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How to Construct Pseudorandom and Super Pseudorandom Permutations from One Single Pseudorandom Function

  • Jacques Patarin
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 658)

Abstract

In this paper we will solve two open problems concerning pseudorandom permutations generators.
  1. 1.

    We will see that it is possible to obtain a pseudorandom permutation generator with only three rounds of DES - like permutation and a single pseudorandom function. This will solve an open problem of [6].

     
  2. 2.

    We will see that it is possible to obtain a super pseudorandom permutation generator with a single pseudorandom function. This will solve an open problem of [5]. For this we will use only four rounds of DES — like permutation.

     

For example, we will see that if ζ denotes the rotation of one bit, ψ(f, f, f o ζ o f) is a pseudorandom function generator. And ψ(f, f, f, f o ζ o f) is a super pseudorandom function generator.

Here the number of rounds used is optimal. It should be noted that here we introduce an important new idea in that we do not use a composition of f, i times, but f o ζ o f for the last round, where ζ is a fixed and public function.

References

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    M. Luby and C. Rackoff, How to construct pseudorandom permutations from pseudorandom functions, SIAM Journal and Computing, 17(2): 373–386, April 1988.zbMATHCrossRefMathSciNetGoogle Scholar
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    J. Patarin, New results on pseudorandom permutation generators based on the DES Scheme, Abstracts of Crypto’91, p. 7–2, 7–7.Google Scholar
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    J. Patarin, Etude des générateurs de permutations basés sut le schéma du DES, Thèse, November 1991, INRIA, Domaine de Voluceau, Le Chesnay, France.Google Scholar
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    J. Pieprzyk, How to construct pseudorandom permutations from Single Pseudorandom Functions, EUROCRYPT’90, Århus, Denmark, May 1990.Google Scholar
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    B. Sadeghiyan and J. Pieprzyk, On necessary and sufficient conditions for the construction of super pseudorandom permutations, Abstracts of Asiacrypt’91, November 1991, p. 117–123.Google Scholar
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    Y. Zheng, T. Matsumoto and H. Imai, Impossibility and optimality results on constructing pseudorandom permutations, Abstract of EUROCRYPT’89, Houthalen, Belgium, April 1989, p. 412–421.Google Scholar
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    L. J. Paige, Complete Mappings of finite groups, J. Math. 1, 111–116, 1951.zbMATHMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1993

Authors and Affiliations

  • Jacques Patarin
    • 1
  1. 1.Bull CP8LouveciennesFrance

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