## Cryptology ePrint Archive: Report 2006/437

On Zigzag Functions and Related Objects in New Metric

An Braeken, Ventzislav Nikov, Svetla Nikova

Abstract: In \cite{BCS96}, the concept of zigzag function was introduced in relation with oblivious transfer \cite{R84}. This subject has later been studied in \cite{S99,DS01,CFW01}. The definition of zigzag functions has been generalized to $s$-zigzag functions for $2\leq s\leq n$. It turns out that zigzag functions are also interesting combinatorial objects, thanks to their relation with self-intersecting codes and orthogonal arrays \cite{BCS96,S99}. The aim of this work is to formulate these objects with respect to a new metric following the approach proposed in \cite{BNNP} and to investigate the properties of the generalized zigzag functions and related concepts.

Category / Keywords: foundations / Zigzag functions, Quorum systems, Orthogonal arrays, Self-intersecting codes

Publication Info: Full version of a paper from the 8th Nordic Combinatorial Conference 2004