3 * $Id: pfilt.c,v 1.5 2004/04/01 12:50:09 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 1.5 2004/04/01 12:50:09 mdw
34 * Add cyclic group abstraction, with test code. Separate off exponentation
35 * functions for better static linking. Fix a buttload of bugs on the way.
36 * Generally ensure that negative exponents do inversion correctly. Add
37 * table of standard prime-field subgroups. (Binary field subgroups are
38 * currently unimplemented but easy to add if anyone ever finds a good one.)
40 * Revision 1.4 2000/10/08 12:14:57 mdw
41 * Remove vestiges of @primorial@.
43 * Revision 1.3 2000/08/15 21:44:27 mdw
44 * (pfilt_smallfactor): New function for doing trial division the hard
47 * (pfilt_create): Use @mpx_udivn@ for computing residues, for improved
50 * Pull the `small prime' test into a separate function, and do it
53 * Revision 1.2 2000/06/17 11:54:27 mdw
54 * Use new MP memory management functions.
56 * Revision 1.1 1999/12/22 15:49:39 mdw
57 * Renamed from `pgen'. Reworking for new prime-search system.
59 * Revision 1.3 1999/12/10 23:28:35 mdw
60 * Track suggested destination changes.
62 * Revision 1.2 1999/11/20 22:23:05 mdw
63 * Add multiply-and-add function for Diffie-Hellman safe prime generation.
65 * Revision 1.1 1999/11/19 13:17:57 mdw
66 * Prime number generator and tester.
70 /*----- Header files ------------------------------------------------------*/
78 /*----- Main code ---------------------------------------------------------*/
80 /* --- @smallenough@ --- *
82 * Arguments: @mp *m@ = integer to test
84 * Returns: One of the @PGEN@ result codes.
86 * Use: Assuming that @m@ has been tested by trial division on every
87 * prime in the small-primes array, this function will return
88 * @PGEN_DONE@ if the number is less than the square of the
89 * largest small prime.
92 static int smallenough(mp
*m
)
98 max
= mp_fromuint(MP_NEW
, MAXPRIME
);
99 max
= mp_sqr(max
, max
);
100 max
->a
->n
--; /* Permanent allocation */
102 if (MP_CMP(m
, <, max
))
107 /* --- @pfilt_smallfactor@ --- *
109 * Arguments: @mp *m@ = integer to test
111 * Returns: One of the @PGEN@ result codes.
113 * Use: Tests a number by dividing by a number of small primes. This
114 * is a useful first step if you're testing random primes; for
115 * sequential searches, @pfilt_create@ works better.
118 int pfilt_smallfactor(mp
*m
)
122 size_t sz
= MP_LEN(m
);
123 mparena
*a
= m
->a ? m
->a
: MPARENA_GLOBAL
;
124 mpw
*v
= mpalloc(a
, sz
);
126 /* --- Fill in the residues --- */
128 for (i
= 0; i
< NPRIME
; i
++) {
129 if (!mpx_udivn(v
, v
+ sz
, m
->v
, m
->vl
, primetab
[i
])) {
130 if (MP_LEN(m
) == 1 && m
->v
[0] == primetab
[i
])
137 /* --- Check for small primes --- */
148 /* --- @pfilt_create@ --- *
150 * Arguments: @pfilt *p@ = pointer to prime filtering context
151 * @mp *m@ = pointer to initial number to test
153 * Returns: One of the @PGEN@ result codes.
155 * Use: Tests an initial number for primality by computing its
156 * residue modulo various small prime numbers. This is fairly
157 * quick, but not particularly certain. If a @PGEN_TRY@
158 * result is returned, perform Rabin-Miller tests to confirm.
161 int pfilt_create(pfilt
*p
, mp
*m
)
165 size_t sz
= MP_LEN(m
);
166 mparena
*a
= m
->a ? m
->a
: MPARENA_GLOBAL
;
167 mpw
*v
= mpalloc(a
, sz
);
169 /* --- Take a copy of the number --- */
174 /* --- Fill in the residues --- */
176 for (i
= 0; i
< NPRIME
; i
++) {
177 p
->r
[i
] = mpx_udivn(v
, v
+ sz
, m
->v
, m
->vl
, primetab
[i
]);
178 if (!p
->r
[i
] && rc
== PGEN_TRY
) {
179 if (MP_LEN(m
) == 1 && m
->v
[0] == primetab
[i
])
186 /* --- Check for small primes --- */
197 /* --- @pfilt_destroy@ --- *
199 * Arguments: @pfilt *p@ = pointer to prime filtering context
203 * Use: Discards a context and all the resources it holds.
