A Construction for Super Pseudorandom Permutations from A Single Pseudorandom Function

In this paper, we show how to construct a super pseudorandom permutation generator from a single pseudorandom function generator, based on DES-like permutations. First, we show ψ(g, 1, f, g, 1, f), which consists of six rounds of DES-like permutations with two different pseudorandom functions and a fixed permutation, is super psuedorandom. Then, we show that with replacing a two-fold composition of one of the pseudorandom functions instead of the other one it is possible to construct a super pseudorandom permutation from a single pseudorandom function, where we need six rounds of DES-like permutations and six references to the pseudorandom function.