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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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