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