A simple tracing algorithm for binary fingerprinting code under averaging attack

When a binary fingerprinting codeword is embedded into digital contents using a spread-spectrum (SS) watermarking scheme, the marking assumption is not valid anymore because it is difficult for colluders to perform the symbol-wise attack for their codewords. As discussed in the SS-type fingerprinting schemes, veraging their copies is the cost-effective attack from the signal processing point of view. In this paper, we propose an optimal detector under the averaging attack and addition of white Gaussian noise. If the detector knows the number of colluders in advance, it first estimates the variance of additive noise, and then calculates the correlation scores using a log-likelihood-based approach. However, the number of colluders is not given in a real situation. We discover in this study that the characteristic of parameters for generating codewords enables us to eliminate the number of colluders as well as the estimation of the variance of noise at the calculation of correlation score, and propose a simplified detector by analyzing the scoring function in the optimal detector. We evaluate the performance of the simplified detector through simulation using not only codewords, but also a digital image.