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/*
* seedrandom - seed the cryptographically strong Blum generator
*
* Copyright (C) 1999 Landon Curt Noll
*
* Calc is open software; you can redistribute it and/or modify it under
* the terms of the version 2.1 of the GNU Lesser General Public License
* as published by the Free Software Foundation.
*
* Calc is distributed in the hope that it will be useful, but WITHOUT
* ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
* or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General
* Public License for more details.
*
* A copy of version 2.1 of the GNU Lesser General Public License is
* distributed with calc under the filename COPYING-LGPL. You should have
* received a copy with calc; if not, write to Free Software Foundation, Inc.
* 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
*
* Under source code control: 1996/01/01 08:21:00
* File existed as early as: 1996
*
* chongo <was here> /\oo/\ http://www.isthe.com/chongo/
* Share and enjoy! :-) http://www.isthe.com/chongo/tech/comp/calc/
*/
/*
* The period of Blum generators with modulus 'n=p*q' (where p and
* q are primes 3 mod 4) is:
*
* lambda(n) = lcm(factors of p-1 & q-1)
*
* One can construct a generator with a maximal period when
* 'p' and 'q' have the fewest possible factors in common.
* The quickest way to select such primes is only use 'p'
* and 'q' when '(p-1)/2' and '(q-1)/2' are both primes.
* This function will seed the random() generator that uses
* such primes.
*
* given:
* seed1 - a large random value (at least 10^20 and perhaps < 10^314)
* seed2 - a large random value (at least 10^20 and perhaps < 10^314)
* size - min Blum modulus as a power of 2 (at least 32, perhaps >= 512)
* trials - number of ptest() trials (default 25)
*
* returns:
* the previous random state
*
* NOTE: The [10^20, 10^314) range comes from the fact that the 13th internal
* modulus is ~10^315. We want the lower bound seed to be reasonably big.
*/
define seedrandom(seed1, seed2, size, trials)
{
local p; /* first Blum prime */
local fp; /* prime co-factor of p-1 */
local sp; /* min bit size of p */
local q; /* second Blum prime */
local fq; /* prime co-factor of q-1 */
local sq; /* min bit size of q */
local n; /* Blum modulus */
local binsize; /* smallest power of 2 > n=p*q */
local r; /* initial quadratic residue */
local random_state; /* the initial rand state */
local random_junk; /* rand state that is not needed */
local old_state; /* old random state to return */
/*
* firewall
*/
if (!isint(seed1)) {
quit "1st arg (seed1) is not an int";
}
if (!isint(seed2)) {
quit "2nd arg (seed2) is not an int";
}
if (!isint(size)) {
quit "3rd arg (size) is not an int";
}
if (!isint(trials)) {
trials = 25;
}
if (digits(seed1) <= 20) {
quit "1st arg (seed1) must be > 10^20 and perhaps < 10^314";
}
if (digits(seed2) <= 20) {
quit "2nd arg (seed2) must be > 10^20 and perhaps < 10^314";
}
if (size < 32) {
quit "3rd arg (size) needs to be >= 32 (perhaps >= 512)";
}
if (trials < 1) {
quit "4th arg (trials) must be > 0";
}
/*
* determine the search parameters
*/
++size; /* convert power of 2 to bit length */
sp = int((size/2)-(size*0.03)+1);
sq = size - sp;
/*
* find the first Blum prime
*/
random_state = srandom(seed1, 13);
do {
do {
fp = nextcand(2^sp+randombit(sp), 1, 1, 3, 4);
p = 2*fp+1;
} while (ptest(p,1,0) == 0);
} while(ptest(p, trials) == 0 || ptest(fp, trials) == 0);
if (config("resource_debug") & 8) {
print "/* 1st Blum prime */ p=", p;
}
/*
* find the 2nd Blum prime
*/
random_junk = srandom(seed2, 13);
do {
do {
fq = nextcand(2^sq+randombit(sq), 1, 1, 3, 4);
q = 2*fq+1;
} while (ptest(q,1,0) == 0);
} while(ptest(q, trials) == 0 || ptest(fq, trials) == 0);
if (config("resource_debug") & 8) {
print "/* 2nd Blum prime */ q=", q;
}
/*
* seed the Blum generator
*/
n = p*q; /* the Blum modulus */
binsize = highbit(n)+1; /* smallest power of 2 > p*q */
r = pmod(rand(1<<ceil(binsize*4/5), 1<<(binsize-2)), 2, n);
if (config("resource_debug") & 8) {
print "/* seed quadratic residue */ r=", r;
print "/* newn", binsize, "bit quadratic residue*/ newn=", n;
}
old_state = srandom(r, n);
/*
* restore other states that we altered
*/
random_junk = srandom(random_state);
/*
* return the previous random state
*/
return old_state;
}
if (config("resource_debug") & 3) {
print "seedrandom(seed1, seed2, size [, trials]) defined";
}