3 * $Id: gfreduce.c,v 1.4 2004/03/27 00:04:46 mdw Exp $
5 * Efficient reduction modulo sparse binary polynomials
7 * (c) 2004 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 --------------------------------------------------*
32 * $Log: gfreduce.c,v $
33 * Revision 1.4 2004/03/27 00:04:46 mdw
34 * Implement efficient reduction for pleasant-looking primes.
36 * Revision 1.3 2004/03/23 15:19:32 mdw
37 * Test elliptic curves more thoroughly.
39 * Revision 1.2 2004/03/21 22:52:06 mdw
40 * Merge and close elliptic curve branch.
42 * Revision 1.1.2.1 2004/03/21 22:39:46 mdw
43 * Elliptic curves on binary fields work.
47 /*----- Header files ------------------------------------------------------*/
49 #include <mLib/alloc.h>
50 #include <mLib/darray.h>
51 #include <mLib/macros.h>
55 #include "gfreduce-exp.h"
59 /*----- Data structures ---------------------------------------------------*/
61 DA_DECL(instr_v
, gfreduce_instr
);
63 /*----- Main code ---------------------------------------------------------*/
65 /* --- What's going on here? --- *
67 * Let's face it, @gfx_div@ sucks. It works (I hope), but it's not in any
68 * sense fast. Here, we do efficient reduction modulo sparse polynomials.
70 * Suppose we have a polynomial @X@ we're trying to reduce mod @P@. If we
71 * take the topmost nonzero word of @X@, call it @w@, then we can eliminate
72 * it by subtracting off @w P x^{k}@ for an appropriate value of @k@. The
73 * trick is in observing that if @P@ is sparse we can do this multiplication
74 * and subtraction efficiently, just by XORing appropriate shifts of @w@ into
77 * The first tricky bit is in working out when to stop. I'll use eight-bit
78 * words to demonstrate what I'm talking about.
80 * xxxxxx xxxxxxxx xxxxxxxx xxxxxxxx xxxxxxxx xxxxxxxx
81 * 001ppppp pppppppp pppppppp pppppppp
83 * |<------------ bp ------------->|
84 * |<------------ nw --------------->|
86 * The trick of taking whole words off of @X@ stops working when there are
87 * only @nw@ words left. Then we have to mask off the bottom bits of @w@
91 /* --- @gfreduce_create@ --- *
93 * Arguments: @gfreduce *r@ = structure to fill in
94 * @mp *x@ = a (hopefully sparse) polynomial
98 * Use: Initializes a context structure for reduction.
101 void gfreduce_create(gfreduce
*r
, mp
*p
)
103 instr_v iv
= DA_INIT
;
110 size_t w
, ww
, wi
, wl
, ll
;
112 /* --- Sort out the easy stuff --- */
114 d
= mp_bits(p
); assert(d
); d
--;
120 r
->mask
= MPW(((mpw
)-1) << dw
);
125 /* --- Stash a new instruction --- */
127 #define INSTR(op_, arg_) do { \
129 DA(&iv)[DA_LEN(&iv)].op = (op_); \
130 DA(&iv)[DA_LEN(&iv)].arg = (arg_); \
136 w
= (d
+ MPW_BITS
- 1)/MPW_BITS
;
141 for (i
= 0, mp_scan(&sc
, p
); mp_step(&sc
) && i
< d
; i
++) {
144 ww
= (d
- i
+ MPW_BITS
- 1)/MPW_BITS
;
147 INSTR(GFRI_STORE
, w
);
151 INSTR(GFRI_LOAD
, ww
);
153 INSTR(GFRI_LOAD
, w
- 1);
154 for (; wi
< wl
; wi
++) {
156 assert(ip
->op
== GFRI_LSL
);
158 INSTR(GFRI_LSR
, MPW_BITS
- ip
->arg
);
161 INSTR(GFRI_STORE
, w
- 1);
162 INSTR(GFRI_LOAD
, ww
);
169 INSTR(GFRI_LSL
, (MPW_BITS
+ i
- d
)%MPW_BITS
);
170 if ((MPW_BITS
+ i
- d
)%MPW_BITS
)
174 INSTR(GFRI_STORE
, w
);
178 INSTR(GFRI_LOAD
, w
- 1);
179 for (; wi
< wl
; wi
++) {
181 assert(ip
->op
== GFRI_LSL
);
183 INSTR(GFRI_LSR
, MPW_BITS
- ip
->arg
);
185 INSTR(GFRI_STORE
, w
- 1);
191 r
->iv
= xmalloc(r
->in
* sizeof(gfreduce_instr
));
193 memcpy(r
->iv
, DA(&iv
), r
->in
* sizeof(gfreduce_instr
));
197 /* --- @gfreduce_destroy@ --- *
199 * Arguments: @gfreduce *r@ = structure to free
203 * Use: Reclaims the resources from a reduction context.
