Block QIM Watermarking Games

Abstract

While binning is a fundamental approach to blind data embedding and watermarking, an attacker may devise various strategies to reduce the effectiveness of practical binning schemes. The problem analyzed in this paper is design of worst-case noise distributions against L-dimensional lattice Quantization Index Modulation (QIM) watermarking codes. The cost functions considered are (1) probability of error of the maximum-likelihood decoder, and (2) the more tractable Bhattacharyya upper bound on error probability, which is tight at low embedding rates. Both problems are addressed under the following constraints on the attacker's strategy: the noise is independent of the marked signal, blockwise memoryless with block length L, and may not exceed a specified quadratic-distortion level. The embedder's quadratic distortion is limited as well. Three strategies are considered for the embedder: optimization of the lattice inflation parameter (aka Costa parameter), dithering, and randomized lattice rotation. Critical in this analysis are the symmetry properties of QIM nested lattices and convexity properties of probability of error and related functionals of the noise distribution. We derive the minmax optimal embedding and attack strategies and obtain explicit solutions as well as numerical solutions for the worst-case noise. The role of the attacker's memory is investigated; in particular, we demonstrate the remarkable effectiveness of impulsive-noise attacks as L increases. The formulation proposed in this paper is also used to evaluate the capacity of lattice QIM under worst-noise conditions.

Security of Lattice-Based Data Hiding Against the Watermarked-Only Attack

“…A possible improvement using permutations was briefly considered in Section VII, but dither estimation attacks still seem to be possible, at least with low-dimensional lattices. A new strategy, recently proposed in [39], is the application of secret rotations to the embedding lattice. This approach, in conjunction with permutations, still keeps the structure of the codebook (which is desirable from an implementation point of view) while increasing its a priori entropy.…”

“…If the covariance matrix of the estimation error is given by , then it is immediate to upperbound its entropy by (37) Furthermore, note that (38) since is a function of the observations. Thus (39) where the second inequality follows from the fact that …”

Security of Lattice-Based Data Hiding Against the Known Message Attack

“…If the covariance matrix of the estimation error is given by , then it is immediate to upperbound its entropy by (37) Furthermore, note that (38) since is a function of the observations. Thus (39) where the second inequality follows from the fact that ([6] Theorem 16.8.4). Let us define the variance per dimension of the estimation error as .…”

Optimal watermark power and host samples allocation under random gain attack

“…Among different types of watermarking methods, quantization index modulation (QIM) is one of the most popular techniques due to its lossless perfonnance with lattice-based codebooks. As a matter of fact, several optimized QIM watennarking schemes, namely asymptotically optimal scalar quantizers for watermark detection [1], distortion-compensated lat tice QIM using nearly spherical Voronoi cells for asymptotically capacity-achieving [2], block QIM watermarking game [3], minmax strategies subjects to attacker's memory [4] and several other solutions are proposed. Since watennarking on compressed host data is highly demanding in recent times, optimization in the context of joint watennarking and compression (JWC) also draws attention to research community.…”