3 * $Id: rabin.c,v 1.8 2004/04/02 01:03:49 mdw Exp $
5 * Miller-Rabin primality test
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 /*----- Revision history --------------------------------------------------*
33 * Revision 1.8 2004/04/02 01:03:49 mdw
34 * Miscellaneous constification.
36 * Revision 1.7 2002/01/13 13:42:53 mdw
37 * More efficient Rabin-Miller test: with random witnesses, skip redundant
38 * Montgomerization. (Being bijective, it can't affect the distribution.)
40 * Revision 1.6 2001/06/16 12:56:38 mdw
41 * Fixes for interface change to @mpmont_expr@ and @mpmont_mexpr@.
43 * Revision 1.5 2000/10/08 12:11:22 mdw
44 * Use @MP_EQ@ instead of @MP_CMP@.
46 * Revision 1.4 2000/06/22 19:03:02 mdw
47 * Use the new @mp_odd@ function.
49 * Revision 1.3 1999/12/22 15:50:29 mdw
50 * Reworking for new prime-search system. Add function for working out how
51 * many iterations to use for a particular number.
53 * Revision 1.2 1999/12/10 23:29:48 mdw
54 * Change header file guard names.
56 * Revision 1.1 1999/11/19 13:17:57 mdw
57 * Prime number generator and tester.
61 /*----- Header files ------------------------------------------------------*/
64 #include "mpbarrett.h"
69 /*----- Main code ---------------------------------------------------------*/
71 /* --- @rabin_create@ --- *
73 * Arguments: @rabin *r@ = pointer to Rabin-Miller context
74 * @mp *m@ = pointer to number to test
78 * Use: Precomputes some useful values for performing the
79 * Miller-Rabin probabilistic primality test.
82 void rabin_create(rabin
*r
, mp
*m
)
84 mp
*m1
= mp_sub(MP_NEW
, m
, MP_ONE
);
85 mpmont_create(&r
->mm
, m
);
86 r
->r
= mp_odd(MP_NEW
, m1
, &r
->s
);
87 r
->m1
= mp_sub(MP_NEW
, m
, r
->mm
.r
);
91 /* --- @rabin_destroy@ --- *
93 * Arguments: @rabin *r@ = pointer to Rabin-Miller context
97 * Use: Disposes of a Rabin-Miller context when it's no longer
101 void rabin_destroy(rabin
*r
)
105 mpmont_destroy(&r
->mm
);
108 /* --- @rabin_test@, @rabin_rtest@ --- *
110 * Arguments: @rabin *r@ = pointer to Rabin-Miller context
111 * @mp *g@ = base to test the number against
113 * Returns: Either @PGEN_FAIL@ if the test failed, or @PGEN_PASS@
116 * Use: Performs a single iteration of the Rabin-Miller primality
117 * test. The @rtest@ variant assumes that %$g$% is either
118 * already in Montgomery representation, or you don't care.
121 int rabin_rtest(rabin
*r
, mp
*g
)
124 mp
*dd
, *spare
= MP_NEW
;
128 /* --- Calculate %$y R = g^r R \bmod m$% --- *
130 * If %$y = 1$% or %$y = m - 1$% then %$m$% is prime. If course, note that
131 * @y@ here has an extra factor of %$R$%.
134 y
= mpmont_expr(&r
->mm
, MP_NEW
, g
, r
->r
);
135 if (MP_EQ(y
, r
->mm
.r
) || MP_EQ(y
, r
->m1
)) {
140 /* --- Now for the main loop --- *
142 * If %$y^{2^j} \ne m - 1$% for any %$0 \le j < s$% then %$m$% is
143 * composite. Of course, %$j = 0$% has already been tested.
146 for (j
= 1; j
< r
->s
; j
++) {
147 dd
= mp_sqr(spare
, y
);
148 dd
= mpmont_reduce(&r
->mm
, dd
, dd
);
150 if (MP_EQ(y
, r
->mm
.r
))
152 if (MP_EQ(y
, r
->m1
)) {
167 int rabin_test(rabin
*r
, mp
*g
)
170 g
= mpmont_mul(&r
->mm
, MP_NEW
, g
, r
->mm
.r2
);
171 rc
= rabin_rtest(r
, g
);
176 /* --- @rabin_iters@ --- *
178 * Arguments: @unsigned len@ = number of bits in value
180 * Returns: Number of iterations recommended.
182 * Use: Returns the recommended number of iterations to ensure that a
183 * number with @len@ bits is really prime.
186 int rabin_iters(unsigned len
)
188 static const struct {
208 /* --- Binary search through the table --- */
211 q
= tab
+ (sizeof(tab
)/sizeof(tab
[0]));
216 if (len
>= p
[i
].b
&& len
< p
[i
+ 1].b
)
226 /*----- That's all, folks -------------------------------------------------*/