Counting RSA-integers

Abstract

In the RSA cryptosystem integers of the form n = p • q with p and q primes of comparable size ('RSA-integers') play an important role. It is a folklore result of cryptographers that C r (x), the number of integers n ≤ x that are of the form n = pq with p and q primes such that p < q < rp, is for fixed r > 1 asymptotically equal to c r x log-2 x for some constant c r > 0. Here we prove this and show that c r = 2logr. © 2008 Birkhaueser.