Counting RSA-integers
Number Theory
2012-07-30 v1
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.
Cite
@article{arxiv.0801.1451,
title = {Counting RSA-integers},
author = {Andreas Decker and Pieter Moree},
journal= {arXiv preprint arXiv:0801.1451},
year = {2012}
}
Comments
to appear in Results in Mathematics, 5 pages, with the view of possible interest by cryptographers we aimed for a very short paper, rather than a more extensive technical one with stronger results