206 void gfreduce_destroy(gfreduce
*r
)
212 /* --- @gfreduce_dump@ --- *
214 * Arguments: @gfreduce *r@ = structure to dump
215 * @FILE *fp@ = file to dump on
219 * Use: Dumps a reduction context.
222 void gfreduce_dump(gfreduce
*r
, FILE *fp
)
226 fprintf(fp
, "poly = "); mp_writefile(r
->p
, fp
, 16);
227 fprintf(fp
, "\n lim = %lu; mask = %lx\n",
228 (unsigned long)r
->lim
, (unsigned long)r
->mask
);
229 for (i
= 0; i
< r
->in
; i
++) {
230 static const char *opname
[] = { "load", "lsl", "lsr", "store" };
231 assert(r
->iv
[i
].op
< N(opname
));
232 fprintf(fp
, " %s %lu\n",
234 (unsigned long)r
->iv
[i
].arg
);
238 /* --- @gfreduce_do@ --- *
240 * Arguments: @gfreduce *r@ = reduction context
241 * @mp *d@ = destination
244 * Returns: Destination, @x@ reduced modulo the reduction poly.
247 static void run(const gfreduce_instr
*i
, const gfreduce_instr
*il
,
252 for (; i
< il
; i
++) {
254 case GFRI_LOAD
: w
= *(v
- i
->arg
); break;
255 case GFRI_LSL
: w
^= z
<< i
->arg
; break;
256 case GFRI_LSR
: w
^= z
>> i
->arg
; break;
257 case GFRI_STORE
: *(v
- i
->arg
) = MPW(w
); break;
263 mp
*gfreduce_do(gfreduce
*r
, mp
*d
, mp
*x
)
266 const gfreduce_instr
*il
;
269 /* --- Try to reuse the source's space --- */
273 MP_DEST(x
, MP_LEN(x
), x
->f
);
275 /* --- Do the reduction --- */
278 if (MP_LEN(x
) >= r
->lim
) {
285 run(r
->iv
, il
, vl
, z
);
289 while (*vl
& r
->mask
) {
292 run(r
->iv
, il
, vl
, z
);
303 /* --- @gfreduce_sqrt@ --- *
305 * Arguments: @gfreduce *r@ = pointer to reduction context
306 * @mp *d@ = destination
307 * @mp *x@ = some polynomial
309 * Returns: The square root of @x@ modulo @r->p@, or null.
312 mp
*gfreduce_sqrt(gfreduce
*r
, mp
*d
, mp
*x
)
315 mp
*z
, *spare
= MP_NEW
;
316 unsigned long m
= mp_bits(r
->p
) - 1;
319 for (i
= 0; i
< m
- 1; i
++) {
320 mp
*t
= gf_sqr(spare
, y
);
322 y
= gfreduce_do(r
, t
, t
);
324 z
= gf_sqr(spare
, y
);
325 z
= gfreduce_do(r
, z
, z
);
335 /* --- @gfreduce_trace@ --- *
337 * Arguments: @gfreduce *r@ = pointer to reduction context
338 * @mp *x@ = some polynomial
340 * Returns: The trace of @x@. (%$\Tr(x)=x + x^2 + \cdots + x^{2^{m-1}}$%
341 * if %$x \in \gf{2^m}$%).
344 int gfreduce_trace(gfreduce
*r
, mp
*x
)
348 unsigned long m
= mp_bits(r
->p
) - 1;
352 for (i
= 0; i
< m
- 1; i
++) {
353 mp
*t
= gf_sqr(spare
, y
);
355 y
= gfreduce_do(r
, t
, t
);
364 /* --- @gfreduce_halftrace@ --- *
366 * Arguments: @gfreduce *r@ = pointer to reduction context
367 * @mp *d@ = destination
368 * @mp *x@ = some polynomial
370 * Returns: The half-trace of @x@.
371 * (%$\HfTr(x)= x + x^{2^2} + \cdots + x^{2^{m-1}}$%
372 * if %$x \in \gf{2^m}$% with %$m$% odd).
375 mp
*gfreduce_halftrace(gfreduce
*r
, mp
*d
, mp
*x
)
379 unsigned long m
= mp_bits(r
->p
) - 1;
383 for (i
= 0; i
< m
- 1; i
+= 2) {
384 mp
*t
= gf_sqr(spare
, y
);
386 y
= gfreduce_do(r
, t
, t
);
387 t
= gf_sqr(spare
, y
);
389 y
= gfreduce_do(r
, t
, t
);
396 /* --- @gfreduce_quadsolve@ --- *
398 * Arguments: @gfreduce *r@ = pointer to reduction context
399 * @mp *d@ = destination
400 * @mp *x@ = some polynomial
402 * Returns: A polynomial @y@ such that %$y^2 + y = x$%, or null.
