Certifying variant of RSA with generalized moduli

Abstract

Let N be an arbitrary integer with unknown factorization. In Asiacrypt 2012, Kakvi et al. proposed an algorithm that, given prime (Formula Presented), certifies whether the RSA function RSAN,e(x):= xe mod N defines a permutation over (Formula Presented) or not. In this paper, we extend Kakvi et al.’s work by considering the case with generalized moduli (Formula Presented). Surprisingly, when {Z1,...,Zn} ≥ 2, we show that it can be efficiently decided whether the RSA function defines a permutation over (Formula Presented) or not even for the prime (Formula Presented). Our result can be viewed as an extension of Kakvi et al.’s result.