Digital Watermarking under a Filtering and Additive Noise Attack Condition

Abstract

We consider a private zero-bit watermark (WM) system in which an unauthorized removal of the WM is restricted by a linear filtering of the watermarked message combined with additive noise attack. It is assumed that a WM detector knows both the original cover message (CM) and the pulse (or frequency) response of the attack filter. The formulas to calculate the WM-missing and WM-false alarm probabilities are developed and proved. We conclude that whenever some filtering of the watermarked message is yet acceptable with respect to CM quality then there results in a degradation of the WM system even if the designer of the WM uses an optimal signal. This fact is different than most that can be found at current WM literature. The main properties of a WM system under a filtering and additive noise attack condition are confirmed by simulations of the watermarked images.