Short collusion-secure fingerprint codes against three pirates

In this article, we propose a new construction of probabilistic collusion-secure fingerprint codes against up to three pirates and give a theoretical security evaluation. Our pirate tracing algorithm combines a scoring method analogous to Tardos codes (J. ACM, 2008) with an extension of parent search techniques of some preceding 2-secure codes. Numerical examples show that our code lengths are significantly shorter than (about 30% to 40% of) the shortest known c-secure codes by Nuida et al. (Des. Codes Cryptogr., 2009) with c = 3. Some preliminary proposal for improving efficiency of our tracing algorithm is also given

Gossip Codes for Fingerprinting: Construction, Erasure Analysis and Pirate Tracing

This work presents two new construction techniques for q-ary Gossip codes from tdesigns and Traceability schemes. These Gossip codes achieve the shortest code length specified in terms of code parameters and can withstand erasures in digital fingerprinting applications. This work presents the construction of embedded Gossip codes for extending an existing Gossip code into a bigger code. It discusses the construction of concatenated codes and realisation of erasure model through concatenated codes.Comment: 28 page

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

A Robust Distortion Minimization Fingerprinting Technique for Relational DatabaseÂ

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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

Making Collusion-Secure Codes (More) Robust against Bit Erasure

A collusion-secure code is called robust if it is secure against erasure of a limited number of undetectable bits, in addition to collusion attacks under Marking Assumption. In this article, we propose the first general conversion method of (non-robust) $c$-secure codes to robust $c$-secure codes. Also, the same method amplifies robustness of given robust $c$-secure codes. By applying our conversion to $c$-secure codes given by Nuida et al. (AAECC 2007), we present robust $c$-secure codes with code length of order $\Theta(c^2 \log^2 c)$ with respect to $c$. This code length improves preceding results by Sirvent (WCC 2007) and by Boneh and Naor (ACM CCS 2008) and is close to the one by Billet and Phan (ICITS 2008), although our construction is based on a weaker assumption than those preceding results. As an application, applying our resulting code to construction by Boneh and Naor also improves their traitor tracing scheme against imperfect decoders in efficiency of both key sizes and pirate tracing procedure