23 research outputs found
Discrete Distributions in the Tardos Scheme, Revisited
The Tardos scheme is a well-known traitor tracing scheme to protect
copyrighted content against collusion attacks. The original scheme contained
some suboptimal design choices, such as the score function and the distribution
function used for generating the biases. Skoric et al. previously showed that a
symbol-symmetric score function leads to shorter codes, while Nuida et al.
obtained the optimal distribution functions for arbitrary coalition sizes.
Later, Nuida et al. showed that combining these results leads to even shorter
codes when the coalition size is small. We extend their analysis to the case of
large coalitions and prove that these optimal distributions converge to the
arcsine distribution, thus showing that the arcsine distribution is
asymptotically optimal in the symmetric Tardos scheme. We also present a new,
practical alternative to the discrete distributions of Nuida et al. and give a
comparison of the estimated lengths of the fingerprinting codes for each of
these distributions.Comment: 5 pages, 2 figure
Enhanced blind decoding of Tardos codes with new map-based functions
This paper presents a new decoder for probabilistic binary traitor tracing
codes under the marking assumption. It is based on a binary hypothesis testing
rule which integrates a collusion channel relaxation so as to obtain numerical
and simple accusation functions. This decoder is blind as no estimation of the
collusion channel prior to the accusation is required. Experimentations show
that using the proposed decoder gives better performance than the well-known
symmetric version of the Tardos decoder for common attack channels
Dynamic Traitor Tracing Schemes, Revisited
We revisit recent results from the area of collusion-resistant traitor
tracing, and show how they can be combined and improved to obtain more
efficient dynamic traitor tracing schemes. In particular, we show how the
dynamic Tardos scheme of Laarhoven et al. can be combined with the optimized
score functions of Oosterwijk et al. to trace coalitions much faster. If the
attack strategy is known, in many cases the order of the code length goes down
from quadratic to linear in the number of colluders, while if the attack is not
known, we show how the interleaving defense may be used to catch all colluders
about twice as fast as in the dynamic Tardos scheme. Some of these results also
apply to the static traitor tracing setting where the attack strategy is known
in advance, and to group testing.Comment: 7 pages, 1 figure (6 subfigures), 1 tabl
Dynamic Traitor Tracing for Arbitrary Alphabets: Divide and Conquer
We give a generic divide-and-conquer approach for constructing
collusion-resistant probabilistic dynamic traitor tracing schemes with larger
alphabets from schemes with smaller alphabets. This construction offers a
linear tradeoff between the alphabet size and the codelength. In particular, we
show that applying our results to the binary dynamic Tardos scheme of Laarhoven
et al. leads to schemes that are shorter by a factor equal to half the alphabet
size. Asymptotically, these codelengths correspond, up to a constant factor, to
the fingerprinting capacity for static probabilistic schemes. This gives a
hierarchy of probabilistic dynamic traitor tracing schemes, and bridges the gap
between the low bandwidth, high codelength scheme of Laarhoven et al. and the
high bandwidth, low codelength scheme of Fiat and Tassa.Comment: 6 pages, 1 figur
Asymptotically false-positive-maximizing attack on non-binary Tardos codes
We use a method recently introduced by Simone and Skoric to study accusation
probabilities for non-binary Tardos fingerprinting codes. We generalize the
pre-computation steps in this approach to include a broad class of collusion
attack strategies. We analytically derive properties of a special attack that
asymptotically maximizes false accusation probabilities. We present numerical
results on sufficient code lengths for this attack, and explain the abrupt
transitions that occur in these results
Efficient Probabilistic Group Testing Based on Traitor Tracing
Inspired by recent results from collusion-resistant traitor tracing, we
provide a framework for constructing efficient probabilistic group testing
schemes. In the traditional group testing model, our scheme asymptotically
requires T ~ 2 K ln N tests to find (with high probability) the correct set of
K defectives out of N items. The framework is also applied to several noisy
group testing and threshold group testing models, often leading to improvements
over previously known results, but we emphasize that this framework can be
applied to other variants of the classical model as well, both in adaptive and
in non-adaptive settings.Comment: 8 pages, 3 figures, 1 tabl
Optimal symmetric Tardos traitor tracing schemes
For the Tardos traitor tracing scheme, we show that by combining the
symbol-symmetric accusation function of Skoric et al. with the improved
analysis of Blayer and Tassa we get further improvements. Our construction
gives codes that are up to 4 times shorter than Blayer and Tassa's, and up to 2
times shorter than the codes from Skoric et al. Asymptotically, we achieve the
theoretical optimal codelength for Tardos' distribution function and the
symmetric score function. For large coalitions, our codelengths are
asymptotically about 4.93% of Tardos' original codelengths, which also improves
upon results from Nuida et al.Comment: 16 pages, 1 figur