A note on the average number of RSA fixed points

Recently, Chmielowiec (2010) [3] studied an upper bound for the average number of fixed points in RSA encryption and asserted that it is on the order of (logn)2 for randomly chosen RSA parameters (n,e). In this paper, we point out some error in his estimation and present detailed procedures for correct evaluation. It is shown that the expected number of RSA fixed points is in fact O((logn)3).