Some considerations concerning the selection of RSA moduli

Abstract

In this contribution two conditions are stated which safe RSA moduli n = p-q must fulfill. Otherwise the factors of n can be found. First we consider the cycle-lengths of the recursion c ← cφ(n)-1 +1 mod n which leads to a condition in terms of Fibonacci numbers. The second condition involves a property of Euler's function. We introduce a number-theoretic distance measure - the power-of-two distance (ptd) - which may be useful for evaluating the security of RSA moduli against ‘number-theoretic integration’. The ptd of an RSA prime p must not be too small.