An Image Secret Sharing Method Based on Matrix Theory

Abstract

Most of today’s secret image sharing technologies are based on the polynomial-based secret sharing scheme proposed by shamir. At present, researchers mostly focus on the development of properties such as small shadow size and lossless recovery, instead of the principle of Shamir’s polynomial-based SS scheme. In this paper, matrix theory is used to analyze Shamir’s polynomial-based scheme, and a general (k, n) threshold secret image sharing scheme based on matrix theory is proposed. The effectiveness of the proposed scheme is proved by theoretical and experimental results. Moreover, it has been proved that the Shamir’s polynomial-based SS scheme is a special case of our proposed scheme.

Keywords

• threshold construction
• Shamir’s polynomial-based scheme
• secret image sharing
• matrix theory
• Vandermonde matrix