On the Construction of Pseudorandom Permutations: Luby—Rackoff Revisited
Luby and Rackoff  showed a method for constructing a pseudorandom permutation from a pseudorandom function. The method is based on composing four (or three for weakened security) so-called Feistel permutations, each of which requires the evaluation of a pseudorandom function. We reduce somewhat the complexity of the construction and simplify its proof of security by showing that two Feistel permutations are sufficient together with initial and final pairwise independent permutations. The revised construction and proof provide a framework in which similar constructions may be brought up and their security can be easily proved. We demonstrate this by presenting some additional adjustments of the construction that achieve the following:
• Reduce the success probability of the adversary.
• Provide a construction of pseudorandom permutations with large input-length using pseudorandom functions with small input-length.
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