4(impl) \
173 extern void mpxmont_mul4_##impl(mpw *dv, \
174 const mpw *av, const mpw *bv, \
176 size_t n, const mpw *mi); \
177 static void maybe_mul4_##impl(mpw *dv, mpw *dvl, \
178 const mpw *av, const mpw *avl, \
179 const mpw *bv, const mpw *bvl, \
180 const mpw *mv, size_t n, const mpw *mi) \
182 size_t an = avl - av, bn = bvl - bv; \
183 if (n%4 || an != n || bn != n) \
184 simple_mulcore(dv, dvl, av, avl, bv, bvl, mv, n, mi); \
186 mpxmont_mul4_##impl(dv, av, bv, mv, n, mi); \
187 MPX_ZERO(dv + 2*n + 1, dvl); \
196 MAYBE_MUL4(amd64_sse2
)
199 static mulcore__functype
*pick_mulcore(void)
202 DISPATCH_PICK_COND(mpmont_mul
, maybe_mul4_x86_sse2
,
203 cpu_feature_p(CPUFEAT_X86_SSE2
));
206 DISPATCH_PICK_COND(mpmont_mul
, maybe_mul4_amd64_sse2
,
207 cpu_feature_p(CPUFEAT_X86_SSE2
));
209 DISPATCH_PICK_FALLBACK(mpmont_mul
, simple_mulcore
);
212 /* --- @finish@ --- *
214 * Arguments: @mpmont *mm@ = pointer to a Montgomery reduction context
215 * *mp *d@ = pointer to mostly-reduced operand
219 * Use: Applies the finishing touches to Montgomery reduction. The
220 * operand @d@ is a multiple of %$R%$ at this point, so it needs
221 * to be shifted down; the result might need a further
222 * subtraction to get it into the right interval; and we may
223 * need to do an additional subtraction if %$d$% is negative.
226 static void finish(mpmont
*mm
, mp
*d
)
228 mpw
*dv
= d
->v
, *dvl
= d
->vl
;
231 memmove(dv
, dv
+ n
, MPWS(dvl
- (dv
+ n
)));
234 if (MPX_UCMP(dv
, dvl
, >=, mm
->m
->v
, mm
->m
->vl
))
235 mpx_usub(dv
, dvl
, dv
, dvl
, mm
->m
->v
, mm
->m
->vl
);
238 mpx_usub(dv
, dvl
, mm
->m
->v
, mm
->m
->vl
, dv
, dvl
);
248 /*----- Reduction and multiplication --------------------------------------*/
250 /* --- @mpmont_create@ --- *
252 * Arguments: @mpmont *mm@ = pointer to Montgomery reduction context
253 * @mp *m@ = modulus to use
255 * Returns: Zero on success, nonzero on error.
257 * Use: Initializes a Montgomery reduction context ready for use.
258 * The argument @m@ must be a positive odd integer.
261 #ifdef MPMONT_DISABLE
263 int mpmont_create(mpmont
*mm
, mp
*m
)
275 int mpmont_create(mpmont
*mm
, mp
*m
)
277 size_t n
= MP_LEN(m
);
278 mp
*r2
= mp_new(2 * n
+ 1, 0);
281 /* --- Take a copy of the modulus --- */
283 if (!MP_POSP(m
) || !MP_ODDP(m
))
287 /* --- Determine %$R^2$% --- */
290 MPX_ZERO(r2
->v
, r2
->vl
- 1);
293 /* --- Find the magic value @mi@ --- */
295 mp_build(&r
, r2
->v
+ n
, r2
->vl
);
296 mm
->mi
= mp_modinv(MP_NEW
, m
, &r
);
297 mm
->mi
= mp_sub(mm
->mi
, &r
, mm
->mi
);
298 MP_ENSURE(mm
->mi
, n
);
300 /* --- Discover the values %$R \bmod m$% and %$R^2 \bmod m$% --- */
303 mp_div(0, &mm
->r2
, r2
, m
);
304 mm
->r
= mpmont_reduce(mm
, MP_NEW
, mm
->r2
);
311 /* --- @mpmont_destroy@ --- *
313 * Arguments: @mpmont *mm@ = pointer to a Montgomery reduction context
317 * Use: Disposes of a context when it's no longer of any use to
321 void mpmont_destroy(mpmont
*mm
)
329 /* --- @mpmont_reduce@ --- *
331 * Arguments: @mpmont *mm@ = pointer to Montgomery reduction context
332 * @mp *d@ = destination
333 * @mp *a@ = source, assumed positive
335 * Returns: Result, %$a R^{-1} \bmod m$%.
338 #ifdef MPMONT_DISABLE
340 mp
*mpmont_reduce(mpmont
*mm
, mp
*d
, mp
*a
)
342 mp_div(0, &d
, a
, mm
->m
);
348 mp
*mpmont_reduce(mpmont
*mm
, mp
*d
, mp
*a
)
352 /* --- Check for serious Karatsuba reduction --- */
354 if (n
> MPMONT_KTHRESH
) {
359 if (MP_LEN(a
) >= n
) vl
= a
->v
+ n
;
361 mp_build(&al
, a
->v
, vl
);
362 u
= mp_mul(MP_NEW
, &al
, mm
->mi
);
363 if (MP_LEN(u
) > n
) u
->vl
= u
->v
+ n
;
364 u
= mp_mul(u
, u
, mm
->m
);
370 /* --- Otherwise do it the hard way --- */
376 MP_DEST(d
, 2*mm
->n
+ 1, a
->f
);
377 redccore(d
->v
, d
->vl
, mm
->m
->v
, mm
->n
, mm
->mi
->v
);
380 /* --- Wrap everything up --- */
388 /* --- @mpmont_mul@ --- *
390 * Arguments: @mpmont *mm@ = pointer to Montgomery reduction context
391 * @mp *d@ = destination
392 * @mp *a, *b@ = sources, assumed positive
394 * Returns: Result, %$a b R^{-1} \bmod m$%.
