Hierarchical Threshold Secret Image Sharing Scheme Based on Birkhoff Interpolation and Matrix Projection

This paper focuses on how to protect confidential image based on hierarchical threshold secret sharingscheme, against fake shadow attacks, collusion attacks and shadow information leakage problem.Inspired by existing research, we propose a novel hierarchical threshold secret sharing scheme basedon Birkhoff interpolation and matrix projection, hierarchical secret distribution mathematical processesand hierarchical threshold reconstruction mathematical processes are proposed in detail inthis paper, by designing random matrix generation, polynomial multiple derivatives, and Birkhoffinterpolation method in Galois field. Simulations and analysis validate the proposed scheme cantolerate fake shadow attacks and collusion attacks, and has the ability to avoid information leakage.Experiments also prove that shadow secret embedding capacity of secret cover image is bigger thanthe existing schemes.