Construction of the simplest super pseudorandom permutation generator

Abstract

In this paper we consider one of the two open problems proposed by Pieprzyk [6], i.e. whether a permutation generator which is designed using five rounds of the Data Encryption Standard and a single pseudorandom function is a super pseudorandom permutation generator. First, we show that $\psi(f,f,f^2,f)$ is pseudorandom. Then, using the pseudorandomness of $\psi(f^2,f,f,f)$ and $\psi(f,f,f^2,f)$, we show $\psi(f,f^2,f,f,f)$ is the simplest super pseudorandom.