Optimal sequential fingerprinting: Wald vs. Tardos

We study sequential collusion-resistant fingerprinting, where the fingerprinting code is generated in advance but accusations may be made between rounds, and show that in this setting both the dynamic Tardos scheme and schemes building upon Wald's sequential probability ratio test (SPRT) are asymptotically optimal. We further compare these two approaches to sequential fingerprinting, highlighting differences between the two schemes. Based on these differences, we argue that Wald's scheme should in general be preferred over the dynamic Tardos scheme, even though both schemes have their merits. As a side result, we derive an optimal sequential group testing method for the classical model, which can easily be generalized to different group testing models.Comment: 12 pages, 10 figure

A capacity-achieving simple decoder for bias-based traitor tracing schemes

We investigate alternative suspicion functions for bias-based traitor tracing schemes, and present a practical construction of a simple decoder that attains capacity in the limit of large coalition size c. We derive optimal suspicion functions in both the Restricted- Digit Model and the Combined-Digit Model. These functions depend on information that is usually not available to the tracer – the attack strategy or the tallies of the symbols received by the colluders. We discuss how such results can be used in realistic contexts. We study several combinations of coalition attack strategy versus suspicion function optimized against some attack (another attack or the same). In many of these combinations the usual codelength scaling $\ell \propto c^2$ changes to a lower power of $c$, e.g., $c^{3/2}$. We find that the interleaving strategy is an especially powerful attack. The suspicion function tailored against interleaving is the key ingredient of the capacity-achieving construction

Capacities and Capacity-Achieving Decoders for Various Fingerprinting Games

Combining an information-theoretic approach to fingerprinting with a more constructive, statistical approach, we derive new results on the fingerprinting capacities for various informed settings, as well as new log-likelihood decoders with provable code lengths that asymptotically match these capacities. The simple decoder built against the interleaving attack is further shown to achieve the simple capacity for unknown attacks, and is argued to be an improved version of the recently proposed decoder of Oosterwijk et al. With this new universal decoder, cut-offs on the bias distribution function can finally be dismissed. Besides the application of these results to fingerprinting, a direct consequence of our results to group testing is that (i) a simple decoder asymptotically requires a factor 1.44 more tests to find defectives than a joint decoder, and (ii) the simple decoder presented in this paper provably achieves this bound.Comment: 13 pages, 2 figure

A Capacity-Achieving Simple Decoder for Bias-Based Traitor Tracing Schemes

We investigate alternative suspicion functions for bias-based traitor tracing schemes, and present a practical construction of a simple decoder that attains capacity in the limit of large coalition size $c$. We derive optimal suspicion functions in both the Restricted-Digit Model and the Combined-Digit Model. These functions depend on information that is usually not available to the tracer -- the attack strategy or the tallies of the symbols received by the colluders. We discuss how such results can be used in realistic contexts. We study several combinations of coalition attack strategy versus suspicion function optimized against some attack (another attack or the same). In many of these combinations the usual codelength scaling $\ell \propto c^2$ changes to a lower power of $c$, e.g. $c^{3/2}$. We find that the interleaving strategy is an especially powerful attack. The suspicion function tailored against interleaving is the key ingredient of the capacity-achieving construction

The Holey Grail: A special score function for non-binary traitor tracing

We study collusion-resistant traitor tracing in the simple decoder approach, i.e. assignment of scores for each user separately. We introduce a new score function for non-binary bias-based traitor tracing. It has three special properties that have long been sought after: (i) The expected score of an innocent user is zero in each content position. (ii) The variance of an innocent user\u27s score is~1 in each content position. (iii) The expectation of the coalition\u27s score does not depend on the collusion strategy. We also find a continuous bias distribution that optimizes the asymptotic (large coalition) performance. In the case of a binary alphabet our scheme reduces exactly to the symmetrized Tardos traitor tracing system. Unfortunately, the asymptotic fingerprinting rate of our new scheme decreases with growing alphabet size. We regret to inform you that this grail has holes

Tardos fingerprinting is better than we thought

We review the fingerprinting scheme by Tardos and show that it has a much better performance than suggested by the proofs in Tardos' original paper. In particular, the length of the codewords can be significantly reduced. First we generalize the proofs of the false positive and false negative error probabilities with the following modifications: (1) we replace Tardos' hard-coded numbers by variables and (2) we allow for independently chosen false positive and false negative error rates. It turns out that all the collusion-resistance properties can still be proven when the code length is reduced by a factor of more than 2. Second, we study the statistical properties of the fingerprinting scheme, in particular the average and variance of the accusations. We identify which colluder strategy forces the content owner to employ the longest code. Using a gaussian approximation for the probability density functions of the accusations, we show that the required false negative and false positive error rate can be achieved with codes that are a factor 2 shorter than required for rigid proofs. Combining the results of these two approaches, we show that the Tardos scheme can be used with a code length approximately 5 times shorter than in the original construction.Comment: Modified presentation of result