A Novel (2, 3) Reversible Secret Image Sharing Based on Fractal Matrix

Abstract

This paper first proposes two types of three-dimensional (3D) fractal reference matrices. Then, a new reversible (2, 3) secret image sharing scheme based on a fractal matrix is presented. With the help of the fractal reference matrix, the secret data can be embedded in an original image to generate three meaningful shadow images. It is worth mentioning that these two types of fractal matrices are designed for different hiding capacity, meanwhile the characteristics of the fractal matrix can guarantee good visual quality of the generated shadow images. Moreover, we provide two authentication mechanisms according to different situations, one of the authentication mechanisms can achieve 100% ability cheat detection. When the authentication is passed, we only need two of the three shadow images to extract the correct secret data and perfectly restore the original image. Experimental results show that our proposed scheme provides excellent authentication ability and good visual quality.

An Authenticatable (2, 3) Secret Sharing Scheme Using Meaningful Share Images Based on Hybrid Fractal Matrix

“…In this section, we briefly introduce the fractal matrix proposed by Gao et al in [36]. Then, a modified fractal matrix based on the same concept is proposed to fit our new problem formulation.…”

“…With irreversibility comes the problem that when one of the shares is tampered with, the secret data cannot be recovered at all, even though the share is authenticatable. In order to reduce the risk of tampering attacks, Gao et al [36] proposed a (2, 3) reversible SIS scheme based on the fractal matrix. Through ingenious design of the fractal matrix, any two out of the three shares can cooperate to retrieve the secret data.…”

“…The fractal matrix was first proposed by Gao et al [36]. It is a special type of reference matrix which is applied to guide the production of shares in their secret sharing scheme.…”

“…As shown in Fig. 2, the fractal matrix proposed in [36] contains a long series of concatenated fractal groups on its main diagonal. The elements in a fractal model are so ingeniously arranged that the projections of all elements in a fractal group onto each axial plane constitute a perfect square matrix.…”

“…In other words, each element in the fractal group is unique and indispensable. This property was exploited to design the (2, 3) SIS scheme in [36]. To achieve a similar purpose, the fractal matrix proposed in this paper is a modified version of the above matrix and will be described in the next subsection.…”