3 * $Id: limlee.c,v 1.3 2000/07/29 09:58:32 mdw Exp $
5 * Generate Lim-Lee primes
7 * (c) 2000 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 --------------------------------------------------*
33 * Revision 1.3 2000/07/29 09:58:32 mdw
34 * (limlee): Bug fix. Old versions didn't set the filter step if @ql@ was
35 * an exact divisor of @pl@.
37 * Revision 1.2 2000/07/26 18:00:00 mdw
40 * Revision 1.1 2000/07/09 21:30:58 mdw
41 * Lim-Lee prime generation.
45 /*----- Header files ------------------------------------------------------*/
47 #include <mLib/alloc.h>
48 #include <mLib/dstr.h>
54 #include "primorial.h"
57 /*----- Main code ---------------------------------------------------------*/
61 * Arguments: @const char *name@ = pointer to name root
62 * @mp *d@ = pointer to destination integer
63 * @mp *newp@ = how to generate factor primes
64 * @unsigned ql@ = size of individual factors
65 * @unsigned pl@ = size of large prime
66 * @grand *r@ = a random number source
67 * @unsigned on@ = number of outer attempts to make
68 * @pgen_proc *oev@ = outer event handler function
69 * @void *oec@ = argument for the outer event handler
70 * @pgen_proc *iev@ = inner event handler function
71 * @void *iec@ = argument for the inner event handler
72 * @size_t *nf@, @mp ***f@ = output array for factors
74 * Returns: A Lim-Lee prime, or null if generation failed.
76 * Use: Generates Lim-Lee primes. A Lim-Lee prime %$p$% is one which
77 * satisfies %$p = 2 \prod_i q_i + 1$%, where all of the %$q_i$%
78 * are large enough to resist square-root discrete log
81 * If we succeed, and @f@ is non-null, we write the array of
82 * factors chosen to @f@ for the benefit of the caller.
85 static void comb_init(octet
*c
, unsigned n
, unsigned r
)
88 memset(c
+ (n
- r
), 1, r
);
91 static int comb_next(octet
*c
, unsigned n
, unsigned r
)
95 /* --- How the algorithm works --- *
97 * Set bits start at the end and work their way towards the start.
98 * Excepting bits already at the start, we scan for the lowest set bit, and
99 * move it one place nearer the start. A group of bits at the start are
100 * counted and reset just below the `moved' bit. If there is no moved bit
104 /* --- Count the group at the start --- */
113 /* --- Move the next bit down one --- *
115 * There must be one, because otherwise we'd have counted %$r$% bits
128 mp
*limlee(const char *name
, mp
*d
, mp
*newp
,
129 unsigned ql
, unsigned pl
, grand
*r
,
130 unsigned on
, pgen_proc
*oev
, void *oec
,
131 pgen_proc
*iev
, void *iec
,
142 unsigned long seq
= 0;
148 /* --- First of all, decide on a number of factors to make --- */
154 else if (qql
&& nn
> 1) {
159 /* --- Now decide on how many primes I'll actually generate --- *
161 * The formula %$m = \max(3 n + 5, 25)$% comes from GPG's prime generation
169 /* --- Now allocate the working memory --- */
172 v
= xmalloc(mm
* sizeof(mp
*));
175 /* --- Initialize everything and try to find a prime --- */
180 ev
.tests
= ntest
= rabin_iters(pl
);
183 if (oev
&& oev(PGEN_BEGIN
, &ev
, oec
) == PGEN_ABORT
)
188 dstr_putf(&dn
, "%s [+]", name
);
189 qq
= mprand(d
, qql
, r
, 1);
190 qq
= pgen(dn
.buf
, qq
, qq
, iev
, iec
,
191 0, pgen_filter
, &pf
, rabin_iters(qql
), pgen_test
, &rb
);
195 comb_init(c
, mm
, nn
);
196 for (i
= 0; i
< mm
; i
++)
199 /* --- The main combinations loop --- */
202 mpmul mmul
= MPMUL_INIT
;
204 /* --- Multiply a bunch of primes together --- */
207 mpmul_add(&mmul
, qq
);
209 for (i
= 0; i
< mm
; i
++) {
216 dstr_putf(&dn
, "%s [%lu] = ", name
, seq
++);
217 z
= mprand(newp
, ql
, ev
.r
, 1);
218 z
= pgen(dn
.buf
, z
, z
, iev
, iec
,
219 0, pgen_filter
, &pf
, rabin_iters(ql
), pgen_test
, &rb
);
222 mpmul_add(&mmul
, v
[i
]);
225 /* --- Now do some testing --- */
228 mp
*p
= mpmul_done(&mmul
);
232 /* --- Check for small factors --- */
235 p
= mp_add(p
, p
, MP_ONE
);
236 mp_gcd(&g
, 0, 0, p
, primorial
);
237 if (MP_CMP(g
, !=, MP_ONE
)) {
244 /* --- Send an event out --- */
247 if (oev
&& oev(PGEN_TRY
, &ev
, oec
) == PGEN_ABORT
) {
252 /* --- Do the Rabin testing --- */
254 rabin_create(&rb
, p
);
257 g
= mprand_range(g
, p
, ev
.r
, 1);
258 rc
= rabin_test(&rb
, g
);
259 if (rc
== PGEN_PASS
) {
264 if (oev
&&oev(rc
, &ev
, oec
) == PGEN_ABORT
)
266 } while (rc
== PGEN_PASS
);
274 if (rc
== PGEN_ABORT
)
281 } while (comb_next(c
, mm
, nn
));
283 /* --- That failed --- */
289 oev(PGEN_ABORT
, &ev
, &oec
);
294 for (i
= 0; i
< mm
; i
++)
298 /* --- We did it! --- */
306 *f
= vv
= xmalloc(nn
* sizeof(mp
*));
309 for (i
= 0; i
< mm
; i
++) {
327 /* --- We blew it --- */
330 for (i
= 0; i
< mm
; i
++)
340 /*----- That's all, folks -------------------------------------------------*/