a

libsec/genstrongprime.c

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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);
+}