Distributive weighted threshold secret sharing schemes

Abstract

The concept of distributive weighted threshold access structure is introduced, which is an weighted threshold access structure where the participants are distributed on levels, the participants on the same level are assigned the same weight, and the threshold of the access structure is 1. The weight of the participants on the ith level is of the form 1/ki and, therefore, the ith level induces a standard threshold access structure with threshold ki.We propose a CRT-based realization of distributive weighted threshold access structures, which is asymptotically perfect and perfect zero-knowledge. We also show that distributive weighted threshold access structures do not generally have ideal realizations. In case of just one level, our scheme can be viewed as an asymptotically perfect and perfect zero-knowledge variation of the Asmuth–Bloom secret sharing scheme.