Optimal Watermark Embedding and Detection Strategies Under Limited Detection Resources

TL;DR

This paper develops optimal watermark embedding and detection strategies under limited detection resources using an information-theoretic approach, addressing attack-free and attack scenarios with Gaussian covertext.

Contribution

It introduces asymptotically optimal decision regions and embedding rules for resource-limited detection, including strategies for Gaussian covertext and adversarial attacks.

Findings

Optimal decision regions and embedding rules are derived.

Proposed strategies outperform linear embedding in exponential decay rate.

Results extend to various attack models, identifying worst-case channels.

Abstract

An information-theoretic approach is proposed to watermark embedding and detection under limited detector resources. First, we consider the attack-free scenario under which asymptotically optimal decision regions in the Neyman-Pearson sense are proposed, along with the optimal embedding rule. Later, we explore the case of zero-mean i.i.d. Gaussian covertext distribution with unknown variance under the attack-free scenario. For this case, we propose a lower bound on the exponential decay rate of the false-negative probability and prove that the optimal embedding and detecting strategy is superior to the customary linear, additive embedding strategy in the exponential sense. Finally, these results are extended to the case of memoryless attacks and general worst case attacks. Optimal decision regions and embedding rules are offered, and the worst attack channel is identified.