Fingerprinting with Minimum Distance Decoding

This work adopts an information theoretic framework for the design of collusion-resistant coding/decoding schemes for digital fingerprinting. More specifically, the minimum distance decision rule is used to identify 1 out of t pirates. Achievable rates, under this detection rule, are characterized in two distinct scenarios. First, we consider the averaging attack where a random coding argument is used to show that the rate 1/2 is achievable with t=2 pirates. Our study is then extended to the general case of arbitrary $t$ highlighting the underlying complexity-performance tradeoff. Overall, these results establish the significant performance gains offered by minimum distance decoding as compared to other approaches based on orthogonal codes and correlation detectors. In the second scenario, we characterize the achievable rates, with minimum distance decoding, under any collusion attack that satisfies the marking assumption. For t=2 pirates, we show that the rate $1-H(0.25)\approx 0.188$ is achievable using an ensemble of random linear codes. For $t\geq 3$, the existence of a non-resolvable collusion attack, with minimum distance decoding, for any non-zero rate is established. Inspired by our theoretical analysis, we then construct coding/decoding schemes for fingerprinting based on the celebrated Belief-Propagation framework. Using an explicit repeat-accumulate code, we obtain a vanishingly small probability of misidentification at rate 1/3 under averaging attack with t=2. For collusion attacks which satisfy the marking assumption, we use a more sophisticated accumulate repeat accumulate code to obtain a vanishingly small misidentification probability at rate 1/9 with t=2. These results represent a marked improvement over the best available designs in the literature.Comment: 26 pages, 6 figures, submitted to IEEE Transactions on Information Forensics and Securit

A new fingerprint design using optical orthogonal codes

Digital fingerprinting has been proposed to restrict illegal distribution of digital media, where every piece of media has a unique fingerprint as an identifying feature that can be traceable. However, fingerprint systems are vulnerable when multiple users form collusion by combining their copies to create a forged copy. The collusion is modeled as an average linear attack, where multiple weighted copies are averaged and the Gaussian noise is then added to the averaged copy. In this thesis, a new fingerprint design with robustness to collusion is proposed, which is to accommodate more users and parameters than other existing fingerprint designs. A base matrix is constructed by cyclic shifts of binary sequences in an optical orthogonal code and then extended by a Hadamard matrix. Finally, each column of the resulting matrix is used as a fingerprint. The focused detection is used to determine whether a user is innocent or guilty in average linear attacks. Simulation results show that the performance of our new fingerprint design is comparable to that of orthogonal and simplex fingerprints