7 research outputs found
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
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: 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
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