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

Authors: Kamel Mohamed Faraoun

Addresses: Computer Science Department, Evolutionary Engineering and Distributed Information Systems Laboratory (EEDIS), Djilalli Liabbes University, Sidi Bel Abbès, Algeria

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.

Keywords: verifiable multi-secrets sharing; overdetermined systems of linear equations; Galois field; unconditional security.

DOI: 10.1504/IJICS.2019.096849

International Journal of Information and Computer Security, 2019 Vol.11 No.1, pp.61 - 82

Accepted: 09 May 2017
Published online: 19 Nov 2018 *

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