Symmetric Tardos fingerprinting codes for arbitrary alphabet sizes

  • Authors:
  • Boris Škorić;Stefan Katzenbeisser;Mehmet U. Celik

  • Affiliations:
  • Information and System Security, Philips Research Europe, Eindhoven, The Netherlands 5656AA;Information and System Security, Philips Research Europe, Eindhoven, The Netherlands 5656AA;Information and System Security, Philips Research Europe, Eindhoven, The Netherlands 5656AA

  • Venue:
  • Designs, Codes and Cryptography
  • Year:
  • 2008

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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 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.