Designs, Codes and Cryptography

, Volume 71, Issue 1, pp 83–103 | Cite as

Optimal symmetric Tardos traitor tracing schemes

  • Thijs Laarhoven
  • Benne de Weger
Open Access


For the Tardos traitor tracing scheme, we show that by combining the symbol-symmetric accusation function of Škorić et al. 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 Škorić et al. 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 Nuida et al.


Traitor tracing schemes Fingerprinting codes Watermarking 

Mathematics Subject Classification (2000)

68P30 94B60 



The authors would like to thank Boris Škorić, Jeroen Doumen and Peter Roelse for many useful discussions and valuable comments. We are also grateful to the anonymous reviewers for their valuable comments.

Open Access

This article is distributed under the terms of the Creative Commons Attribution License which permits any use, distribution, and reproduction in any medium, provided the original author(s) and the source are credited.


  1. 1.
    Tardos G.: Optimal probabilistic fingerprint codes. In: Proceedings of the Thirty-Fifth Annual ACM Symposium on Theory of Computing, STOC ’03, pp. 116–125. ACM, New York, NY, USA (2003). doi: 10.1145/780542.780561.
  2. 2.
    Amiri E., Tardos G.: High rate fingerprinting codes and the fingerprinting capacity. In: Proceedings of the Twentieth Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 336–345 (2009).Google Scholar
  3. 3.
    Huang Y.W., Moulin P.: Saddle-point solution of the fingerprinting capacity game under the marking assumption. In: Proceedings of the 2009 IEEE International Conference on Symposium on Information Theory, vol. 4, pp. 2256–2260 (2009).
  4. 4.
    Nuida K., Fujitsu S., Hagiwara M., Kitagawa T., Watanabe H., Ogawa K., Imai H.: An improvement of discrete Tardos fingerprinting codes. Des. Codes Cryptogr. 52, 339–362 (2009). doi: 10.1007/s10623-009-9285-z CrossRefzbMATHMathSciNetGoogle Scholar
  5. 5.
    Skoric B., Vladimirova T., Celik M., Talstra J.: Tardos fingerprinting is better than we thought. IEEE Trans. Inf. Theory 54(8), 3663–3676 (2008). doi: 10.1109/TIT.2008.926307 CrossRefMathSciNetGoogle Scholar
  6. 6.
    Blayer O., Tassa T.: Improved versions of Tardos fingerprinting scheme. Des. Codes Cryptogr. 48, 79–103 (2008)CrossRefzbMATHMathSciNetGoogle Scholar
  7. 7.
    Skoric B., Katzenbeisser S., Celik M.: Symmetric Tardos fingerprinting codes for arbitrary alphabet sizes. Des. Codes Cryptogr. 46, 137–166 (2008). doi: 10.1007/s10623-007-9142-x CrossRefMathSciNetGoogle Scholar

Copyright information

© The Author(s) 2012

Authors and Affiliations

  1. 1.Eindhoven University of TechnologyEindhovenThe Netherlands

Personalised recommendations