LSB-Based Steganography Using Hamiltonian Paths

Abstract

In the graph theory, a Hamiltonian path is defined as a path in a graph which includes every vertex exactly once. The proposed method divides the cover image into some m×n blocks and partitions the binary secret data into some vectors with the length of m*n. For each block, one Hamiltonian path is first found such that the LSB of pixels of the block along this path have the maximum similarity to the corresponding vector of data. Then this part of data is embedded into the first LSB of pixels of the block along the best path using the modified LSB matching and the code of this path is embedded into the second LSB of the pixels using a novel method such that the minimum MSE value between the block of the cover image and the block of the stego-image is achieved. The experimental results evaluated on 8000 natural images reveal that the proposed method produces minimum distortion in the stego-images. Security of our method against one of the most effective steganalyzers is demonstrated.