3 * $Id: rabin.c,v 1.9 2004/04/08 01:36:15 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 /*----- Header files ------------------------------------------------------*/
33 #include "mpbarrett.h"
38 /*----- Main code ---------------------------------------------------------*/
40 /* --- @rabin_create@ --- *
42 * Arguments: @rabin *r@ = pointer to Rabin-Miller context
43 * @mp *m@ = pointer to number to test
47 * Use: Precomputes some useful values for performing the
48 * Miller-Rabin probabilistic primality test.
51 void rabin_create(rabin
*r
, mp
*m
)
53 mp
*m1
= mp_sub(MP_NEW
, m
, MP_ONE
);
54 mpmont_create(&r
->mm
, m
);
55 r
->r
= mp_odd(MP_NEW
, m1
, &r
->s
);
56 r
->m1
= mp_sub(MP_NEW
, m
, r
->mm
.r
);
60 /* --- @rabin_destroy@ --- *
62 * Arguments: @rabin *r@ = pointer to Rabin-Miller context
66 * Use: Disposes of a Rabin-Miller context when it's no longer
70 void rabin_destroy(rabin
*r
)
74 mpmont_destroy(&r
->mm
);
77 /* --- @rabin_test@, @rabin_rtest@ --- *
79 * Arguments: @rabin *r@ = pointer to Rabin-Miller context
80 * @mp *g@ = base to test the number against
82 * Returns: Either @PGEN_FAIL@ if the test failed, or @PGEN_PASS@
85 * Use: Performs a single iteration of the Rabin-Miller primality
86 * test. The @rtest@ variant assumes that %$g$% is either
87 * already in Montgomery representation, or you don't care.
90 int rabin_rtest(rabin
*r
, mp
*g
)
93 mp
*dd
, *spare
= MP_NEW
;
97 /* --- Calculate %$y R = g^r R \bmod m$% --- *
99 * If %$y = 1$% or %$y = m - 1$% then %$m$% is prime. If course, note that
100 * @y@ here has an extra factor of %$R$%.
103 y
= mpmont_expr(&r
->mm
, MP_NEW
, g
, r
->r
);
104 if (MP_EQ(y
, r
->mm
.r
) || MP_EQ(y
, r
->m1
)) {
109 /* --- Now for the main loop --- *
111 * If %$y^{2^j} \ne m - 1$% for any %$0 \le j < s$% then %$m$% is
112 * composite. Of course, %$j = 0$% has already been tested.
115 for (j
= 1; j
< r
->s
; j
++) {
116 dd
= mp_sqr(spare
, y
);
117 dd
= mpmont_reduce(&r
->mm
, dd
, dd
);
119 if (MP_EQ(y
, r
->mm
.r
))
121 if (MP_EQ(y
, r
->m1
)) {
136 int rabin_test(rabin
*r
, mp
*g
)
139 g
= mpmont_mul(&r
->mm
, MP_NEW
, g
, r
->mm
.r2
);
140 rc
= rabin_rtest(r
, g
);
145 /* --- @rabin_iters@ --- *
147 * Arguments: @unsigned len@ = number of bits in value
149 * Returns: Number of iterations recommended.
151 * Use: Returns the recommended number of iterations to ensure that a
152 * number with @len@ bits is really prime.
155 int rabin_iters(unsigned len
)
157 static const struct {
177 /* --- Binary search through the table --- */
180 q
= tab
+ (sizeof(tab
)/sizeof(tab
[0]));
185 if (len
>= p
[i
].b
&& len
< p
[i
+ 1].b
)
195 /*----- That's all, folks -------------------------------------------------*/