Luby–Rackoff Revisited: On the Use of Permutations as Inner Functions of a Feistel Scheme

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Abstract

In this paper we are dealing with the security of the Feistel structure in the Luby–Rackoff model when the round functions are replaced by permutations. There is a priori no reason to think that the security bounds remain the same in this case, as illustrated by Knudsen's attack [5]. It is why we revisit Luby–Rackoff's proofs [6] in this specific case. The conclusion is that when the inner functions are random permutations, a 3-round (resp. 4-round) Feistel scheme remains secure against pseudorandom (resp. superpseudorandom) distinguishers as long as m ≪ 2n/2 (with m the number of queries and 2n the block size).

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