Designs, Codes and Cryptography

, Volume 74, Issue 1, pp 75–111 | Cite as

Binary and \(q\)-ary Tardos codes, revisited



The Tardos code is a much studied collusion-resistant fingerprinting code, with the special property that it has asymptotically optimal length \(m\propto c_0^2\), where \(c_0\) is the number of colluders. In this paper we give alternative security proofs for the Tardos code, working with the assumption that the strongest coalition strategy is position-independent. We employ the Bernstein inequality and Bennett inequality instead of the typically used Markov inequality. This proof technique requires fewer steps and slightly improves the tightness of the bound on the false negative error probability. We present new results on code length optimization, for both small and asymptotically large coalition sizes.


Traitor tracing Tardos fingerprinting Collusion 

Mathematics Subject Classification




We thank Dion Boesten, Jeroen Doumen, Thijs Laarhoven, Antonino Simone, and Benne de Weger for useful discussions. We thank Wil Kortsmit for his help with numerical integrations. This research was funded by STW Sentinels (CREST project, 10518).


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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Eindhoven University of Technology EindhovenThe Netherlands

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