Advertisement

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)

Abstract

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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Aiello, W., Venkatesan, R.: Foiling Birthday Attacks in Lenght-Doubling Transformations - Benes: a non-reversible alternative to Feistel. In: Maurer, U.M. (ed.) EUROCRYPT 1996. LNCS, vol. 1070, pp. 307–320. Springer, Heidelberg (1996)CrossRefGoogle Scholar
  2. 2.
    Luby, M., Rackoff, C.: How to construct pseudorandom permutations from pseudorandom functions. SIAM Journal on Computing 17(2), 373–386 (1988)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Maurer, U.: A simplified and generalized treatment of Luby-Rackoff pseudorandom permutation generators. In: Rueppel, R.A. (ed.) EUROCRYPT 1992. LNCS, vol. 658, pp. 239–255. Springer, Heidelberg (1993)Google Scholar
  4. 4.
    Maurer, U., Pietrzak, K.: The security of Many-Round Luby-Rackoff Pseudo-Random Permutations. In: Biham, E. (ed.) EUROCRYPT 2003. LNCS, vol. 2656, pp. 544–561. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  5. 5.
    Naor, M., Reingold, O.: On the construction of pseudo-random permutations: Luby-Rackoff revisited. Journal of Cryptology 12, 29–66 (1999); Extended abstract was published in Proc. 29th Ann. ACM Symp. on Theory of Computing, pp. 189–199 (1997)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Patarin, J.: New results on pseudorandom permutation generators based on the DES scheme. In: Feigenbaum, J. (ed.) CRYPTO 1991. LNCS, vol. 576, pp. 301–312. Springer, Heidelberg (1992)Google Scholar
  7. 7.
    Patarin, J.: Luby-Rackoff: 7 Rounds are Enough for 2n(1 − ε) Security. In: Boneh, D. (ed.) CRYPTO 2003. LNCS, vol. 2729, pp. 513–529. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  8. 8.
    Patarin, J.: Security of Random Feistel Scemes with 5 or more rounds. In: Franklin, M. (ed.) CRYPTO 2004. LNCS, vol. 3152, pp. 106–122. Springer, Heidelberg (2004)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

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

Personalised recommendations