## Cryptology ePrint Archive: Report 2010/293

Security of balanced and unbalanced Feistel Schemes with Linear Non Equalities

Jacques Patarin

Abstract: \begin{abstract} In this paper we will study 2 security results above the birthday bound'' related to secret key cryptographic problems.\\ 1. The classical problem of the security of 4, 5, 6 rounds balanced Random Feistel Schemes.\\ 2. The problem of the security of unbalanced Feistel Schemes with contracting functions from $2n$ bits to $n$ bits. This problem was studied by Naor and Reingold~\cite{NR99} and by~\cite{YPL} with a proof of security up to the birthday bound.\\ These two problems are included here in the same paper since their analysis is closely related, as we will see. In problem 1 we will obtain security result very near the information bound (in $O(\frac {2^n}{n})$) with improved proofs and stronger explicit security bounds than previously known. In problem 2 we will cross the birthday bound of Naor and Reingold. For some of our proofs we will use~\cite{A2} submitted to Crypto 2010. \end{abstract}

Category / Keywords: secret-key cryptography / Luby-Rackoff constructions, Balanced random Feistel schemes, Unbalanced random Feistel schemes, Security Proofs, linear equalities and linear non equalities.

Date: received 17 May 2010

Contact author: valerie nachef at u-cergy fr

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