206 void pfilt_destroy(pfilt
*p
)
211 /* --- @pfilt_step@ --- *
213 * Arguments: @pfilt *p@ = pointer to prime filtering context
214 * @mpw step@ = how much to step the number
216 * Returns: One of the @PGEN@ result codes.
218 * Use: Steps a number by a small amount. Stepping is much faster
219 * than initializing with a new number. The test performed is
220 * the same simple one used by @primetab_create@, so @PGEN_TRY@
221 * results should be followed up by a Rabin-Miller test.
224 int pfilt_step(pfilt
*p
, mpw step
)
229 /* --- Add the step on to the number --- */
231 p
->m
= mp_split(p
->m
);
232 mp_ensure(p
->m
, MP_LEN(p
->m
) + 1);
233 mpx_uaddn(p
->m
->v
, p
->m
->vl
, step
);
236 /* --- Update the residue table --- */
238 for (i
= 0; i
< NPRIME
; i
++) {
239 p
->r
[i
] = (p
->r
[i
] + step
) % primetab
[i
];
240 if (!p
->r
[i
] && rc
== PGEN_TRY
) {
241 if (MP_LEN(p
->m
) == 1 && p
->m
->v
[0] == primetab
[i
])
248 /* --- Check for small primes --- */
251 rc
= smallenough(p
->m
);
258 /* --- @pfilt_muladd@ --- *
260 * Arguments: @pfilt *p@ = destination prime filtering context
261 * @const pfilt *q@ = source prime filtering context
262 * @mpw m@ = number to multiply by
263 * @mpw a@ = number to add
265 * Returns: One of the @PGEN@ result codes.
267 * Use: Multiplies the number in a prime filtering context by a
268 * small value and then adds a small value. The destination
269 * should either be uninitialized or the same as the source.
271 * Common things to do include multiplying by 2 and adding 0 to
272 * turn a prime into a jump for finding other primes with @q@ as
273 * a factor of @p - 1@, or multiplying by 2 and adding 1.
276 int pfilt_muladd(pfilt
*p
, const pfilt
*q
, mpw m
, mpw a
)
281 /* --- Multiply the big number --- */
284 mp
*d
= mp_new(MP_LEN(q
->m
) + 2, q
->m
->f
);
285 mpx_umuln(d
->v
, d
->vl
, q
->m
->v
, q
->m
->vl
, m
);
286 mpx_uaddn(d
->v
, d
->vl
, a
);
293 /* --- Gallivant through the residue table --- */
295 for (i
= 0; i
< NPRIME
; i
++) {
296 p
->r
[i
] = (q
->r
[i
] * m
+ a
) % primetab
[i
];
297 if (!p
->r
[i
] && rc
== PGEN_TRY
) {
298 if (MP_LEN(p
->m
) == 1 && p
->m
->v
[0] == primetab
[i
])
305 /* --- Check for small primes --- */
308 rc
= smallenough(p
->m
);
310 /* --- Finished --- */
315 /* --- @pfilt_jump@ --- *
317 * Arguments: @pfilt *p@ = pointer to prime filtering context
318 * @const pfilt *j@ = pointer to another filtering context
320 * Returns: One of the @PGEN@ result codes.
322 * Use: Steps a number by a large amount. Even so, jumping is much
323 * faster than initializing a new number. The test peformed is
324 * the same simple one used by @primetab_create@, so @PGEN_TRY@
325 * results should be followed up by a Rabin-Miller test.
327 * Note that the number stored in the @j@ context is probably
328 * better off being even than prime. The important thing is
329 * that all of the residues for the number have already been
333 int pfilt_jump(pfilt
*p
, const pfilt
*j
)
338 /* --- Add the step on --- */
340 p
->m
= mp_add(p
->m
, p
->m
, j
->m
);
342 /* --- Update the residue table --- */
344 for (i
= 0; i
< NPRIME
; i
++) {
345 p
->r
[i
] = p
->r
[i
] + j
->r
[i
];
346 if (p
->r
[i
] > primetab
[i
])
347 p
->r
[i
] -= primetab
[i
];
348 if (!p
->r
[i
] && rc
== PGEN_TRY
) {
349 if (MP_LEN(p
->m
) == 1 && p
->m
->v
[0] == primetab
[i
])
356 /* --- Check for small primes --- */
359 rc
= smallenough(p
->m
);
366 /*----- That's all, folks -------------------------------------------------*/