Benchmarking for Steganography

With the increasing number of new steganographic algorithms as well as methods for detecting them, the issue of comparing security of steganographic schemes in a fair manner is of the most importance. A fair benchmark for steganography should only be dependent on the model chosen to represent cover and stego objects. In particular, it should be independent of any specific steganalytic technique. We first discuss the implications of this requirement and then investigate the use of two quantities for benchmarking--the KL divergence between the empirical probability distribution of cover and stego images and the recently proposed two-sample statistics called Maximum Mean Discrepancy (MMD). While the KL divergence is preferable for benchmarking because it is the more fundamental quantity, we point out some practical difficulties of computing it from data obtained from a test database of images. The MMD is well understood theoretically and numerically stable even in high-dimensional spaces, which makes it an excellent candidate for benchmarking in steganography. We demonstrate the benchmark based on MMD on specific steganographic algorithms for the JPEG format.