A Higher Order Analysis of the Joint Capacity of Digital FIngerprinting Codes against the Interleaving Attack
A Higher Order Analysis of the Joint Capacity of Digital FIngerprinting Codes against the Interleaving Attack
复制标题
数字指纹码抗交织攻击联合能力的高阶分析
DOI：
10.1145/2909827.2930788
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发表时间：
2016
期刊：
影响因子：
--
通讯作者：
Hiroki Koga and Kaoru Itabashi
中科院分区：
文献类型：
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作者：
M. Murao;K. Nakago;M. Hajdusek and S. Nakayama;Jesper Jansson;Hiroki Koga and Kaoru Itabashi
数字指纹代码嵌入到许可的数字内容中，以防止共谋者非法分发。通常要求数字指纹代码能够高概率地指定部分（或全部）共谋者生成盗版副本。在本文中，我们评估了数字指纹代码对抗共谋者交错攻击的联合能力C(PINT)。最近，Laarhoven 证明，对于足够大的 c，C(PINT) = 1.1604/(2c2ln 2)。然而，该公式包含数值优化，对于较小的 c 值来说，并不是容量 C(PINT) 的良好近似值。在本文中，我们获得了两个序列，分别产生不同的 C(PINT) 上限和下限，这两个序列在较大的 c 范围内给出了 C(PINT) 的相当好的近似值。上限和下限是通过使用 Furon 和 Pérez-Freire [8] 指出的泰勒展开式以及对 l≥2 均值周围二项式分布的 l 阶矩的分析来获得的。特别是，下界给出了不同范围的 c2C(PINT) 的近似值。
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 capacityC(PINT) of the digital fingerprinting code against the interleaving attack byccolluders. Quite recently, Laarhoven shows thatC(PINT) = 1.1604/(2c2ln 2) for sufficiently largec. However, this formula includes numerical optimization and is not a good approximation of the capacityC(PINT) for small values ofc. In this paper we obtain two series that yield various upper and lower bounds ofC(PINT), respectively, which give fairly well approximation ofC(PINT) for a wide range ofc. 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 ofc2C(PINT) for various ranges ofc.