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#include "os.h"
#include <mp.h>
#include <libsec.h>
/* Gordon's algorithm for generating a strong prime */
/* Menezes et al () Handbook, p.150 */
void
genstrongprime(mpint *p, int n, int accuracy)
{
mpint *s, *t, *r, *i;
if(n < 64)
n = 64;
s = mpnew(n/2);
genprime(s, (n/2)-16, accuracy);
t = mpnew(n/2);
genprime(t, n-mpsignif(s)-32, accuracy);
/* first r = 2it + 1 that's prime */
i = mpnew(16);
r = mpnew(0);
itomp(0x8000, i);
mpleft(t, 1, t); /* 2t */
mpmul(i, t, r); /* 2it */
mpadd(r, mpone, r); /* 2it + 1 */
for(;;){
if(probably_prime(r, 18))
break;
mpadd(r, t, r); /* r += 2t */
}
/* p0 = 2(s**(r-2) mod r)s - 1 */
itomp(2, p);
mpsub(r, p, p);
mpexp(s, p, r, p);
mpmul(s, p, p);
mpleft(p, 1, p);
mpsub(p, mpone, p);
/* first p = p0 + 2irs that's prime */
itomp(0x8000, i);
mpleft(r, 1, r); /* 2r */
mpmul(r, s, r); /* 2rs */
mpmul(r, i, i); /* 2irs */
mpadd(p, i, p); /* p0 + 2irs */
for(;;){
if(probably_prime(p, accuracy))
break;
mpadd(p, r, p); /* p += 2rs */
}
mpfree(i);
mpfree(s);
mpfree(r);
mpfree(t);
}
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