3 * Efficient reduction modulo nice primes
5 * (c) 2004 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 ------------------------------------------------------*/
30 #include <mLib/darray.h>
31 #include <mLib/macros.h>
35 #include "mpreduce-exp.h"
37 /*----- Data structures ---------------------------------------------------*/
39 DA_DECL(instr_v
, mpreduce_instr
);
41 /*----- Main code ---------------------------------------------------------*/
43 /* --- @mpreduce_create@ --- *
45 * Arguments: @gfreduce *r@ = structure to fill in
46 * @mp *x@ = an integer
48 * Returns: Zero if successful; nonzero on failure.
50 * Use: Initializes a context structure for reduction.
53 int mpreduce_create(mpreduce
*r
, mp
*p
)
56 enum { Z
= 0, Z1
= 2, X
= 4, X0
= 6 };
63 /* --- Fill in the easy stuff --- */
74 /* --- Stash a new instruction --- */
76 #define INSTR(op_, argx_, argy_) do { \
78 DA(&iv)[DA_LEN(&iv)].op = (op_); \
79 DA(&iv)[DA_LEN(&iv)].argx = (argx_); \
80 DA(&iv)[DA_LEN(&iv)].argy = (argy_); \
84 /* --- Main loop --- *
86 * A simple state machine decomposes @p@ conveniently into positive and
87 * negative powers of 2. The pure form of the state machine is left below
88 * for reference (and in case I need inspiration for a NAF exponentiator).
92 for (i
= 0, mp_scan(&sc
, p
); mp_step(&sc
); i
++) {
93 switch (st
| mp_bit(&sc
)) {
94 case Z
| 1: st
= Z1
; break;
95 case Z1
| 0: st
= Z
; printf("+ %lu\n", i
- 1); break;
96 case Z1
| 1: st
= X
; printf("- %lu\n", i
- 1); break;
97 case X
| 0: st
= X0
; break;
98 case X0
| 1: st
= X
; printf("- %lu\n", i
- 1); break;
99 case X0
| 0: st
= Z
; printf("+ %lu\n", i
- 1); break;
102 if (st
>= X
) printf("+ %lu\n", i
- 1);
106 bb
= MPW_BITS
- (d
+ 1)%MPW_BITS
;
107 for (i
= 0, mp_scan(&sc
, p
); i
< d
&& mp_step(&sc
); i
++) {
108 switch (st
| mp_bit(&sc
)) {
109 case Z
| 1: st
= Z1
; break;
110 case Z1
| 0: st
= Z
; op
= MPRI_SUB
; goto instr
;
111 case Z1
| 1: st
= X
; op
= MPRI_ADD
; goto instr
;
112 case X
| 0: st
= X0
; break;
113 case X0
| 1: st
= X
; op
= MPRI_ADD
; goto instr
;
114 case X0
| 0: st
= Z
; op
= MPRI_SUB
; goto instr
;
116 w
= (d
- i
)/MPW_BITS
+ 1;
117 b
= (bb
+ i
)%MPW_BITS
;
118 INSTR(op
| !!b
, w
, b
);
121 if (DA_LEN(&iv
) && (DA(&iv
)[DA_LEN(&iv
) - 1].op
& ~1u) == MPRI_SUB
) {
129 /* --- Wrap up --- */
135 r
->iv
= xmalloc(r
->in
* sizeof(mpreduce_instr
));
136 memcpy(r
->iv
, DA(&iv
), r
->in
* sizeof(mpreduce_instr
));
138 r
->iv
= xmalloc(r
->in
* 2 * sizeof(mpreduce_instr
));
139 for (i
= 0; i
< r
->in
; i
++) {
140 r
->iv
[i
] = DA(&iv
)[i
];
141 op
= r
->iv
[i
].op
& ~1u;
150 r
->iv
[i
+ r
->in
].op
= op
;
151 r
->iv
[i
+ r
->in
].argx
= w
;
152 r
->iv
[i
+ r
->in
].argy
= b
;
158 mpreduce_dump(r
, stdout
);
163 /* --- @mpreduce_destroy@ --- *
165 * Arguments: @mpreduce *r@ = structure to free
169 * Use: Reclaims the resources from a reduction context.
