Symmetric Tardos fingerprinting codes for arbitrary alphabet sizes

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.