Space-Efficient Secret Sharing Based on Matrix Normal Forms
Year: 2026
Type: article
Abstract: Secret sharing schemes distribute a secret among participants so that only authorised subsets can reconstruct it. In this paper, we focus on space-efficient secret sharing and show that matrix normal forms can significantly reduce share sizes while achieving computational security properties. Our scheme is implemented within an online secret sharing architecture, where authenticated public data P is maintained and shares of private data Q are issued over a secure channel. We study an existing probabilistic matrix-based approach to share size reduction and prove that the expected number of iterations of the underlying cyclic vector algorithm is small, yielding an expected polynomial runtime. We then design a novel deterministic method based on the Frobenius canonical normal form, avoiding reliance on cyclic vector techniques, and derive its runtime complexity. This yields a space-efficient secret sharing scheme that is computationally secure under a suitably defined adversary model. We have implemented our algorithm in the computer algebra system Maple as an Open Source project and provide an evaluation of its performance. Our results demonstrate that matrix normal forms can provide a suitable mathematical framework for secure and practical secret sharing.
Source: Cryptography
Authors: Eckhard Pfluegel, Razi Arshad, Mark Jones
Institution: Kingston University London
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $1,930
OpenAlex ID: W7160067782