172 void mpreduce_destroy(mpreduce
*r
)
175 if (r
->iv
) xfree(r
->iv
);
178 /* --- @mpreduce_dump@ --- *
180 * Arguments: @mpreduce *r@ = structure to dump
181 * @FILE *fp@ = file to dump on
185 * Use: Dumps a reduction context.
188 void mpreduce_dump(mpreduce
*r
, FILE *fp
)
191 static const char *opname
[] = { "add", "addshift", "sub", "subshift" };
193 fprintf(fp
, "mod = "); mp_writefile(r
->p
, fp
, 16);
194 fprintf(fp
, "\n lim = %lu; s = %d\n", (unsigned long)r
->lim
, r
->s
);
195 for (i
= 0; i
< r
->in
; i
++) {
196 assert(r
->iv
[i
].op
< N(opname
));
197 fprintf(fp
, " %s %lu %lu\n",
199 (unsigned long)r
->iv
[i
].argx
,
200 (unsigned long)r
->iv
[i
].argy
);
203 fprintf(fp
, "tail end charlie\n");
204 for (i
= r
->in
; i
< 2 * r
->in
; i
++) {
205 assert(r
->iv
[i
].op
< N(opname
));
206 fprintf(fp
, " %s %lu %lu\n",
208 (unsigned long)r
->iv
[i
].argx
,
209 (unsigned long)r
->iv
[i
].argy
);
214 /* --- @mpreduce_do@ --- *
216 * Arguments: @mpreduce *r@ = reduction context
217 * @mp *d@ = destination
220 * Returns: Destination, @x@ reduced modulo the reduction poly.
223 static void run(const mpreduce_instr
*i
, const mpreduce_instr
*il
,
226 for (; i
< il
; i
++) {
229 mp_build(&vv
, v
- i
->argx
, v
+ 1);
230 printf(" 0x"); mp_writefile(&vv
, stdout
, 16);
231 printf(" %c (0x%lx << %u) == 0x",
232 (i
->op
& ~1u) == MPRI_ADD ?
'+' : '-',
237 case MPRI_ADD
: MPX_UADDN(v
- i
->argx
, v
+ 1, z
); break;
238 case MPRI_ADDLSL
: mpx_uaddnlsl(v
- i
->argx
, v
+ 1, z
, i
->argy
); break;
239 case MPRI_SUB
: MPX_USUBN(v
- i
->argx
, v
+ 1, z
); break;
240 case MPRI_SUBLSL
: mpx_usubnlsl(v
- i
->argx
, v
+ 1, z
, i
->argy
); break;
245 mp_build(&vv
, v
- i
->argx
, v
+ 1);
246 mp_writefile(&vv
, stdout
, 16);
252 mp
*mpreduce_do(mpreduce
*r
, mp
*d
, mp
*x
)
255 const mpreduce_instr
*il
;
259 mp
*_r
= 0, *_rr
= 0;
262 /* --- If source is negative, divide --- */
265 mp_div(0, &d
, x
, r
->p
);
269 /* --- Try to reuse the source's space --- */
273 MP_DEST(x
, MP_LEN(x
), x
->f
);
275 /* --- Do the reduction --- */
279 mp_div(0, &_r
, x
, r
->p
);
285 if (MP_LEN(x
) >= r
->lim
) {
292 run(r
->iv
, il
, vl
, z
);
295 mp_div(0, &_rr
, x
, r
->p
);
296 assert(MP_EQ(_r
, _rr
));
301 while (*vl
>> r
->s
) {
303 *vl
&= ((1 << r
->s
) - 1);
304 run(r
->iv
+ r
->in
, il
+ r
->in
, vl
, z
);
307 mp_div(0, &_rr
, x
, r
->p
);
308 assert(MP_EQ(_r
, _rr
));
314 /* --- Finishing touches --- */
317 if (MP_CMP(x
, >=, r
->p
))
318 x
= mp_sub(x
, x
, r
->p
);
323 assert(MP_EQ(_r
, x
));
330 /* --- @mpreduce_exp@ --- *
332 * Arguments: @mpreduce *mr@ = pointer to reduction context
333 * @mp *d@ = fake destination
337 * Returns: Result, %$a^e \bmod m$%.
