Multipartite Verifiable Secret Sharing Based on CRT

Abstract

In (t, n) threshold secret sharing scheme, the dealer distributes secret among a group of n participants, and any t threshold number of participants can reconstruct the secret. However, t- 1 or lesser number of participants can not retrieve the secret. In verifiable secret sharing schemes (VSSS), participants can verify their share after receiving shares from the dealer to ensure that a dealer is not malicious. In multipartite secret sharing based on CRT scheme, a set of participants is divided into disjoint partitions, and whatever action performed at a single level is repeated at all other partitions. However, till date there is no mechanism to verify if dealer is malicious or not in multipartite secret sharing based on CRT. Two schemes are proposed for verification of a dealer, namely multipartite verifiable secret sharing based on CRT by using Iften, and multipartite verifiable secret sharing-based CRT by using kameer Kaya. Both proposed schemes are perfectly secure, and the security of both the schemes dependent on discrete logarithm problem.