1 September 2019

1 May 2020

17 June 2020

#### Abstract

*n*participants in such a way that any

*k*participants are able to use their shares collectively to reconstruct the secret image, while fewer than

*k*shares do not reveal any information about the secret image. In this work, we propose a lossless linear algebraic $(k,n)$-threshold secret image sharing scheme. The scheme associates a vector ${\mathbf{v}_{i}}$ to the

*i*th participant in the vector space ${\mathbb{F}_{{2^{\alpha }}}^{k}}$, where the vectors ${\mathbf{v}_{i}}$ satisfy some admissibility conditions. The

*i*th share is simply a linear combination of the vectors ${\mathbf{v}_{i}}$ with coefficients from the secret image. Simulation results demonstrate the effectiveness and robustness of the proposed scheme compared to standard statistical attacks on secret image sharing schemes. Furthermore, the proposed scheme has a high level of security, error-resilient capability, and the size of each share is $1/k$ the size of the secret image. In comparison with existing work, the scheme is shown to be very competitive.

#### References

#### Biographies

**A. Kanso** is an associate professor of mathematics at Kuwait University, Kuwait. He received his BSc degree in mathematics from Queen Mary and Westfield College (University of London), in 1994. He earned his MSc degree in applied computing technology at the Electronic Engineering department of Middlesex University, in 1996. In 1999 he obtained a PhD in mathematics from Royal Holloway and Bedford New College (University of London). His research interests include chaos-based encryption systems, information hiding, hash functions, secret sharing, and graph theory.

**M. Ghebleh** is an associate professor of mathematics at Kuwait University, Kuwait. He received his BSc and MSc in mathematics from Sharif University of Technology, Tehran, Iran (1997 and 1999), and his PhD in mathematics from Simon Fraser University, Burnaby, British Columbia, Canada (2007). His research interests include graph theory, combinatorics, and digital security topics such as encryption, data hiding, hash functions, and secret sharing.

**A. Alazemi** is an associate professor of mathematics at Kuwait University, Kuwait. He received his BSc in mathematics from Kuwait University, Kuwait. He earned his MSc and PhD in mathematics from Colorado State University, Colorado, the United States (2004 and 2007). His research interests include incidence structures, classification problems, spectral graph theory, graph theory, combinatorics and algebra.