3 * Generate `strong' prime numbers
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 ------------------------------------------------------*/
30 #include <mLib/dstr.h>
40 /*----- Main code ---------------------------------------------------------*/
42 /* --- @strongprime_setup@ --- *
44 * Arguments: @const char *name@ = pointer to name root
45 * @mp *d@ = destination for search start point
46 * @pfilt *f@ = where to store filter jump context
47 * @unsigned nbits@ = number of bits wanted
48 * @grand *r@ = random number source
49 * @unsigned n@ = number of attempts to make
50 * @pgen_proc *event@ = event handler function
51 * @void *ectx@ = argument for the event handler
53 * Returns: A starting point for a `strong' prime search, or zero.
55 * Use: Sets up for a strong prime search, so that primes with
56 * particular properties can be found. It's probably important
57 * to note that the number left in the filter context @f@ is
58 * congruent to 2 (mod 4).
61 mp
*strongprime_setup(const char *name
, mp
*d
, pfilt
*f
, unsigned nbits
,
62 grand
*r
, unsigned n
, pgen_proc
*event
, void *ectx
)
66 unsigned slop
, nb
, u
, i
;
73 /* --- Figure out how large the smaller primes should be --- *
75 * We want them to be `as large as possible', subject to the constraint
76 * that we produce a number of the requested size at the end. This is
77 * tricky, because the final prime search is going to involve quite large
78 * jumps from its starting point; the size of the jumps are basically
79 * determined by our choice here, and if they're too big then we won't find
82 * Let's suppose we're trying to make an %$N$%-bit prime. The expected
83 * number of steps tends to increase linearly with size, i.e., we need to
84 * take about %2^k N$% steps for some %$k$%. If we're jumping by a
85 * %$J$%-bit quantity each time, from an %$N$%-bit starting point, then we
86 * will only be able to find a match if %$2^k N 2^{J-1} \le 2^{N-1}$%,
87 * i.e., if %$J \le N - (k + \log_2 N)$%.
89 * Experimentation shows that taking %$k + \log_2 N = 12$% works well for
90 * %$N = 1024$%, so %$k = 2$%.
93 for (i
= 1; i
&& nbits
>> i
; i
<<= 1); assert(i
);
94 for (slop
= 2, nb
= nbits
; nb
> 1; i
>>= 1) {
96 if (u
) { slop
+= i
; nb
= u
; }
98 if (nbits
/2 <= slop
) return (0);
100 /* --- Choose two primes %$s$% and %$t$% of half the required size --- */
105 rr
= mprand(rr
, nb
, r
, 1);
106 DRESET(&dn
); dstr_putf(&dn
, "%s [s]", name
);
107 if ((s
= pgen(dn
.buf
, MP_NEWSEC
, rr
, event
, ectx
, n
, pgen_filter
, &c
,
108 rabin_iters(nb
), pgen_test
, &rb
)) == 0)
111 rr
= mprand(rr
, nb
, r
, 1);
112 DRESET(&dn
); dstr_putf(&dn
, "%s [t]", name
);
113 if ((t
= pgen(dn
.buf
, MP_NEWSEC
, rr
, event
, ectx
, n
, pgen_filter
, &c
,
114 rabin_iters(nb
), pgen_test
, &rb
)) == 0)
117 /* --- Choose a suitable value for %$r = 2it + 1$% for some %$i$% --- */
119 rr
= mp_lsl(rr
, t
, 1);
120 pfilt_create(&c
.f
, rr
);
121 rr
= mp_lsl(rr
, rr
, slop
- 1);
122 rr
= mp_add(rr
, rr
, MP_ONE
);
123 DRESET(&dn
); dstr_putf(&dn
, "%s [r]", name
);
125 q
= pgen(dn
.buf
, MP_NEW
, rr
, event
, ectx
, n
, pgen_jump
, &j
,
126 rabin_iters(nb
+ slop
), pgen_test
, &rb
);
131 /* --- Select a suitable starting-point for finding %$p$% --- *
133 * This computes %$p_0 = 2 s (s^{r - 2} \bmod r) - 1$%.
139 mpmont_create(&mm
, q
);
140 rr
= mp_sub(rr
, q
, MP_TWO
);
141 rr
= mpmont_exp(&mm
, rr
, s
, rr
);
143 rr
= mp_mul(rr
, rr
, s
);
144 rr
= mp_lsl(rr
, rr
, 1);
145 rr
= mp_sub(rr
, rr
, MP_ONE
);
148 /* --- Now find %$p = p_0 + 2jrs$% for some %$j$% --- */
152 x
= mp_mul(MP_NEW
, q
, s
);
155 y
= mp_lsl(MP_NEW
, MP_ONE
, nbits
- 1);
156 rr
= mp_leastcongruent(rr
, y
, rr
, x
);
157 mp_drop(x
); mp_drop(y
);
160 /* --- Return the result --- */
168 /* --- Tidy up if something failed --- */
180 /* --- @strongprime@ --- *
182 * Arguments: @const char *name@ = pointer to name root
183 * @mp *d@ = destination integer
184 * @unsigned nbits@ = number of bits wanted
185 * @grand *r@ = random number source
186 * @unsigned n@ = number of attempts to make
187 * @pgen_proc *event@ = event handler function
188 * @void *ectx@ = argument for the event handler
190 * Returns: A `strong' prime, or zero.
192 * Use: Finds `strong' primes. A strong prime %$p$% is such that
194 * * %$p - 1$% has a large prime factor %$r$%,
195 * * %$p + 1$% has a large prime factor %$s$%, and
196 * * %$r - 1$% has a large prime factor %$t$%.
199 mp
*strongprime(const char *name
, mp
*d
, unsigned nbits
, grand
*r
,
200 unsigned n
, pgen_proc
*event
, void *ectx
)
208 p
= strongprime_setup(name
, d
, &f
, nbits
, r
, n
, event
, ectx
);
209 if (!p
) { mp_drop(d
); return (0); }
211 p
= pgen(name
, p
, p
, event
, ectx
, n
, pgen_jump
, &j
,
212 rabin_iters(nbits
), pgen_test
, &rb
);
213 if (mp_bits(p
) != nbits
) { mp_drop(p
); return (0); }
219 /*----- That's all, folks -------------------------------------------------*/