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Release calc version 2.11.0t10.5.1
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Landon Curt Noll
72
zrandom.c
72
zrandom.c
@@ -1,31 +1,37 @@
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/*
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* zrandom - Blum-Blum-Shub pseudo-random generator
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* Copyright (c) 1997 by Landon Curt Noll. All Rights Reserved.
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*
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* Copyright (C) 1999 Landon Curt Noll
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* Permission to use, copy, modify, and distribute this software and
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* its documentation for any purpose and without fee is hereby granted,
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* provided that the above copyright, this permission notice and text
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* this comment, and the disclaimer below appear in all of the following:
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*
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* Calc is open software; you can redistribute it and/or modify it under
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* the terms of the version 2.1 of the GNU Lesser General Public License
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* as published by the Free Software Foundation.
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* supporting documentation
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* source copies
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* source works derived from this source
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* binaries derived from this source or from derived source
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*
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* Calc is distributed in the hope that it will be useful, but WITHOUT
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* ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
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* or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General
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* Public License for more details.
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* LANDON CURT NOLL DISCLAIMS ALL WARRANTIES WITH REGARD TO THIS SOFTWARE,
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* INCLUDING ALL IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS. IN NO
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* EVENT SHALL LANDON CURT NOLL BE LIABLE FOR ANY SPECIAL, INDIRECT OR
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* CONSEQUENTIAL DAMAGES OR ANY DAMAGES WHATSOEVER RESULTING FROM LOSS OF
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* USE, DATA OR PROFITS, WHETHER IN AN ACTION OF CONTRACT, NEGLIGENCE OR
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* OTHER TORTIOUS ACTION, ARISING OUT OF OR IN CONNECTION WITH THE USE OR
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* PERFORMANCE OF THIS SOFTWARE.
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*
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* A copy of version 2.1 of the GNU Lesser General Public License is
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* distributed with calc under the filename COPYING-LGPL. You should have
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* received a copy with calc; if not, write to Free Software Foundation, Inc.
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* 59 Temple Place, Suite 330, Boston, MA 02111-1307, USA.
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* Prior to calc 2.9.3t9, these routines existed as a calc library called
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* cryrand.cal. They have been rewritten in C for performance as well
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* as to make them available directly from libcalc.a.
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*
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* @(#) $Revision: 29.1 $
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* @(#) $Id: zrandom.c,v 29.1 1999/12/14 09:16:18 chongo Exp $
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* @(#) $Source: /usr/local/src/cmd/calc/RCS/zrandom.c,v $
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* Comments, suggestions, bug fixes and questions about these routines
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* are welcome. Send EMail to the address given below.
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*
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* Under source code control: 1997/02/15 04:01:56
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* File existed as early as: 1997
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* Happy bit twiddling,
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*
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* chongo <was here> /\oo/\ http://reality.sgi.com/chongo/
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* Share and enjoy! :-) http://reality.sgi.com/chongo/tech/comp/calc/
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* Landon Curt Noll
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* http://reality.sgi.com/chongo/
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*
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* chongo <was here> /\../\
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*/
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/*
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@@ -206,7 +212,7 @@
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* the current Blum modulus. We will successively square mod Blum
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* modulus until we get a smaller value (modulus wrap).
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*
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* The follow calc resource file produces an equivalent effect:
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* The follow calc script produces an equivalent effect:
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*
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* n = default_modulus; (* n is the new Blum modulus *)
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* r = seed;
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@@ -232,7 +238,7 @@
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* have not been disclosed, use srandom(seed, newn) with the
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* appropriate args as noted below.
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*
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* The follow calc resource file produces an equivalent effect:
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* The follow calc script produces an equivalent effect:
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*
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* n = default_modulus; (* as used by the initial state *)
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* r = default_residue; (* as used by the initial state *)
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@@ -266,7 +272,7 @@
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* We will successively square it mod Blum modulus until we get
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* a smaller value (modulus wrap).
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*
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* The follow calc resource file produces an equivalent effect:
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* The follow calc script produces an equivalent effect:
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*
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* if (newn % 4 == 1) {
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* n = newn; (* n is the new Blum modulus *)
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@@ -291,7 +297,7 @@
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* The initial quadratic residue will be as if the default initial
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* quadratic residue arg was given.
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*
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* The follow calc resource file produces an equivalent effect:
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* The follow calc script produces an equivalent effect:
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*
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* srandom(default_residue, newn)
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*
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@@ -326,7 +332,7 @@
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* We will successively square it mod Blum modulus until we get
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* a smaller value (modulus wrap).
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*
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* The follow calc resource file produces an equivalent effect:
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* The follow calc script produces an equivalent effect:
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*
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* n = n[newn]; (* n is new Blum modulus, see below *)
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* r = seed;
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@@ -345,7 +351,7 @@
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* The new quadratic residue will also be set to one of
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* the pre-defined quadratic residues.
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*
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* The follow calc resource file produces an equivalent effect:
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* The follow calc script produces an equivalent effect:
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*
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* srandom(r[newn], n[newn])
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*
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@@ -652,7 +658,7 @@
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* We will successively square it mod Blum modulus until we get
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* a smaller value (modulus wrap).
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*
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* The follow calc resource file produces an equivalent effect:
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* The follow calc script produces an equivalent effect:
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*
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* p = nextcand(ip-2, trials, 0, 3, 4); (* find the 1st Blum prime *)
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* q = nextcand(iq-2, trials, 0, 3, 4); (* find the 2nd Blum prime *)
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@@ -680,7 +686,7 @@
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* The initial quadratic residue will be as if the default initial
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* quadratic residue arg was given.
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*
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* The follow calc resource file produces an equivalent effect:
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* The follow calc script produces an equivalent effect:
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*
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* srandom(default_residue, ip, iq, trials)
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*
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@@ -760,7 +766,7 @@
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* the "Blum-Blum-Shub generator" section above.
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*
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* A final "truth in advertising" issue deals with how the magic numbers
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* found in this file were generated. Detains can be found in the
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* found in this library were generated. Detains can be found in the
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* various functions, while a overview can be found in the "SOURCE FOR
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* MAGIC NUMBERS" section below.
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*/
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@@ -856,8 +862,8 @@
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* q = 2*fq+1;
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* } while (ptest(q, 25) == 0);
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*
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* The above resource file produces the Blum probable primes and initial
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* quadratic residue (line wrapped for readability):
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* The above script produces the Blum probable primes and initial quadratic
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* residue (line wrapped for readability):
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*
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* p= 0x798ac934c7a3318ad446190f3474e57
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*
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@@ -912,7 +918,7 @@
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* lambda(n) = lcm(factors of p-1 & q-1)
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*
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* since 'p' and 'q' are both odd, 'p-1' and 'q-1' have 2 as
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* a factor. The calc resource file above ensures that '(p-1)/2' and
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* a factor. The calc script above ensures that '(p-1)/2' and
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* '(q-1)/2' are probable prime, thus maximizing the period
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* of the default generator to:
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*
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@@ -962,7 +968,7 @@
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*
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***
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*
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* One could take issue with the above resource file that produced a 260 bit
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* One could take issue with the above script that produced a 260 bit
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* Blum modulus. So if that bothers you, then seed your generator
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* with your own Blum modulus and initial quadratic residue. And
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* if you are truly paranoid, why would you want to use the default seed,
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