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 (Formula presented) (for 3 or 4 rounds) to at most (Formula presented). (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 per- mutations”. 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.
CITATION STYLE
Patarin, J. (1998). About Feistel schemes with six (or more) rounds. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 1372, pp. 103–121). Springer Verlag. https://doi.org/10.1007/3-540-69710-1_8
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