Non-ambiguity of blind watermarking: a revisit with analytical resolution

Resistance to ambiguity attack is an important requirement for a secure digital rights management (DRM) system. In this paper, we revisit the non-ambiguity of a blind watermarking based on the computational indistinguishability between pseudo random sequence generator (PRSG) sequence ensemble and truly random sequence ensemble. Ambiguity attacker on a watermarking scheme, which uses a PRSG sequence as watermark, is viewed as an attacker who tries to attack a noisy PRSG sequence. We propose and prove the security theorem for binary noisy PRSG sequence and security theorem for general noisy PRSG sequence. It is shown that with the proper choice of the detection threshold Th = a √n (a is a normalized detection threshold; n is the length of a PRSG sequence) and n ⩾ 1.39 × m/a ² (m is the key length), the success probability of an ambiguity attack and the missed detection probability can both be made negligibly small thus non-ambiguity and robustness can be achieved simultaneously for both practical quantization-based and blind spread spectrum (SS) watermarking schemes. These analytical resolutions may be used in designing practical non-invertible watermarking schemes and measuring the non-ambiguity of the schemes. Supported by the National Natural Science Foundation of China (Grant Nos. 90604008, 60633030, 60403045), Natural Science Foundation of Guangdong Province (Grant No. 04009742) and the National Basic Research Program of China (Grant No. 2006CB303104)