Explaining the Bag Gain in Batch Steganography

In batch steganography, the sender distributes the secret payload among multiple images from a 'bag' to decrease the chance of being caught. Recent work on this topic described an experimentally discovered phenomenon, which we call the 'bag gain': for fixed communication rate, pooled detectors experience a decrease in statistical detectability for initially increasing bag sizes, providing an opportunity for the sender to gain in security. The bag gain phenomenon is universal in the sense of manifesting under a wide spectrum of conditions. In this paper, we explain this experimental observation by adopting a statistical model of detector response. Despite the simplicity of the model, it does capture observed trends in detectability as a function of the bag size, the rate, and cover source properties. Additionally, and surprisingly, the model predicts that in certain cover sources the sender should avoid bag sizes that are too small as this can lead to a bag loss.