Modified Matrix Encoding Technique for Minimal Distortion Steganography

It is well known that all information hiding methods that modify the least significant bits introduce distortions into the cover objects. Those distortions have been utilized by steganalysis algorithms to detect that the objects had been modified. It has been proposed that only coefficients whose modification does not introduce large distortions should be used for embedding. In this paper we propose an efficient algorithm for information hiding in the LSBs of JPEG coefficients. Our algorithm uses modified matrix encoding to choose the coefficients whose modifications introduce minimal embedding distortion. We derive the expected value of the embedding distortion as a function of the message length and the probability distribution of the JPEG quantization errors of cover images. Our experiments show close agreement between the theoretical prediction and the actual embedding distortion. Our algorithm can be used for both steganography and fragile watermarking as well as in other applications in which it is necessary to keep the distortion as low as possible.