Secure watermark detection with nonparametric decision boundaries

Abstract

In this paper we will,address the problem of constructing a nonparameteric decision boundary for watermark detection. Most curre nt watermarking algorithms have a parametric decision boundary that can be undone if the pirate has unlimited access to the detector. In this work we propose a fractal decision boundary which can not be estimated. That boundary is obtained by processing the decision boundary corresponding to the underlying watermarking algorithm. The performance of the new technique is essenti ally similar to any watennarking algorithm from which it is derived.

Noniterative Algorithms for Sensitivity Analysis Attacks

“…In the same paper, the authors recommend processing of the detection boundary to make it fractal-like. This is addressed in another paper by the same authors [5]. According to [5], this new boundary cannot be reliably estimated because it is nonparametric.…”

“…Finally, the detection coefficients, t(s, w) and t(ŝ, w) (see (5)), corresponding to the original unwatermarked signal s and the estimated signalŝ are denoted by d s and dŝ, respectively. The algorithm of Section IV-B was modified as described in Section VII and used to attack these images.…”

“…When µ = 2, the GGD detector is a detector equivalent to the simple correlation detector in (5). The test statistic of (5) is multiplied by 2 and the energy term w 2 is subtracted:…”

“…Sensitivity analysis attacks have been previously addressed by Cox and Linnartz in [1], by Linnartz and Van Dijk [2], by Kalker, Linnartz, and Van Dijk [3], by Tewfik and Mansour [5] and [6], and by…”

Counteracting Oracle attacks

“…If, at the detection, linear correlation is replaced by a quadratic one, more generally by a quadratic form, it is shown in [4] that the most favorable case of such an attack has O(N 2 ) computational complexity. In [11], a decision boundary with a fractal dimension has been exploited to obtain security. Here we are interested in a communication model for the oracle attack in the integrity watermarking case.…”