抗合谋攻击码的构造及其追踪算法设计

Constructing anti-collusion codes (t-ACCs in short) and designing their related tracing algorithms are not only the fundamental problems of Copyright Protection of multimedia contents, but also the important research topics of Combinatorial Design Theory, Graph Theory and Probability Theory. Both of t-separable codes (t-SCs in short) and t-expanded separable codes (t-ESCs in short) can be used as t-ACCs to resist collusion attacks when the number of colluders is less than or equal to t. The performance of t-ESC is weaker than that of t-SC due to its weaker requirements. During the project, we plan to take advantage of several structures of Combinatorial Design Theory (such as difference families, difference matrices, packings, projective spaces, affine spaces, generalized quadrangles and so on) and Graph Theory (such as bipartite graphs, tripartite graphs and so on) to construct t-SCs and t-ESCs respectively. Based on t-ACC, if the number of colluders is less than or equal to t, we can capture all of them easily by deterministic tracing algorithms. If the number of colluders is larger than t, we can not capture any colluder by these deterministic tracing algorithms. Furthermore, there always exists additional noise due to unintentional signal processing and/or intentional attacks to hinder the detection of the ACCs. We plan to propose probabilistic tracing algorithms based on Bayesian inference, which can extract as much information as possible from the underlying ACC and the pirate copies. We will carry on the numerical experiments using Markov chain Monte Carlo method to check whether these probabilistic tracing algorithms have good tracing abilities even if the number of colluders is larger than t, and can handle the additional noise due to the effect of compression and/or from an attack mounted by colluders, and compare whether our probabilistic tracing algorithms are better than the known tracing algorithms.

抗合谋攻击码的构造及其追踪算法的设计是多媒体文件版权保护领域研究的重点，也是组合设计理论、图论和概率论研究的重要内容。t-可分码和 t-扩展可分码虽然其构造方法和追踪算法都不相同，但是都可作为抗合谋攻击码来抵抗不大于t个合谋者的攻击（扩展可分码的抗攻击性能比可分码的抗攻击性能弱）。本项目拟利用差族、差矩阵、Packing、射影空间、仿射空间、广义四边形等组合结构和二部图、三部图等图论方面的知识分别来构造 t-可分码和 t-扩展可分码。考虑追踪算法时，由于多媒体文件在传输过程中，可能会遭受各种故意或无意噪音的干扰，并且参与合谋攻击的用户数是不确定的，当利用基于t-可分码等抗合谋攻击码的追踪算法时，一旦参与合谋攻击的用户数大于t 时，就不能追踪到任何一个参与合谋攻击的用户。本项目拟充分利用抗合谋攻击码的信息，运用贝叶斯推断，马尔可夫链方面的知识设计更实用的追踪算法。

本项目利用组合设计理论、图论和概率论方面的知识，侧重于对多媒体文件版权保护的核心问题，即抗合谋攻击码的构造及其追踪算法的设计，进行系统地研究，并得到如下结果：. 1) 估计出 t-(N, M, q) 可分码的上界, 并构造相应最优或好的 t-(N, M, q) 可分码的无穷类，其中 (t, N)=(2,2), (2,4), (3,3), (3,4);. 2) 估计出 t-(N, M, q) 扩展可分码（后改名为多媒体父辈认证码）的上界, 并构造相应最优或好的 t-(N, M, q) 扩展可分码的无穷类，其中 (t, N)=(3,2), (3,3), (3,4), (4,2);. 3) 对于其它多媒体文件保护环境，提出了两类新的抗合谋攻击码，即强可分码和强多媒体父辈认证码，并对它们展开了初步的研究。. 4) 利用最小角回归法设计了概率追踪算法。 通过仿真验证了该算法不仅可以抵抗用户数大于 t 的合谋攻击，同时还能抵抗各种故意或无意噪音的干扰。. 此外本项目也对与多媒体指纹码密切相关的、目前最热的编码缓存做了一定的前期研究工作，并得到了如下结果：. 1) 提出了一个组合结构，即放置－分发表（简记为 PDA），从而将设计编码缓存方案的问题转化为构造一个 PDA 的问题，从而大大降低了研究难度；. 2) 从应用出发给出了最优 PDA 的定义，并从组合设计角度构造了一些最优 PDA 的无穷类。

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