Counting RSA-integers
Andreas Decker, Pieter Moree

TL;DR
This paper proves the asymptotic count of RSA-integers, integers of the form n=pq with primes p and q of comparable size, and determines the exact constant involved in their distribution.
Contribution
It rigorously establishes the asymptotic formula for RSA-integers and explicitly computes the constant c_r as 2 log r, confirming a folklore result.
Findings
Asymptotic formula for RSA-integers count established
Constant c_r computed as 2 log r
Validates folklore in cryptography literature
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=2log r.
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Taxonomy
TopicsCoding theory and cryptography · Analytic Number Theory Research · Cryptography and Residue Arithmetic