405 mp
*gfreduce_quadsolve(gfreduce
*r
, mp
*d
, mp
*x
)
407 unsigned long m
= mp_bits(r
->p
) - 1;
412 d
= gfreduce_halftrace(r
, d
, x
);
414 mp
*z
, *w
, *rho
= MP_NEW
;
416 grand
*fr
= fibrand_create(0);
420 rho
= mprand(rho
, m
, fr
, 0);
423 for (i
= 0; i
< m
- 1; i
++) {
424 t
= gf_sqr(spare
, z
); spare
= z
; z
= gfreduce_do(r
, t
, t
);
425 t
= gf_sqr(spare
, w
); spare
= w
; w
= gfreduce_do(r
, t
, t
);
426 t
= gf_mul(spare
, w
, x
); t
= gfreduce_do(r
, t
, t
); spare
= t
;
428 w
= gf_add(w
, w
, rho
);
439 fr
->ops
->destroy(fr
);
443 t
= gf_sqr(MP_NEW
, d
); t
= gfreduce_do(r
, t
, t
); t
= gf_add(t
, t
, d
);
450 if (d
) d
->v
[0] &= ~(mpw
)1;
454 /* --- @gfreduce_exp@ --- *
456 * Arguments: @gfreduce *gr@ = pointer to reduction context
457 * @mp *d@ = fake destination
461 * Returns: Result, %$a^e \bmod m$%.
464 mp
*gfreduce_exp(gfreduce
*gr
, mp
*d
, mp
*a
, mp
*e
)
467 mp
*spare
= (e
->f
& MP_BURN
) ? MP_NEWSEC
: MP_NEW
;
472 else if (MP_LEN(e
) < EXP_THRESH
)
481 /*----- Test rig ----------------------------------------------------------*/
485 #define MP(x) mp_readstring(MP_NEW, #x, 0, 0)
487 static int vreduce(dstr
*v
)
489 mp
*d
= *(mp
**)v
[0].buf
;
490 mp
*n
= *(mp
**)v
[1].buf
;
491 mp
*r
= *(mp
**)v
[2].buf
;
496 gfreduce_create(&rr
, d
);
497 c
= gfreduce_do(&rr
, MP_NEW
, n
);
499 fprintf(stderr
, "\n*** reduction failed\n*** ");
500 gfreduce_dump(&rr
, stderr
);
501 fprintf(stderr
, "\n*** n = "); mp_writefile(n
, stderr
, 16);
502 fprintf(stderr
, "\n*** r = "); mp_writefile(r
, stderr
, 16);
503 fprintf(stderr
, "\n*** c = "); mp_writefile(c
, stderr
, 16);
504 fprintf(stderr
, "\n");
507 gfreduce_destroy(&rr
);
508 mp_drop(n
); mp_drop(d
); mp_drop(r
); mp_drop(c
);
509 assert(mparena_count(MPARENA_GLOBAL
) == 0);
513 static int vmodexp(dstr
*v
)
515 mp
*p
= *(mp
**)v
[0].buf
;
516 mp
*g
= *(mp
**)v
[1].buf
;
517 mp
*x
= *(mp
**)v
[2].buf
;
518 mp
*r
= *(mp
**)v
[3].buf
;
523 gfreduce_create(&rr
, p
);
524 c
= gfreduce_exp(&rr
, MP_NEW
, g
, x
);
526 fprintf(stderr
, "\n*** modexp failed\n*** ");
527 fprintf(stderr
, "\n*** p = "); mp_writefile(p
, stderr
, 16);
528 fprintf(stderr
, "\n*** g = "); mp_writefile(g
, stderr
, 16);
529 fprintf(stderr
, "\n*** x = "); mp_writefile(x
, stderr
, 16);
530 fprintf(stderr
, "\n*** c = "); mp_writefile(c
, stderr
, 16);
531 fprintf(stderr
, "\n*** r = "); mp_writefile(r
, stderr
, 16);
532 fprintf(stderr
, "\n");
535 gfreduce_destroy(&rr
);
536 mp_drop(p
); mp_drop(g
); mp_drop(r
); mp_drop(x
); mp_drop(c
);
537 assert(mparena_count(MPARENA_GLOBAL
) == 0);
541 static int vsqrt(dstr
*v
)
543 mp
*p
= *(mp
**)v
[0].buf
;
544 mp
*x
= *(mp
**)v
[1].buf
;
545 mp
*r
= *(mp
**)v
[2].buf
;
550 gfreduce_create(&rr
, p
);
551 c
= gfreduce_sqrt(&rr
, MP_NEW
, x
);
553 fprintf(stderr
, "\n*** sqrt failed\n*** ");
554 fprintf(stderr
, "\n*** p = "); mp_writefile(p
, stderr
, 16);
555 fprintf(stderr
, "\n*** x = "); mp_writefile(x
