Title: Generalised multi-secret sharing scheme for non-monotone access structures

Authors: Shiva Krishna Nallabothu; N. Rukma Rekha; Y.V. Subba Rao

Addresses: School of Computer and Information Sciences, University of Hyderabad, Hyderabad, Telangana, India ' School of Computer and Information Sciences, University of Hyderabad, Hyderabad, Telangana, India ' School of Computer and Information Sciences, University of Hyderabad, Hyderabad, Telangana, India

Abstract: Generalised secret sharing (GSS) schemes for monotone access structures, which always grant access to larger sets, offer flexibility beyond threshold schemes. But often these schemes struggle with practical limitations and an inability to model complex real-world policies involving specific exclusions or conditional access based on the absence of certain participants. We propose a novel GSS scheme specifically designed for non-monotone access structures, enabling true fine-grained control for scenarios where exceptions or negative constraints are paramount. The proposed GSS scheme is then extended to a generalised multi-secret sharing (GMS) scheme, facilitating the secure and controlled distribution of multiple secrets under the non-monotone access structure. GSS and GMS schemes are constructed using maximum distance separable (MDS) codes and require one-way functions. The proposed schemes are ideal and computationally perfect. The correctness, complexity, and security analysis are also given.

Keywords: generalised secret sharing; non-monotone access structure; MDS codes.

DOI: 10.1504/IJICS.2026.151307

International Journal of Information and Computer Security, 2026 Vol.29 No.2, pp.207 - 226

Received: 05 Jan 2025
Accepted: 31 Jul 2025
Published online: 22 Jan 2026 *

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