4b583048acc2cfc9257d87afe0c91f0a237da1eb
3 * $Id: pfilt.c,v 1.3 2000/08/15 21:44:27 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 1.3 2000/08/15 21:44:27 mdw
34 * (pfilt_smallfactor): New function for doing trial division the hard
37 * (pfilt_create): Use @mpx_udivn@ for computing residues, for improved
40 * Pull the `small prime' test into a separate function, and do it
43 * Revision 1.2 2000/06/17 11:54:27 mdw
44 * Use new MP memory management functions.
46 * Revision 1.1 1999/12/22 15:49:39 mdw
47 * Renamed from `pgen'. Reworking for new prime-search system.
49 * Revision 1.3 1999/12/10 23:28:35 mdw
50 * Track suggested destination changes.
52 * Revision 1.2 1999/11/20 22:23:05 mdw
53 * Add multiply-and-add function for Diffie-Hellman safe prime generation.
55 * Revision 1.1 1999/11/19 13:17:57 mdw
56 * Prime number generator and tester.
60 /*----- Header files ------------------------------------------------------*/
67 #include "primorial.h"
69 /*----- Main code ---------------------------------------------------------*/
71 /* --- @smallenough@ --- *
73 * Arguments: @mp *m@ = integer to test
75 * Returns: One of the @PGEN@ result codes.
77 * Use: Assuming that @m@ has been tested by trial division on every
78 * prime in the small-primes array, this function will return
79 * @PGEN_DONE@ if the number is less than the square of the
80 * largest small prime.
83 static int smallenough(mp
*m
)
89 max
= mp_fromuint(MP_NEW
, MAXPRIME
);
90 max
= mp_sqr(max
, max
);
91 max
->a
->n
--; /* Permanent allocation */
93 if (MP_CMP(m
, <, max
))
98 /* --- @pfilt_smallfactor@ --- *
100 * Arguments: @mp *m@ = integer to test
102 * Returns: One of the @PGEN@ result codes.
104 * Use: Tests a number by dividing by a number of small primes. This
105 * is a useful first step if you're testing random primes; for
106 * sequential searches, @pfilt_create@ works better.
109 int pfilt_smallfactor(mp
*m
)
113 size_t sz
= MP_LEN(m
);
114 mpw
*v
= mpalloc(m
->a
, sz
);
116 /* --- Fill in the residues --- */
118 for (i
= 0; i
< NPRIME
; i
++) {
119 if (!mpx_udivn(v
, v
+ sz
, m
->v
, m
->vl
, primetab
[i
])) {
120 if (MP_LEN(m
) == 1 && m
->v
[0] == primetab
[i
])
127 /* --- Check for small primes --- */
138 /* --- @pfilt_create@ --- *
140 * Arguments: @pfilt *p@ = pointer to prime filtering context
141 * @mp *m@ = pointer to initial number to test
143 * Returns: One of the @PGEN@ result codes.
145 * Use: Tests an initial number for primality by computing its
146 * residue modulo various small prime numbers. This is fairly
147 * quick, but not particularly certain. If a @PGEN_TRY@
148 * result is returned, perform Rabin-Miller tests to confirm.
151 int pfilt_create(pfilt
*p
, mp
*m
)
155 size_t sz
= MP_LEN(m
);
156 mpw
*v
= mpalloc(m
->a
, sz
);
158 /* --- Take a copy of the number --- */
163 /* --- Fill in the residues --- */
165 for (i
= 0; i
< NPRIME
; i
++) {
166 p
->r
[i
] = mpx_udivn(v
, v
+ sz
, m
->v
, m
->vl
, primetab
[i
]);
167 if (!p
->r
[i
] && rc
== PGEN_TRY
) {
168 if (MP_LEN(m
) == 1 && m
->v
[0] == primetab
[i
])
175 /* --- Check for small primes --- */
186 /* --- @pfilt_destroy@ --- *
188 * Arguments: @pfilt *p@ = pointer to prime filtering context
192 * Use: Discards a context and all the resources it holds.
195 void pfilt_destroy(pfilt
*p
)
200 /* --- @pfilt_step@ --- *
202 * Arguments: @pfilt *p@ = pointer to prime filtering context
203 * @mpw step@ = how much to step the number
205 * Returns: One of the @PGEN@ result codes.
