3 * $Id: strongprime.c,v 1.5 2004/04/08 01:36:15 mdw Exp $
5 * Generate `strong' prime numbers
7 * (c) 1999 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 /*----- Header files ------------------------------------------------------*/
32 #include <mLib/dstr.h>
43 /*----- Main code ---------------------------------------------------------*/
45 /* --- @strongprime_setup@ --- *
47 * Arguments: @const char *name@ = pointer to name root
48 * @mp *d@ = destination for search start point
49 * @pfilt *f@ = where to store filter jump context
50 * @unsigned nbits@ = number of bits wanted
51 * @grand *r@ = random number source
52 * @unsigned n@ = number of attempts to make
53 * @pgen_proc *event@ = event handler function
54 * @void *ectx@ = argument for the event handler
56 * Returns: A starting point for a `strong' prime search, or zero.
58 * Use: Sets up for a strong prime search, so that primes with
59 * particular properties can be found. It's probably important
60 * to note that the number left in the filter context @f@ is
61 * congruent to 2 (mod 4).
64 mp
*strongprime_setup(const char *name
, mp
*d
, pfilt
*f
, unsigned nbits
,
65 grand
*r
, unsigned n
, pgen_proc
*event
, void *ectx
)
75 /* --- The bitslop parameter --- *
77 * There's quite a lot of prime searching to be done. The constant
78 * @BITSLOP@ is a (low) approximation to the base-2 log of the expected
79 * number of steps to find a prime number. Experimentation shows that
80 * numbers around 10 seem to be good.
85 /* --- Choose two primes %$s$% and %$t$% of half the required size --- */
87 assert(((void)"nbits too small in strongprime_setup", nbits
/2 > BITSLOP
));
88 nbits
= nbits
/2 - BITSLOP
;
91 rr
= mprand(rr
, nbits
, r
, 1);
92 DRESET(&dn
); dstr_putf(&dn
, "%s [s]", name
);
93 if ((s
= pgen(dn
.buf
, MP_NEWSEC
, rr
, event
, ectx
, n
, pgen_filter
, &c
,
94 rabin_iters(nbits
), pgen_test
, &rb
)) == 0)
97 rr
= mprand(rr
, nbits
, r
, 1);
98 DRESET(&dn
); dstr_putf(&dn
, "%s [t]", name
);
99 if ((t
= pgen(dn
.buf
, MP_NEWSEC
, rr
, event
, ectx
, n
, pgen_filter
, &c
,
100 rabin_iters(nbits
), pgen_test
, &rb
)) == 0)
103 /* --- Choose a suitable value for %$r = 2it + 1$% for some %$i$% --- */
105 rr
= mp_lsl(rr
, t
, 1);
106 pfilt_create(&c
.f
, rr
);
107 rr
= mp_lsl(rr
, rr
, BITSLOP
- 1);
108 rr
= mp_add(rr
, rr
, MP_ONE
);
109 DRESET(&dn
); dstr_putf(&dn
, "%s [r]", name
);
112 q
= pgen(dn
.buf
, MP_NEW
, rr
, event
, ectx
, n
, pgen_jump
, &j
,
113 rabin_iters(nbits
), pgen_test
, &rb
);
118 /* --- Select a suitable starting-point for finding %$p$% --- *
120 * This computes %$p_0 = 2(s^{r - 2} \bmod r)s - 1$%.
126 mpmont_create(&mm
, q
);
127 rr
= mp_sub(rr
, q
, MP_TWO
);
128 rr
= mpmont_exp(&mm
, rr
, s
, rr
);
130 rr
= mp_mul(rr
, rr
, s
);
131 rr
= mp_lsl(rr
, rr
, 1);
132 rr
= mp_sub(rr
, rr
, MP_ONE
);
135 /* --- Now find %$p = p_0 + 2jrs$% for some %$j$% --- */
139 x
= mp_mul(MP_NEW
, q
, s
);
142 x
= mp_lsl(x
, x
, BITSLOP
- 1);
143 rr
= mp_add(rr
, rr
, x
);
147 /* --- Return the result --- */
155 /* --- Tidy up if something failed --- */
169 /* --- @strongprime@ --- *
171 * Arguments: @const char *name@ = pointer to name root
172 * @mp *d@ = destination integer
173 * @unsigned nbits@ = number of bits wanted
174 * @grand *r@ = random number source
175 * @unsigned n@ = number of attempts to make
176 * @pgen_proc *event@ = event handler function
177 * @void *ectx@ = argument for the event handler
179 * Returns: A `strong' prime, or zero.
181 * Use: Finds `strong' primes. A strong prime %$p$% is such that
183 * * %$p - 1$% has a large prime factor %$r$%,
184 * * %$p + 1$% has a large prime factor %$s$%, and
185 * * %$r - 1$% has a large prime factor %$t$%.
187 * The numbers produced may be slightly larger than requested,
191 mp
*strongprime(const char *name
, mp
*d
, unsigned nbits
, grand
*r
,
192 unsigned n
, pgen_proc
*event
, void *ectx
)
198 d
= strongprime_setup(name
, d
, &f
, nbits
, r
, n
, event
, ectx
);
200 d
= pgen(name
, d
, d
, event
, ectx
, n
, pgen_jump
, &j
,
201 rabin_iters(nbits
), pgen_test
, &rb
);
206 /*----- That's all, folks -------------------------------------------------*/