A Generalized Secret Sharing Scheme Realizing Ordered Access Structures

Abstract

The authors propose a novel generalized secret sharing scheme that realizes an ordered access structure, in which the participants of a qualified subset can reconstruct the shared secret only if they follow the sequence of share/ subshare presentation specified by the dealer. The security of the proposed scheme is based on the intractability of the discrete logarithm problem and the robustness of the oneway hash function. Besides, the cheating trick by presenting a fake subshare or the violation of the sequence of share/subshare presentation will be effectively identified during secret reconstruction.