Generalized Graph-Based Visual Secret Sharing Schemes for Multiple Secrets

A visual secret sharing scheme with an access structure based on a given graph has been proposed, and can be considered an extension of (2, n)-threshold visual secret sharing schemes. Ateniese et al. presented a decomposition method in which a dealer decomposes a given graph into star graphs, with qualified participants (vertices in a given graph) who have a common edge if and only if the participants can reconstruct the secret image by stacking their shares. This paper classifies graph-based visual secret sharing schemes, presents several optimal examples, and proposes an ideal graph-based visual secret sharing scheme with real world applications, because the pixel expansion is not greater than 4. This paper also proposes some new methods for the construction of a graph-based visual secret sharing scheme for multiple secrets with practical pixel expansion.