Locally Square Distortion and Batch Steganographic Capacity

Abstract

A fundamental question of the steganography problem is to determine the amount of data which can be hidden undetectably. Its answer is of direct importance to the embedder, but also aids a forensic investigator in bounding the size of payload which might be communicated. Recent results on the information theory of steganography suggest that the detectability of payload in an individual object is proportional to the square of the number of changes caused by the embedding. Here, we follow up the implications when a payload is to be spread amongst multiple cover objects, and give asymptotic results about the maximum secure payload. Two embedding scenarios are distinguished: embedding in a fixed finite batch of covers, and continuous embedding in an infinite stream. The steganographic capacity, as a function of the number of objects, is sublinear and strictly asymptotically lower in the second case. This work consolidates and extends our previous results on batch and sequential steganographic capacity.