Reducing the embedding impact in steganography using Hamiltonian paths and writing on wet paper

Abstract

The distortion introduced in the cover image is one of the most important factors influencing image steganography. The lower the distortion is, the higher the quality of the stego image, and thus the higher the resistance to steganalysis would be. This paper proposes an image steganographic method which employs the Hamiltonian paths in order to decrease the distortion produced by the LSB substitution scheme. The proposed method divides the cover image into non-overlapping blocks. For each block, the arrangement of the pixels of the block is first changed according to a Hamiltonian path. Next, the pixels whose LSB is not equal to the secret data are determined. The path that results in minimum distortion is chosen, and its binary code as well as the mismatched pixels are recorded. Repeating this process for all blocks, the pixels that should be modified during data embedding and a binary key that includes the codes of the best Hamiltonian path in all blocks are determined. Then, the new values of the second LSB of the changeable pixels are computed using writing on wet paper approach with regard to the compressed key. Finally, +1 or ?1 is added to each changeable pixel according to the value computed for its second LSB. By this strategy, the distortion of each pixel of the stego image is at most 1. Experimental results evaluated on 2000 natural images reveal that the proposed method can significantly decrease the image distortion and thus enhance security.