Estimation of Collusion Attack in Bias-based Binary Fingerprinting Code

An optimal detector known as MAP detector has been proposed for the probabilistic fingerprinting codes such as Tardos and Nuida codes. However, it needs two kinds of important information. One is the collusion strategy which is used at the generation of a pirated codeword from colluders' codewords, and the other is the number of colluders. In this study, we propose an estimator which outputs these two parameters from a pirated codeword. At the estimation, we measure a bias in the pirated codeword by observing the number of symbols '0' and '1', and compare with possible bias patterns calculated from collusion strategies and number of colluders. As a result of computer simulation, it is confirmed that a collusion strategy and number of colluders can be estimated with high probability. In addition, it is revealed that the traceability of the detector using the proposed estimator is extremely close to the optimal detector.