397 #ifdef MPMONT_DISABLE
399 mp
*mpmont_mul(mpmont
*mm
, mp
*d
, mp
*a
, mp
*b
)
402 mp_div(0, &d
, d
, mm
->m
);
408 mp
*mpmont_mul(mpmont
*mm
, mp
*d
, mp
*a
, mp
*b
)
412 if (n
> MPMONT_KTHRESH
) {
414 d
= mpmont_reduce(mm
, d
, d
);
416 a
= MP_COPY(a
); b
= MP_COPY(b
);
417 MP_DEST(d
, 2*n
+ 1, a
->f
| b
->f
| MP_UNDEF
);
418 mulcore(d
->v
, d
->vl
, a
->v
, a
->vl
, b
->v
, b
->vl
,
419 mm
->m
->v
, mm
->n
, mm
->mi
->v
);
420 d
->f
= ((a
->f
| b
->f
) & MP_BURN
) | ((a
->f
^ b
->f
) & MP_NEG
);
422 MP_DROP(a
); MP_DROP(b
);
430 /*----- Test rig ----------------------------------------------------------*/
434 static int tcreate(dstr
*v
)
436 mp
*m
= *(mp
**)v
[0].buf
;
437 mp
*mi
= *(mp
**)v
[1].buf
;
438 mp
*r
= *(mp
**)v
[2].buf
;
439 mp
*r2
= *(mp
**)v
[3].buf
;
444 mpmont_create(&mm
, m
);
446 if (mm
.mi
->v
[0] != mi
->v
[0]) {
447 fprintf(stderr
, "\n*** bad mi: found %lu, expected %lu",
448 (unsigned long)mm
.mi
->v
[0], (unsigned long)mi
->v
[0]);
449 fputs("\nm = ", stderr
); mp_writefile(m
, stderr
, 10);
454 if (!MP_EQ(mm
.r
, r
)) {
455 fputs("\n*** bad r", stderr
);
456 fputs("\nm = ", stderr
); mp_writefile(m
, stderr
, 10);
457 fputs("\nexpected ", stderr
); mp_writefile(r
, stderr
, 10);
458 fputs("\n found ", stderr
); mp_writefile(mm
.r
, stderr
, 10);
463 if (!MP_EQ(mm
.r2
, r2
)) {
464 fputs("\n*** bad r2", stderr
);
465 fputs("\nm = ", stderr
); mp_writefile(m
, stderr
, 10);
466 fputs("\nexpected ", stderr
); mp_writefile(r2
, stderr
, 10);
467 fputs("\n found ", stderr
); mp_writefile(mm
.r2
, stderr
, 10);
477 assert(mparena_count(MPARENA_GLOBAL
) == 0);
481 static int tmul(dstr
*v
)
483 mp
*m
= *(mp
**)v
[0].buf
;
484 mp
*a
= *(mp
**)v
[1].buf
;
485 mp
*b
= *(mp
**)v
[2].buf
;
486 mp
*r
= *(mp
**)v
[3].buf
;
490 mpmont_create(&mm
, m
);
493 mp
*qr
= mp_mul(MP_NEW
, a
, b
);
494 mp_div(0, &qr
, qr
, m
);
497 fputs("\n*** classical modmul failed", stderr
);
498 fputs("\n m = ", stderr
); mp_writefile(m
, stderr
, 10);
499 fputs("\n a = ", stderr
); mp_writefile(a
, stderr
, 10);
500 fputs("\n b = ", stderr
); mp_writefile(b
, stderr
, 10);
501 fputs("\n r = ", stderr
); mp_writefile(r
, stderr
, 10);
502 fputs("\nqr = ", stderr
); mp_writefile(qr
, stderr
, 10);
511 mp
*ar
= mpmont_mul(&mm
, MP_NEW
, a
, mm
.r2
);
512 mp
*br
= mpmont_mul(&mm
, MP_NEW
, b
, mm
.r2
);
513 mp
*mr
= mpmont_mul(&mm
, MP_NEW
, ar
, br
);
514 mr
= mpmont_reduce(&mm
, mr
, mr
);
516 fputs("\n*** montgomery modmul failed", stderr
);
517 fputs("\n m = ", stderr
); mp_writefile(m
, stderr
, 10);
518 fputs("\n a = ", stderr
); mp_writefile(a
, stderr
, 10);
519 fputs("\n b = ", stderr
); mp_writefile(b
, stderr
, 10);
520 fputs("\n r = ", stderr
); mp_writefile(r
, stderr
, 10);
521 fputs("\nmr = ", stderr
); mp_writefile(mr
, stderr
, 10);
525 MP_DROP(ar
); MP_DROP(br
);
535 assert(mparena_count(MPARENA_GLOBAL
) == 0);
539 static test_chunk tests
[] = {
540 { "create", tcreate
, { &type_mp
, &type_mp
, &type_mp
, &type_mp
, 0 } },
541 { "mul", tmul
, { &type_mp
, &type_mp
, &type_mp
, &type_mp
, 0 } },
545 int main(int argc
, char *argv
[])
548 test_run(argc
, argv
, tests
, SRCDIR
"/t/mpmont");
554 /*----- That's all, folks -------------------------------------------------*/