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A Simplified and Generalized Treatment of {L}uby-{R}ackoff Pseudorandom Permutation Generators

Ueli Maurer

A paper by Luby and Rackoff on the construction of pseudorandom permutations from pseudorandom functions based on a design principle of the DES has recently initiated a burst of research activities on applications and generalizations of these results. This paper presents a strongly simplified treatment of these results and generalizes them by pointing out the relation to locally random functions, thereby providing new insight into the relation between probability-theoretic and complexity-theoretic results in cryptography. The first asymptotically-optimal construction of a locally random function is presented and new design strategies for block ciphers based on these results are proposed.

Keywords: Locally random function, Pseudorandom function, Pseudorandom permutation, Luby-Rackoff permutation generator.