The security of many round Luby Rackoff pseudo random permutations Conference Paper

Author(s): Maurer, Ueli M; Pietrzak, Krzysztof
Title: The security of many round Luby Rackoff pseudo random permutations
Title Series: LNCS
Abstract: Luby and Rackoff showed how to construct a (super-)pseudo-random permutation {0,1}2n→ {0,1}2n from some number r of pseudo-random functions {0,1}n → {0,1}n. Their construction, motivated by DES, consists of a cascade of r Feistel permutations. A Feistel permutation 1for a pseudo-random function f is defined as (L, R) → (R,L ⊕ f (R)), where L and R are the left and right part of the input and ⊕ denotes bitwise XOR or, in this paper, any other group operation on {0,1}n. The only non-trivial step of the security proof consists of proving that the cascade of r Feistel permutations with independent uniform random functions {0,1}n → {0,1}n, denoted Ψ2nr is indistinguishable from a uniform random permutation {0,1}2n → {0,1}2n by any computationally unbounded adaptive distinguisher making at most O(2cn) combined chosen plaintext/ciphertext queries for any c < α, where a is a security parameter. Luby and Rackoff proved α = 1/2 for r = 4. A natural problem, proposed by Pieprzyk is to improve on α for larger r. The best known result, α = 3/4 for r = 6, is due to Patarin. In this paper we prove a = 1 -O(1/r), i.e., the trivial upper bound α = 1 can be approached. The proof uses some new techniques that can be of independent interest.
Conference Title: EUROCRYPT: Theory and Applications of Cryptographic Techniques
Volume: 2656
Conference Dates: May 4-8, 2003
Conference Location: Warsaw, Poland
Publisher: Springer  
Date Published: 2003-06-04
Start Page: 544
End Page: 561
Copyright Statement: © International Association for Cryptologic Research 2003.
DOI: 10.1007/3-540-39200-9_34
Open access: no
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