Impact of rounding error on spread spectrum fingerprinting scheme

In spread spectrum fingerprinting, it has been considered that the strength of the embedded signal is reduced to 1/c of its original value when c copies are averaged by colluders. In this study, we analyze the model of the averaging attack by considering quantization that causes nonlinear changes in the fingerprint sequence. Our detailed analysis reveals that the attenuation of the signal energy strongly depends on the quantization performed during the embedding and averaging stages. We estimate the actual attenuation factor from the perspective of a stochastic model in the spatial domain and derive an attenuation factor that differs considerably from the conventional one. Our simulation result indicates that the actual attenuation factor is classified into the best and worst cases from the detector's perspective. Furthermore, we demonstrate that colluders can select the worst case by comparing their fingerprinted copies. A countermeasure for preventing the worst-case scenario is also proposed in this paper.