Sum Covers in Steganography

We extend the study of steganography schemes with pooling to the case when two changes per cell are allowed. We show that such schemes are equivalent to a new, symmetric version of sum covers known in combinatorial design theory. We give a construction that is better in the information versus distortion metric than the schemes with one change per cell. A number of interesting questions concerning the underlying sum cover sets remain open. 1 Steganography background Steganography is the science of information hiding. The sender starts with a cover object, such as for example a digital multimedia file, and (s)he embeds a hidden message into the cover object by slightly distorting it in a way that enables the intended recipient to retrieve the hidden message from the distorted cover object; at the same time the very existence of the hidden message should be impossible to detect by any third party. Typically the cover object is a sequence of elements of D, where D = {0, . . . ,m− 1}, m = 2e. In current applications we usually have e ∈ {8, 12, 16}. For example, e = 8 for grayscale digital images and e = 16 for CD quality audio. Let S denote the set of message symbols. A message to be communicated by the sender to the recipient is a string of elements of S. In most steganographic schemes, the sender and the recipient agree on a symbol-assignment function