A Graph Theoretic Approach to Sustainable Steganography

Abstract

An algorithm based on graph-theoretic approach is introduced in this paper. A bipartite graph is created from message and cover object. Message M is broken into units of x (= 2, 4, or 8) bits long. For each x, a matching with m number of such x bits from cover file is determined using the bipartite graph. Wherever a matching for a node in left side is found with a node in right side then this part of the message is treated as either naturally or cross embedded in that port of the cover. Nodes in left side correspond to bits in message and those in right side correspond to group of bits in cover. The matching relationship is then embedded in the extra bytes of cover, fully utilizing the available redundancy or alternatively the sequence of indices is compressed and sent through separate channel. The algorithm achieves almost 100% matching for message elements in cover elements. The embedding algorithm has been put through mathematical and statistical test to ensure that it not only retains visual similarity in stego with cover file but also leaves other statistics of cover undistorted after embedding. Therefore it achieves sustainability. In this paper, we have taken BMP file to implement the algorithm.