3 * $Id: pfilt.c,v 1.4 2000/10/08 12:14:57 mdw Exp $
5 * Finding and testing 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 /*----- Revision history --------------------------------------------------*
33 * Revision 1.4 2000/10/08 12:14:57 mdw
34 * Remove vestiges of @primorial@.
36 * Revision 1.3 2000/08/15 21:44:27 mdw
37 * (pfilt_smallfactor): New function for doing trial division the hard
40 * (pfilt_create): Use @mpx_udivn@ for computing residues, for improved
43 * Pull the `small prime' test into a separate function, and do it
46 * Revision 1.2 2000/06/17 11:54:27 mdw
47 * Use new MP memory management functions.
49 * Revision 1.1 1999/12/22 15:49:39 mdw
50 * Renamed from `pgen'. Reworking for new prime-search system.
52 * Revision 1.3 1999/12/10 23:28:35 mdw
53 * Track suggested destination changes.
55 * Revision 1.2 1999/11/20 22:23:05 mdw
56 * Add multiply-and-add function for Diffie-Hellman safe prime generation.
58 * Revision 1.1 1999/11/19 13:17:57 mdw
59 * Prime number generator and tester.
63 /*----- Header files ------------------------------------------------------*/
71 /*----- Main code ---------------------------------------------------------*/
73 /* --- @smallenough@ --- *
75 * Arguments: @mp *m@ = integer to test
77 * Returns: One of the @PGEN@ result codes.
79 * Use: Assuming that @m@ has been tested by trial division on every
80 * prime in the small-primes array, this function will return
81 * @PGEN_DONE@ if the number is less than the square of the
82 * largest small prime.
85 static int smallenough(mp
*m
)
91 max
= mp_fromuint(MP_NEW
, MAXPRIME
);
92 max
= mp_sqr(max
, max
);
93 max
->a
->n
--; /* Permanent allocation */
95 if (MP_CMP(m
, <, max
))
100 /* --- @pfilt_smallfactor@ --- *
102 * Arguments: @mp *m@ = integer to test
104 * Returns: One of the @PGEN@ result codes.
106 * Use: Tests a number by dividing by a number of small primes. This
107 * is a useful first step if you're testing random primes; for
108 * sequential searches, @pfilt_create@ works better.
111 int pfilt_smallfactor(mp
*m
)
115 size_t sz
= MP_LEN(m
);
116 mpw
*v
= mpalloc(m
->a
, sz
);
118 /* --- Fill in the residues --- */
120 for (i
= 0; i
< NPRIME
; i
++) {
121 if (!mpx_udivn(v
, v
+ sz
, m
->v
, m
->vl
, primetab
[i
])) {
122 if (MP_LEN(m
) == 1 && m
->v
[0] == primetab
[i
])
129 /* --- Check for small primes --- */
140 /* --- @pfilt_create@ --- *
142 * Arguments: @pfilt *p@ = pointer to prime filtering context
143 * @mp *m@ = pointer to initial number to test
145 * Returns: One of the @PGEN@ result codes.
147 * Use: Tests an initial number for primality by computing its
148 * residue modulo various small prime numbers. This is fairly
149 * quick, but not particularly certain. If a @PGEN_TRY@
150 * result is returned, perform Rabin-Miller tests to confirm.
153 int pfilt_create(pfilt
*p
, mp
*m
)
157 size_t sz
= MP_LEN(m
);
158 mpw
*v
= mpalloc(m
->a
, sz
);
160 /* --- Take a copy of the number --- */
165 /* --- Fill in the residues --- */
167 for (i
= 0; i
< NPRIME
; i
++) {
168 p
->r
[i
] = mpx_udivn(v
, v
+ sz
, m
->v
, m
->vl
, primetab
[i
]);
169 if (!p
->r
[i
] && rc
== PGEN_TRY
) {
170 if (MP_LEN(m
) == 1 && m
->v
[0] == primetab
[i
])
177 /* --- Check for small primes --- */
188 /* --- @pfilt_destroy@ --- *
190 * Arguments: @pfilt *p@ = pointer to prime filtering context
194 * Use: Discards a context and all the resources it holds.
