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. previously showed that a symbol-symmetric score function leads to shorter codes, while obtained the optimal distribution functions for arbitrary coalition sizes. Later, 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 and give a comparison of the estimated lengths of the fingerprinting codes for each of these distributions.
Over the last ten years, improvements to the Tardos scheme have lead to a significant decrease in the code length parameter @math . We previously showed @cite_7 that combining the symbol-symmetric score function of S kori ' c et al @cite_4 with the improved analysis of Blayer and Tassa @cite_11 leads to an asymptotic code length constant of @math for large @math . For small coalitions, @cite_3 showed that even smaller values @math can be obtained by combining the symmetric score function with the optimized, discrete distribution functions previously obtained by @cite_0 . For large @math , this lead to an asymptotic code length constant of about @math .
@cite_4 @cite_7 @cite_3 @cite_0 @cite_11
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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 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. 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. previously showed that a symbol-symmetric score function leads to shorter codes, while obtained the optimal distribution functions for arbitrary coalition sizes. Later, 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 and give a comparison of the estimated lengths of the fingerprinting codes for each of these distributions.