33 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
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
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
Towards joint decoding of binary Tardos fingerprinting codes
The class of joint decoder of probabilistic fingerprinting codes is of utmost
importance in theoretical papers to establish the concept of fingerprint
capacity. However, no implementation supporting a large user base is known to
date. This article presents an iterative decoder which is, as far as we are
aware of, the first practical attempt towards joint decoding. The
discriminative feature of the scores benefits on one hand from the
side-information of previously accused users, and on the other hand, from
recently introduced universal linear decoders for compound channels. Neither
the code construction nor the decoder make precise assumptions about the
collusion (size or strategy). The extension to incorporate soft outputs from
the watermarking layer is straightforward. An extensive experimental work
benchmarks the very good performance and offers a clear comparison with
previous state-of-the-art decoders.Comment: submitted to IEEE Trans. on Information Forensics and Security. -
typos corrected, one new plot, references added about ECC based
fingerprinting code
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
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
BLIND DECODER FOR BINARY PROBABILISTIC TRAITOR TRACING CODES
This paper presents a new decoder for probabilistic binary traitor tracing codes which is based on classical hypothesis testing and estimation theory. This new decoder is blind, in the sense of ignoring a priori the collusion attack it is facing. It basically performs a joint estimation of the collusion channel and the probability that each user takes part in the collusion. The experimental results shown in the paper have been obtained with the classical Tardos code, although the proposed decoder works with arbitrary probabilistic binary codes. Another remarkable advantage of this blind decoder is its ability to successfully cope with collusion channels far more general than the classical Marking Assumption, including channels that produce erasures and random decoding errors. Index Terms â Traitor tracing, Tardos code, collusion channel estimation, likelihood ratio, optimal decoding
Asymptotics of Fingerprinting and Group Testing: Tight Bounds from Channel Capacities
In this work we consider the large-coalition asymptotics of various
fingerprinting and group testing games, and derive explicit expressions for the
capacities for each of these models. We do this both for simple decoders (fast
but suboptimal) and for joint decoders (slow but optimal).
For fingerprinting, we show that if the pirate strategy is known, the
capacity often decreases linearly with the number of colluders, instead of
quadratically as in the uninformed fingerprinting game. For many attacks the
joint capacity is further shown to be strictly higher than the simple capacity.
For group testing, we improve upon known results about the joint capacities,
and derive new explicit asymptotics for the simple capacities. These show that
existing simple group testing algorithms are suboptimal, and that simple
decoders cannot asymptotically be as efficient as joint decoders. For the
traditional group testing model, we show that the gap between the simple and
joint capacities is a factor 1.44 for large numbers of defectives.Comment: 14 pages, 6 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 â 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