An approximate expression related with RSA fixed points

Abstract

Let T=T(n,e,a) be the number of fixed points of RSA (n,e) that are co-prime with n=pq, and A,B be sets of prime numbers in (1,x) and (1,y) respectively. An estimation on the mean-value \(M\left( {A,B,e,a} \right) = \frac{1}{{\left( {\# A} \right)\left( {\# B} \right)}}\sum\limits_{p \in A,q \in B,\left( {p,q} \right) = 1} {log} T\left( {pq,e,a} \right)\) is given.