340 mp
*mpreduce_exp(mpreduce
*mr
, mp
*d
, mp
*a
, mp
*e
)
343 mp
*spare
= (e
->f
& MP_BURN
) ? MP_NEWSEC
: MP_NEW
;
351 a
= mp_modinv(a
, a
, mr
->p
);
352 if (MP_LEN(e
) < EXP_THRESH
)
363 /*----- Test rig ----------------------------------------------------------*/
368 #define MP(x) mp_readstring(MP_NEW, #x, 0, 0)
370 static int vreduce(dstr
*v
)
372 mp
*d
= *(mp
**)v
[0].buf
;
373 mp
*n
= *(mp
**)v
[1].buf
;
374 mp
*r
= *(mp
**)v
[2].buf
;
379 mpreduce_create(&rr
, d
);
380 c
= mpreduce_do(&rr
, MP_NEW
, n
);
382 fprintf(stderr
, "\n*** reduction failed\n*** ");
383 mpreduce_dump(&rr
, stderr
);
384 fprintf(stderr
, "\n*** n = "); mp_writefile(n
, stderr
, 10);
385 fprintf(stderr
, "\n*** r = "); mp_writefile(r
, stderr
, 10);
386 fprintf(stderr
, "\n*** c = "); mp_writefile(c
, stderr
, 10);
387 fprintf(stderr
, "\n");
390 mpreduce_destroy(&rr
);
391 mp_drop(n
); mp_drop(d
); mp_drop(r
); mp_drop(c
);
392 assert(mparena_count(MPARENA_GLOBAL
) == 0);
396 static int vmodexp(dstr
*v
)
398 mp
*p
= *(mp
**)v
[0].buf
;
399 mp
*g
= *(mp
**)v
[1].buf
;
400 mp
*x
= *(mp
**)v
[2].buf
;
401 mp
*r
= *(mp
**)v
[3].buf
;
406 mpreduce_create(&rr
, p
);
407 c
= mpreduce_exp(&rr
, MP_NEW
, g
, x
);
409 fprintf(stderr
, "\n*** modexp failed\n*** ");
410 fprintf(stderr
, "\n*** p = "); mp_writefile(p
, stderr
, 10);
411 fprintf(stderr
, "\n*** g = "); mp_writefile(g
, stderr
, 10);
412 fprintf(stderr
, "\n*** x = "); mp_writefile(x
, stderr
, 10);
413 fprintf(stderr
, "\n*** c = "); mp_writefile(c
, stderr
, 10);
414 fprintf(stderr
, "\n*** r = "); mp_writefile(r
, stderr
, 10);
415 fprintf(stderr
, "\n");
418 mpreduce_destroy(&rr
);
419 mp_drop(p
); mp_drop(g
); mp_drop(r
); mp_drop(x
); mp_drop(c
);
420 assert(mparena_count(MPARENA_GLOBAL
) == 0);
424 static test_chunk defs
[] = {
425 { "reduce", vreduce
, { &type_mp
, &type_mp
, &type_mp
, 0 } },
426 { "modexp", vmodexp
, { &type_mp
, &type_mp
, &type_mp
, &type_mp
, 0 } },
430 int main(int argc
, char *argv
[])
432 test_run(argc
, argv
, defs
, SRCDIR
"/t/mpreduce");
438 /*----- That's all, folks -------------------------------------------------*/