Permutation codes and steganography

The role of permutation coding in minimum-distortion perfect counterforensics

“…Thus, under the knowledge of the legitimacy of x, the ensemble of signals among which the forger can choose a perfect post-processed forgery is the same as the set of Slepian's Variant I permutation codewords with base codeword x [6]. If one replaces "decoy" by "host" and "post-processed forgery" by "watermarked signal", the parallel with perfect steganography is evident (see [5]). …”

“…Instead, the steganographer wishes to attach unique labels to all signals in the set, thus maximising the number of messages that can be conveyed (maximum-rate steganography), and also must be able to produce a signal in the set given its label, and vice versa 1 . In a recent paper [5] we showed that Slepian's variant I permutation codes [6] implement maximum-rate perfect steganography if the steganographic detector only examines first-order statistics (or if the host is memoryless). In the light of the discussion above, it follows that Slepian's variant I permutation codes must also be central to implementing minimum-distortion perfect counterforensics when the forensic detector only examines first-order statistics.…”

How to (possibly) foil multimedia security?

“…Equivalently, the so-called embedding distortion must be bounded in expectation or deterministically, i.e. y − x be easily achieved by partitioning x into subvectors containing values within close vicinity of each other, as described in [1]; partitioning will decrease the embedding distortion but also the embedding rate. However, the rate-distortion tradeoff achieved through partitioning is near optimal [2].…”

“…• In digital steganography the adversary is a warden who intercepts a signal sent between two communicating parties and tries to ascertain whether it carries hidden information or not 1 . This operation is usually called steganalysis.…”

“…The second question has become the subject of intense activity halfway through the last decade with the advent of the field of digital forensics, and it has been labeled counterforensics. Only recently [1], [2], [3] it has been realized that the very same codes which were originally proposed by Slepian in 1965 for the scenario of communication through a noisy channel, are in fact the theoretical and practical optimum solution to canonical problems both in steganography and counterforensics.…”