Designs, Codes and Cryptography

, Volume 71, Issue 1, pp 83–103

Optimal symmetric Tardos traitor tracing schemes


  • Thijs Laarhoven
    • Eindhoven University of Technology
    • Eindhoven University of Technology

DOI: 10.1007/s10623-012-9718-y


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.

Copyright information

© The Author(s) 2012