Paper 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 $$) 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}