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 can be combined with the optimized score functions of 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.
Even more recently, @cite_9 studied the score function used in Tardos' static scheme, and showed how to choose better score functions when the pirate attack is known. In one particular case, they came across a score function that turned out to work well against attack. More precisely, for asymptotically large @math , they showed that this score function achieves capacity, i.e., attains the known exact lower bound on the code length of @math in the binary setting @cite_12 . So for large @math , using this new score function in the static setting may lead to a decrease in the length of the code of almost $60
@cite_9 @cite_12
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We study the Tardos' probabilistic fingerprinting scheme and show that its codeword length may be shortened by a factor of approximately 4. We achieve this by retracing Tardos' analysis of the scheme and extracting from it all constants that were arbitrarily selected. We replace those constants with parameters and derive a set of inequalities that those parameters must satisfy so that the desired security properties of the scheme still hold. Then we look for a solution of those inequalities in which the parameter that governs the codeword length is minimal. A further reduction in the codeword length is achieved by decoupling the error probability of falsely accusing innocent users from the error probability of missing all colluding pirates. Finally, we simulate the Tardos scheme and show that, in practice, one may use codewords that are shorter than those in the original Tardos scheme by a factor of at least 16. For the Tardos traitor tracing scheme, we show that by combining the symbol-symmetric accusation function of ? with the improved analysis of Blayer and Tassa we get further improvements. Our construction gives codes that are up to four times shorter than Blayer and Tassa's, and up to two times shorter than the codes from ? 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 We study the asymptotic-capacity-achieving score function that was recently proposed by for bias-based traitor tracing codes. For the bias function, we choose the Dirichlet distribution with a cutoff. Using Bernstein's inequality and Bennett's inequality, we upper bound the false-positive and false-negative error probabilities. From these bounds we derive sufficient conditions for the scheme parameters. We solve these conditions in the limit of large coalition size c0 and obtain asymptotic solutions for the cutoff, the sufficient code length, and the corresponding accusation threshold. We find that the code length converges to its asymptote approximately as c0?1 2 @math , which is faster than the c0?1 3 @math of Tardos' score function. MSC:94B60 We investigate alternative suspicion functions for Tardos traitor tracing schemes. In the simple decoder approach (computation of a score for every user independently) we derive suspicion functions that optimize a performance indicator related to the sufficient code length l in the limit of large coalition size c. Our results hold for the Restricted-Digit Model as well as the Combined-Digit Model. The scores depend on information that is usually not available to the tracer -- 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 scaling l c2 is replaced by a lower power of c, e.g. c3 2. We find that the interleaving strategy is an especially powerful attack, and the suspicion function tailored against interleaving is effective against all considered attacks.