Asymptotic channel capacity of collusion resistant watermarking for non-binary alphabets

1. originalcontent originalcontent watermarked content unique watermark unique watermark watermark detector watermark embedding Asymptotic channel capacity of collusion resistant watermarking for non-binary alphabets ir. Dion Boesten, dr. Boris Škorić Introduction Forensic watermarking is a technique to combat the unauthorized distribution of digital content. Each copy is embedded with an imperceptible and unique watermark. The main challenge in this area is to create codes that are resistant to collusion attacks. In a collusion attack a group of users (pirates) compare their copies and try to create an untraceable copy. Information theory can provide a lower bound on the required code length of a reliable collusion resistant code. • Channel capacity • The mutual information measures how much information reveals about the identity of the pirates (equivalent with ) • The channel capacity is derived as the optimal value of a max-min game: • Asymptotic solution () • Binary case was solved by Huang and Moulin[2010]: • Non-binary case was solved by us: Forensic watermarking • Bias based codes • Code generation • Bias vectors are drawn from a distribution • Codeword symbol is generated stochasticallly using bias : • Attack • Pirates choose one of the allowed symbols in each segment • By the Marking Assumption they cannot modify a segment in which they all received the same symbol • Accusation • An accusation algorithm compares the detected watermark with the matrix to produce candidate coalitions. This is most often done by assigning scores to individual users and then applying a threshold procedure (Tardos). • Attack channel • Optimal attack is segment independent and can be seen as a noisy communication channel • counts the number of symbols that the pirates received • Channel output is generated stochastically: pirate attack strategy counter variable output symbol pirate attack m content segments biases bias vectors code matrix X • Proof outline • Sion’s Theorem: • Continuum approximation of the strategy: • Taylor of around and expanding the payoff function yields a result containing the Fisher Information of conditioned on . This result can also be expressed as where is the Jacobian matrix . • We use the inequality and topological properties of the mapping to bound • Finally we identify a which achieves this lower bound. Discussion The fingerprinting capacity is an increasing function of . Hence it makes sense to switch to higher alphabets if the embedding scheme allows this. nusers c pirates watermark after attack allowed attack symbols