Watermarking of binary messages in conditions of an additive binary noise attack

We consider a private watermarking system (WM) for binary cover messages (CMs). The goal of an attacker is to render unable the WM-owner of WM detection without noticeable corruption of CMs. Here, we restrict the attacker's activity to modulo two addition of a binary noise sequence to the watermarked stegomessage (SM). The formulas for the probabilities of WM-missing and WM-false alarm are obtained. We prove that the WM procedure can be designed to be reliable without significant distortions and for medium length of CMs even in the case in which CMs are unknown by the WM detector.