Generalized zig-zag functions and oblivious transfer reductions

Abstract

In this paper we show some efficient and unconditionally secure oblivious transfer reductions. Our main tool is a class of functions that generalizes the Zig-zag functions, introduced by Brassard, Crepéau, and Sántha in [6]. We show necessary and sufficient conditions for the existence of such generalized functions, and some characterizations in terms of well known combinatorial structures. Moreover, we point out an interesting relation between these functions and ramp secret sharing schemes where each share is a single bit.