On Linear Systems of Equations with Distinct Variables and Small Block Size

  • Jacques Patarin
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3935)


In this paper we will prove the Conjecture 8.1. of [7]. We call it “Conjecture P i P j ”. It is a purely combinatorial conjecture that has however some cryptographic consequence. For example, from this result we can improve the proven security bounds on random Feistel schemes with 5 rounds: we will prove that no adaptive chosen plaintext/chosen ciphertext attack can exist on 5 rounds Random Feistel Schemes when m≪2 n . This result reach the optimal bound of security against an adversary with unlimited computing power (but limited by m queries) with the minimum number of rounds. It solves the last case of a famous open problem (cf [8]).

An extended version of this paper is available from the author.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Jacques Patarin
    • 1
  1. 1.Université de VersaillesVersaillesFrance

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