Abstract
This paper is a continuation of the work initiated in [2] by M. Luby and C. Rackoff on Feistel schemes used as pseudorandom permutation generators. The aim of this paper is to study the qualitative improvements of “strong pseudorandomness” of the Luby-Rackoff construction when the number of rounds increase. We prove that for 6 rounds (or more), the success probability of the distinguisher is reduced from \( \mathcal{O}\left( {\tfrac{{m^2 }} {{2^n }}} \right) \) (for 3 or 4 rounds) to at most \( \mathcal{O}\left( {\tfrac{{m^4 }} {{2^{3n} }} + \tfrac{{m^2 }} {{2^{2n} }}} \right) \). (Here m denotes the number of cleartext or ciphertext queries obtained by the enemy in a dynamic way, and 2n denotes the number of bits of the cleartexts and ciphertexts).
We then introduce two new concepts that are stronger than strong pseudorandomness: “very strong pseudorandomness” and “homogeneous permutations”. We explain why we think that those concepts are natural, and we study the values k for which the Luby-Rackoff construction with k rounds satisfy these notions.
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© 1998 Springer-Verlag Berlin Heidelberg
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Patarin, J. (1998). About Feistel Schemes with Six (or More) Rounds. In: Vaudenay, S. (eds) Fast Software Encryption. FSE 1998. Lecture Notes in Computer Science, vol 1372. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-69710-1_8
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DOI: https://doi.org/10.1007/3-540-69710-1_8
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