, stderr
, 16);
556 fprintf(stderr
, "\n*** c = "); mp_writefile(c
, stderr
, 16);
557 fprintf(stderr
, "\n*** r = "); mp_writefile(r
, stderr
, 16);
558 fprintf(stderr
, "\n");
561 gfreduce_destroy(&rr
);
562 mp_drop(p
); mp_drop(r
); mp_drop(x
); mp_drop(c
);
563 assert(mparena_count(MPARENA_GLOBAL
) == 0);
567 static int vtr(dstr
*v
)
569 mp
*p
= *(mp
**)v
[0].buf
;
570 mp
*x
= *(mp
**)v
[1].buf
;
571 int r
= *(int *)v
[2].buf
, c
;
575 gfreduce_create(&rr
, p
);
576 c
= gfreduce_trace(&rr
, x
);
578 fprintf(stderr
, "\n*** trace failed\n*** ");
579 fprintf(stderr
, "\n*** p = "); mp_writefile(p
, stderr
, 16);
580 fprintf(stderr
, "\n*** x = "); mp_writefile(x
, stderr
, 16);
581 fprintf(stderr
, "\n*** c = %d", c
);
582 fprintf(stderr
, "\n*** r = %d", r
);
583 fprintf(stderr
, "\n");
586 gfreduce_destroy(&rr
);
587 mp_drop(p
); mp_drop(x
);
588 assert(mparena_count(MPARENA_GLOBAL
) == 0);
592 static int vhftr(dstr
*v
)
594 mp
*p
= *(mp
**)v
[0].buf
;
595 mp
*x
= *(mp
**)v
[1].buf
;
596 mp
*r
= *(mp
**)v
[2].buf
;
601 gfreduce_create(&rr
, p
);
602 c
= gfreduce_halftrace(&rr
, MP_NEW
, x
);
604 fprintf(stderr
, "\n*** halftrace failed\n*** ");
605 fprintf(stderr
, "\n*** p = "); mp_writefile(p
, stderr
, 16);
606 fprintf(stderr
, "\n*** x = "); mp_writefile(x
, stderr
, 16);
607 fprintf(stderr
, "\n*** c = "); mp_writefile(c
, stderr
, 16);
608 fprintf(stderr
, "\n*** r = "); mp_writefile(r
, stderr
, 16);
609 fprintf(stderr
, "\n");
612 gfreduce_destroy(&rr
);
613 mp_drop(p
); mp_drop(r
); mp_drop(x
); mp_drop(c
);
614 assert(mparena_count(MPARENA_GLOBAL
) == 0);
618 static int vquad(dstr
*v
)
620 mp
*p
= *(mp
**)v
[0].buf
;
621 mp
*x
= *(mp
**)v
[1].buf
;
622 mp
*r
= *(mp
**)v
[2].buf
;
627 gfreduce_create(&rr
, p
);
628 c
= gfreduce_quadsolve(&rr
, MP_NEW
, x
);
630 fprintf(stderr
, "\n*** quadsolve failed\n*** ");
631 fprintf(stderr
, "\n*** p = "); mp_writefile(p
, stderr
, 16);
632 fprintf(stderr
, "\n*** x = "); mp_writefile(x
, stderr
, 16);
633 fprintf(stderr
, "\n*** c = "); mp_writefile(c
, stderr
, 16);
634 fprintf(stderr
, "\n*** r = "); mp_writefile(r
, stderr
, 16);
635 fprintf(stderr
, "\n");
638 gfreduce_destroy(&rr
);
639 mp_drop(p
); mp_drop(r
); mp_drop(x
); mp_drop(c
);
640 assert(mparena_count(MPARENA_GLOBAL
) == 0);
644 static test_chunk defs
[] = {
645 { "reduce", vreduce
, { &type_mp
, &type_mp
, &type_mp
, 0 } },
646 { "modexp", vmodexp
, { &type_mp
, &type_mp
, &type_mp
, &type_mp
, 0 } },
647 { "sqrt", vsqrt
, { &type_mp
, &type_mp
, &type_mp
, 0 } },
648 { "trace", vtr
, { &type_mp
, &type_mp
, &type_int
, 0 } },
649 { "halftrace", vhftr
, { &type_mp
, &type_mp
, &type_mp
, 0 } },
650 { "quadsolve", vquad
, { &type_mp
, &type_mp
, &type_mp
, 0 } },
654 int main(int argc
, char *argv
[])
656 test_run(argc
, argv
, defs
, SRCDIR
"/tests/gfreduce");
662 /*----- That's all, folks -------------------------------------------------*/