Steganographic strategies for a square distortion function

Recent results on the information theory of steganography suggest, and under some conditions prove, that the detectability of payload is proportional to the square of the number of changes caused by the embedding. Assuming that result in general, this paper examines the implications for an embedder when a payload is to be spread amongst multiple cover objects. A number of variants are considered: embedding with and without adaptive source coding, in uniform and nonuniform covers, and embedding in both a fixed number of covers (so-called batch steganography) as well as establishing a covert channel in an infinite stream (sequential steganography, studied here for the first time). The results show that steganographic capacity is sublinear, and strictly asymptotically greater in the case of a fixed batch than an infinite stream. In the former it is possible to describe optimal embedding strategies; in the latter the situation is much more complex, with a continuum of strategies which approach the unachievable asymptotic optimum.