19 research outputs found
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 β 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 changes to a lower power of , e.g., . 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 .
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 changes to a lower power of , e.g. . 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