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≪2n. 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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
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)
Luby, M., Rackoff, C.: How to construct pseudorandom permutations from pseudorandom functions. SIAM Journal on Computing 17(2), 373–386 (1988)
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)
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)
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)
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)
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)
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)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Patarin, J. (2006). On Linear Systems of Equations with Distinct Variables and Small Block Size. In: Won, D.H., Kim, S. (eds) Information Security and Cryptology - ICISC 2005. ICISC 2005. Lecture Notes in Computer Science, vol 3935. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11734727_25
Download citation
DOI: https://doi.org/10.1007/11734727_25
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-33354-8
Online ISBN: 978-3-540-33355-5
eBook Packages: Computer ScienceComputer Science (R0)