A novel verifiable and unconditionally secure (m, t, n)-threshold multi-secret sharing scheme using overdetermined systems of linear equations over finite Galois fields
by Kamel Mohamed Faraoun
International Journal of Information and Computer Security (IJICS), Vol. 11, No. 1, 2019

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(2^r), 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.

Online publication date: Wed, 12-Dec-2018

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