Batch Steganography and the Threshold Game

摘要

In Batch Steganography we assume that a Steganographer has to choose how to allocate a fixed amount of data between a large number of covers. Given the existence of a steganalysis method for individual objects (satisfying certain assumptions) we assume that a Warden attempts to detect the payload by pooling the evidence from all the objects. This paper works out the details of a particular method for the Warden, which counts the number of objects of which the detection statistic surpasses a certain threshold. This natural pooling method leads to a game between the Warden and Steganographer, and there are different varieties depending on whether the moves are sequential or simultaneous. The solutions are intriguing, suggesting that the Steganographer should always concentrate the payload in as few covers as possible, or exactly the reverse, but never adopt an intermediate strategy. Furthermore, the Warden's optimal strategies are instructive for the benchmarking of quantitative steganalysis methods. Experimental results show that some steganography and steganalysis methods' empirical performance accords with this theory.