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

Abstract

This paper focuses on how to protect confidential image based on hierarchical threshold secret sharing
scheme, against fake shadow attacks, collusion attacks and shadow information leakage problem.
Inspired by existing research, we propose a novel hierarchical threshold secret sharing scheme based
on Birkhoff interpolation and matrix projection, hierarchical secret distribution mathematical processes
and hierarchical threshold reconstruction mathematical processes are proposed in detail in
this paper, by designing random matrix generation, polynomial multiple derivatives, and Birkhoff
interpolation method in Galois field. Simulations and analysis validate the proposed scheme can
tolerate 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 than
the existing schemes.