General Secret Sharing Based on the Chinese Remainder Theorem with Applications in E-Voting

Abstract

Threshold secret sharing based on the Chinese remainder theorem has been considered by Mignotte [Mignotte, M., How to share a secret, in: T. Beth, editor, Cryptography-Proceedings of the Workshop on Cryptography, Burg Feuerstein, 1982, Lecture Notes in Computer Science 149 (1983), pp. 371–375] and Asmuth and Bloom [Asmuth, C.A. and J. Bloom, A modular approach to key safeguarding, IEEE Transactions on Information Theory IT-29 (1983), pp. 208–210]. In this paper we demonstrate that the Chinese remainder theorem can be used for realizing more general access structures, as the compartmented or the weighted threshold ones. We also prove that there exist some non-weighted threshold access structures whose realizations require the general variant of the Chinese remainder theorem, i.e., the variant in which the modules are not necessarily pairwise coprime.As an application of the proposed secret sharing schemes, we present a multi-authority e-voting schemes in which, as a novelty, the tallying authorities may have non-equal weights.