On necessary and sufficient conditions for the construction of super pseudorandom permutations

In this paper, we present the necessary and sufficient conditions for super pseudorandomness of DES-like permutations. We show that four rounds of such permutations with a single random function is not super psuedorandom and we present a distinguishing circuit for ψ(f2, f, f, f) and another circuit for ψ(fl, fk, fj, fi). Then, we investigate the necessary and sufficient conditions for super pseudorandomness of type-1 Feistel type transformations, and we show that k2 rounds of this transformation is super pseudorandom.