A novel verifiable and unconditionally secure (m, t, n)-threshold multi-secret sharing scheme using overdetermined systems of linear equations over finite Galois fields

Abstract

Threshold multi-secrets sharing schemes allow sharing a set of m secrets among n participants, while secrets can be revealed only if t or more participants collude. Although many multi-secret sharing schemes have been proposed, several improvements remain essential in order to cope with actual effectiveness and security requirements, including computational performances and compliance for large-scale data. In this paper, we present a novel multi-secrets (m, t, n)-threshold scheme using overdetermined systems of linear equations defined over finite Galois fields. The scheme provides unconditional security, linear sharing/reconstructing complexities and holds secure verifiability and t-consistence. By considering both secrets and shares as elements over finite Galois fields GF(2r), optimal and space-efficient representation is ensured compared to recent sharing schemes. In addition, the scheme provides dynamic secrets sharing, forgery/cheating detection and robustness against common attacks, while lower computational overhead is required.