197 void pfilt_destroy(pfilt
*p
)
202 /* --- @pfilt_step@ --- *
204 * Arguments: @pfilt *p@ = pointer to prime filtering context
205 * @mpw step@ = how much to step the number
207 * Returns: One of the @PGEN@ result codes.
209 * Use: Steps a number by a small amount. Stepping is much faster
210 * than initializing with a new number. The test performed is
211 * the same simple one used by @primetab_create@, so @PGEN_TRY@
212 * results should be followed up by a Rabin-Miller test.
215 int pfilt_step(pfilt
*p
, mpw step
)
220 /* --- Add the step on to the number --- */
222 p
->m
= mp_split(p
->m
);
223 mp_ensure(p
->m
, MP_LEN(p
->m
) + 1);
224 mpx_uaddn(p
->m
->v
, p
->m
->vl
, step
);
227 /* --- Update the residue table --- */
229 for (i
= 0; i
< NPRIME
; i
++) {
230 p
->r
[i
] = (p
->r
[i
] + step
) % primetab
[i
];
231 if (!p
->r
[i
] && rc
== PGEN_TRY
) {
232 if (MP_LEN(p
->m
) == 1 && p
->m
->v
[0] == primetab
[i
])
239 /* --- Check for small primes --- */
242 rc
= smallenough(p
->m
);
249 /* --- @pfilt_muladd@ --- *
251 * Arguments: @pfilt *p@ = destination prime filtering context
252 * @const pfilt *q@ = source prime filtering context
253 * @mpw m@ = number to multiply by
254 * @mpw a@ = number to add
256 * Returns: One of the @PGEN@ result codes.
258 * Use: Multiplies the number in a prime filtering context by a
259 * small value and then adds a small value. The destination
260 * should either be uninitialized or the same as the source.
262 * Common things to do include multiplying by 2 and adding 0 to
263 * turn a prime into a jump for finding other primes with @q@ as
264 * a factor of @p - 1@, or multiplying by 2 and adding 1.
267 int pfilt_muladd(pfilt
*p
, const pfilt
*q
, mpw m
, mpw a
)
272 /* --- Multiply the big number --- */
275 mp
*d
= mp_new(MP_LEN(q
->m
) + 2, q
->m
->f
);
276 mpx_umuln(d
->v
, d
->vl
, q
->m
->v
, q
->m
->vl
, m
);
277 mpx_uaddn(d
->v
, d
->vl
, a
);
284 /* --- Gallivant through the residue table --- */
286 for (i
= 0; i
< NPRIME
; i
++) {
287 p
->r
[i
] = (q
->r
[i
] * m
+ a
) % primetab
[i
];
288 if (!p
->r
[i
] && rc
== PGEN_TRY
) {
289 if (MP_LEN(p
->m
) == 1 && p
->m
->v
[0] == primetab
[i
])
296 /* --- Check for small primes --- */
299 rc
= smallenough(p
->m
);
301 /* --- Finished --- */
306 /* --- @pfilt_jump@ --- *
308 * Arguments: @pfilt *p@ = pointer to prime filtering context
309 * @const pfilt *j@ = pointer to another filtering context
311 * Returns: One of the @PGEN@ result codes.
313 * Use: Steps a number by a large amount. Even so, jumping is much
314 * faster than initializing a new number. The test peformed is
315 * the same simple one used by @primetab_create@, so @PGEN_TRY@
316 * results should be followed up by a Rabin-Miller test.
318 * Note that the number stored in the @j@ context is probably
319 * better off being even than prime. The important thing is
320 * that all of the residues for the number have already been
324 int pfilt_jump(pfilt
*p
, const pfilt
*j
)
329 /* --- Add the step on --- */
331 p
->m
= mp_add(p
->m
, p
->m
, j
->m
);
333 /* --- Update the residue table --- */
335 for (i
= 0; i
< NPRIME
; i
++) {
336 p
->r
[i
] = p
->r
[i
] + j
->r
[i
];
337 if (p
->r
[i
] > primetab
[i
])
338 p
->r
[i
] -= primetab
[i
];
339 if (!p
->r
[i
] && rc
== PGEN_TRY
) {
340 if (MP_LEN(p
->m
) == 1 && p
->m
->v
[0] == primetab
[i
])
347 /* --- Check for small primes --- */
350 rc
= smallenough(p
->m
);
357 /*----- That's all, folks -------------------------------------------------*/