A Higher Order Analysis of the Joint Capacity of Digital Fingerprinting Codes against the Interleaving Attack
Hiroki Koga, Itabashi Kaoru · 2016
Digital fingerprinting codes are embedded to licenced digital contents for preventing illegal distribution by colluders. Digital fingerprinting codes are usually required to have the ability to specify a part (or all) of the colluders with high probability who generate a pirated copy. In this paper we evaluate the joint capacity C(PINT) of the digital fingerprinting code against the interleaving attack by c colluders. Quite recently, Laarhoven shows that C(PINT) = 1.1604/(2c2 ln 2) for sufficiently large c. However, this formula includes numerical optimization and is not a good approximation of the capacity C(PINT) for small values of c. In this paper we obtain two series that yield various upper and lower bounds of C(PINT), respectively, which give fairly well approximation of C(PINT) for a wide range of c. The upper and the lower bounds are obtained by using the Taylor expansion indicated by Furon and Pérez-Freire [8] together with the analysis of the l-th moments of a binomial distribution around its mean for l≥2. In particular, the lower bounds give approximation of c2C(PINT) for various ranges of c.