Designs, Codes and Cryptography

, Volume 46, Issue 2, pp 137–166 | Cite as

Symmetric Tardos fingerprinting codes for arbitrary alphabet sizes

  • Boris ŠkorićEmail author
  • Stefan Katzenbeisser
  • Mehmet U. Celik


Fingerprinting provides a means of tracing unauthorized redistribution of digital data by individually marking each authorized copy with a personalized serial number. In order to prevent a group of users from collectively escaping identification, collusion-secure fingerprinting codes have been proposed. In this paper, we introduce a new construction of a collusion-secure fingerprinting code which is similar to a recent construction by Tardos but achieves shorter code lengths and allows for codes over arbitrary alphabets. We present results for ‘symmetric’ coalition strategies. For binary alphabets and a false accusation probability \(\varepsilon_1\) , a code length of \(m\approx \pi^2 c_0^2\ln\frac{1}{\varepsilon_1}\) symbols is provably sufficient, for large c 0, to withstand collusion attacks of up to c 0 colluders. This improves Tardos’ construction by a factor of 10. Furthermore, invoking the Central Limit Theorem in the case of sufficiently large c 0, we show that even a code length of \(m\approx 1/2\pi^2 c_0^2\ln\frac{1}{\varepsilon_1}\) is adequate. Assuming the restricted digit model, the code length can be further reduced by moving from a binary alphabet to a q-ary alphabet. Numerical results show that a reduction of 35% is achievable for q = 3 and 80% for q = 10.


Traitor tracing Collusion resistance Fingerprint Watermark Copyright protection 

AMS Classification



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  1. Andrews G.E., Askey R., Roy R.: Special Functions. Encyclopedia of Mathematics and its Applications. Cambridge University Press (1999).Google Scholar
  2. Bazant M.Z.: Random walks and diffusion. Technical report, MIT Lecture notes, (2005). Accessed October 2007
  3. Boneh D., Shaw J. (1998). Collusion-secure fingerprinting for digital data. IEEE Trans. Inform. Theory 44(5): 1897–1905zbMATHCrossRefMathSciNetGoogle Scholar
  4. Chor B., Fiat A., Naor M., Pinkas B. (2000). Tracing traitors. IEEE Trans. Inform. Theory 46(3): 893–910zbMATHCrossRefGoogle Scholar
  5. Cox I.J., Miller M.L., Bloom J.A. (2002). Digital Watermarking. Morgan Kaufmann Publishers, San Francisco, CA, USAGoogle Scholar
  6. Devroye L.: Non-Uniform Random Variate Generation. Springer-Verlag (1986). Available online at
  7. Digital Cinema Initiatives, LLC. Digital cinema system specification v1.1. (2007). Accessed October 2007
  8. Hollmann H.D.L., van Lint J.H., Linnartz J-P., Tolhuizen L.M.G.M. (1998). On codes with the identifiable parent property. J. Comb. Theory 82: 472–479CrossRefGoogle Scholar
  9. Langelaar G.C., Setyawan I., Lagendijk R.L. (2000). Watermarking digital image and video data. IEEE SPMAG 17(5): 20–46Google Scholar
  10. Peikert C., Shelat A., Smith A.: Lower bounds for collusion-secure fingerprinting. In: Proceedings of the 14th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), pp. 472–478 (2003).Google Scholar
  11. Škorić B., Vladimirova T.U., Celik M., Talstra J.C.: Tardos fingerprinting is better than we thought. Technical report, Submitted to IEEE Trans. Inform. Theory. Preprint at arXiv repository, (2006).
  12. Staddon J.N., Stinson D.R., Wei R. (2001). Combinatorial properties of frameproof and traceability codes. IEEE Trans. Inform. Theory 47(3): 1042–1049zbMATHCrossRefMathSciNetGoogle Scholar
  13. Tardos G.: Optimal probabilistic fingerprint codes. In: Proceedings of the 35th Annual ACM Symposium on Theory of Computing (STOC), pp. 116–125 (2003).Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  • Boris Škorić
    • 1
    Email author
  • Stefan Katzenbeisser
    • 1
  • Mehmet U. Celik
    • 1
  1. 1.Information and System SecurityPhilips Research EuropeEindhovenThe Netherlands

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