EUROCRYPT 1992: Advances in Cryptology — EUROCRYPT’ 92 pp 256-266

# How to Construct Pseudorandom and Super Pseudorandom Permutations from One Single Pseudorandom Function

• Jacques Patarin
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 658)

## Abstract

In this paper we will solve two open problems concerning pseudorandom permutations generators.
1. 1.

We will see that it is possible to obtain a pseudorandom permutation generator with only three rounds of DES - like permutation and a single pseudorandom function. This will solve an open problem of [6].

2. 2.

We will see that it is possible to obtain a super pseudorandom permutation generator with a single pseudorandom function. This will solve an open problem of [5]. For this we will use only four rounds of DES — like permutation.

For example, we will see that if ζ denotes the rotation of one bit, ψ(f, f, f o ζ o f) is a pseudorandom function generator. And ψ(f, f, f, f o ζ o f) is a super pseudorandom function generator.

Here the number of rounds used is optimal. It should be noted that here we introduce an important new idea in that we do not use a composition of f, i times, but f o ζ o f for the last round, where ζ is a fixed and public function.

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