A construction of the simplest super pseudorandom permutation generator

In this paper, the authors consider one of the two open problems proposed by Pieprzyk, 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, they show that ψ(f,f,f²,f) is pseudorandom. Then, using the pseudorandomness of ψ(f²,f,f,f) and ψ(f,f,f²,f), the authors show ψ(f,f²,f,f,f) is super pseudorandom.