105 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
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
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
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
Asymptotics of Fingerprinting and Group Testing: Capacity-Achieving Log-Likelihood Decoders
We study the large-coalition asymptotics of fingerprinting and group testing,
and derive explicit decoders that provably achieve capacity for many of the
considered models. We do this both for simple decoders (fast but suboptimal)
and for joint decoders (slow but optimal), and both for informed and uninformed
settings.
For fingerprinting, we show that if the pirate strategy is known, the
Neyman-Pearson-based log-likelihood decoders provably achieve capacity,
regardless of the strategy. The decoder built against the interleaving attack
is further shown to be a universal decoder, able to deal with arbitrary attacks
and achieving the uninformed capacity. This universal decoder is shown to be
closely related to the Lagrange-optimized decoder of Oosterwijk et al. and the
empirical mutual information decoder of Moulin. Joint decoders are also
proposed, and we conjecture that these also achieve the corresponding joint
capacities.
For group testing, the simple decoder for the classical model is shown to be
more efficient than the one of Chan et al. and it provably achieves the simple
group testing capacity. For generalizations of this model such as noisy group
testing, the resulting simple decoders also achieve the corresponding simple
capacities.Comment: 14 pages, 2 figure
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
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
On the Saddle-point Solution and the Large-Coalition Asymptotics of Fingerprinting Games
We study a fingerprinting game in which the number of colluders and the
collusion channel are unknown. The encoder embeds fingerprints into a host
sequence and provides the decoder with the capability to trace back pirated
copies to the colluders.
Fingerprinting capacity has recently been derived as the limit value of a
sequence of maximin games with mutual information as their payoff functions.
However, these games generally do not admit saddle-point solutions and are very
hard to solve numerically. Here under the so-called Boneh-Shaw marking
assumption, we reformulate the capacity as the value of a single two-person
zero-sum game, and show that it is achieved by a saddle-point solution.
If the maximal coalition size is k and the fingerprinting alphabet is binary,
we show that capacity decays quadratically with k. Furthermore, we prove
rigorously that the asymptotic capacity is 1/(k^2 2ln2) and we confirm our
earlier conjecture that Tardos' choice of the arcsine distribution
asymptotically maximizes the mutual information payoff function while the
interleaving attack minimizes it. Along with the asymptotic behavior, numerical
solutions to the game for small k are also presented.Comment: submitted to IEEE Trans. on Information Forensics and Securit
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
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
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