Designs, Codes and Cryptography

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

Symmetric Tardos fingerprinting codes for arbitrary alphabet sizes

  • Boris Škorić
  • Stefan Katzenbeisser
  • Mehmet U. Celik
Article

Abstract

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 c0, to withstand collusion attacks of up to c0 colluders. This improves Tardos’ construction by a factor of 10. Furthermore, invoking the Central Limit Theorem in the case of sufficiently large c0, 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.

Keywords

Traitor tracing Collusion resistance Fingerprint Watermark Copyright protection 

AMS Classification

94B60 

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Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

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

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