207 * Use: Steps a number by a small amount. Stepping is much faster
208 * than initializing with a new number. The test performed is
209 * the same simple one used by @primetab_create@, so @PGEN_TRY@
210 * results should be followed up by a Rabin-Miller test.
213 int pfilt_step(pfilt
*p
, mpw step
)
218 /* --- Add the step on to the number --- */
220 p
->m
= mp_split(p
->m
);
221 mp_ensure(p
->m
, MP_LEN(p
->m
) + 1);
222 mpx_uaddn(p
->m
->v
, p
->m
->vl
, step
);
225 /* --- Update the residue table --- */
227 for (i
= 0; i
< NPRIME
; i
++) {
228 p
->r
[i
] = (p
->r
[i
] + step
) % primetab
[i
];
229 if (!p
->r
[i
] && rc
== PGEN_TRY
) {
230 if (MP_LEN(p
->m
) == 1 && p
->m
->v
[0] == primetab
[i
])
237 /* --- Check for small primes --- */
240 rc
= smallenough(p
->m
);
247 /* --- @pfilt_muladd@ --- *
249 * Arguments: @pfilt *p@ = destination prime filtering context
250 * @const pfilt *q@ = source prime filtering context
251 * @mpw m@ = number to multiply by
252 * @mpw a@ = number to add
254 * Returns: One of the @PGEN@ result codes.
256 * Use: Multiplies the number in a prime filtering context by a
257 * small value and then adds a small value. The destination
258 * should either be uninitialized or the same as the source.
260 * Common things to do include multiplying by 2 and adding 0 to
261 * turn a prime into a jump for finding other primes with @q@ as
262 * a factor of @p - 1@, or multiplying by 2 and adding 1.
265 int pfilt_muladd(pfilt
*p
, const pfilt
*q
, mpw m
, mpw a
)
270 /* --- Multiply the big number --- */
273 mp
*d
= mp_new(MP_LEN(q
->m
) + 2, q
->m
->f
);
274 mpx_umuln(d
->v
, d
->vl
, q
->m
->v
, q
->m
->vl
, m
);
275 mpx_uaddn(d
->v
, d
->vl
, a
);
282 /* --- Gallivant through the residue table --- */
284 for (i
= 0; i
< NPRIME
; i
++) {
285 p
->r
[i
] = (q
->r
[i
] * m
+ a
) % primetab
[i
];
286 if (!p
->r
[i
] && rc
== PGEN_TRY
) {
287 if (MP_LEN(p
->m
) == 1 && p
->m
->v
[0] == primetab
[i
])
294 /* --- Check for small primes --- */
297 rc
= smallenough(p
->m
);
299 /* --- Finished --- */
304 /* --- @pfilt_jump@ --- *
306 * Arguments: @pfilt *p@ = pointer to prime filtering context
307 * @const pfilt *j@ = pointer to another filtering context
309 * Returns: One of the @PGEN@ result codes.
311 * Use: Steps a number by a large amount. Even so, jumping is much
312 * faster than initializing a new number. The test peformed is
313 * the same simple one used by @primetab_create@, so @PGEN_TRY@
314 * results should be followed up by a Rabin-Miller test.
316 * Note that the number stored in the @j@ context is probably
317 * better off being even than prime. The important thing is
318 * that all of the residues for the number have already been
322 int pfilt_jump(pfilt
*p
, const pfilt
*j
)
327 /* --- Add the step on --- */
329 p
->m
= mp_add(p
->m
, p
->m
, j
->m
);
331 /* --- Update the residue table --- */
333 for (i
= 0; i
< NPRIME
; i
++) {
334 p
->r
[i
] = p
->r
[i
] + j
->r
[i
];
335 if (p
->r
[i
] > primetab
[i
])
336 p
->r
[i
] -= primetab
[i
];
337 if (!p
->r
[i
] && rc
== PGEN_TRY
) {
338 if (MP_LEN(p
->m
) == 1 && p
->m
->v
[0] == primetab
[i
])
345 /* --- Check for small primes --- */
348 rc
= smallenough(p
->m
);
355 /*----- That's all, folks -------------------------------------------------*/