An Information Hiding Method Based on Computational Intractable Problems

Abstract

This paper presents an information hiding method that can be used for proving copyright ownership of a digital object. In contrast with other methods, the identity of the owner of the object is proved by the owner’s ability to demonstrate knowledge of a certain property of the signature. The method utilizes Zero Knowledge Interactive Proof (ZKIP) protocols for computationally intractable, or NP-complete, problems and in particular for the 3-coloring problem. This problem requires an assignment of a color out of three available colors to the vertices of a graph so that no two adjacent vertices have the same color. The method prescribes the construction of signatures that represent adjacency matrices of graphs while proof of ownership is effected by knowledge of a 3-coloring by an individual. The computational intractability of the 3-coloring problem implies that knowledge of a coloring of the graph/signature presents sufficient evidence of ownership of any digital file containing this signature. The method has the additional advantage that the disclosure of the signature is of no consequence, since it is essentially the knowledge of the property of the signature (the 3-coloring of the graph it represents) that enables one to use it as proof of ownership of the cover data. The paper focuses on the design of the method and presents experiments from its application on high quality color images. From the experiments it is derived that it is feasible to add the 3-colored graph into color images without affecting image quality (PSNR measurements and HVS examples are presented). More importantly, experiments prove the signature tolerance against various attacks even against attacks that significantly reduce image quality.