A Study on Combinatorial Traitor Tracing Schemes for Broadcast Encryption

叛逆者追踪是一种保护数字内容版权免受合谋攻击的数学方法。本课题研究用于叛逆者追踪的组合安全码，重点探索其最大码率和识别算法。所得结果如下：1)将列表译码思想整合到具有完全可追溯性的安全码中，提出了统一的列表译码安全码概念；2)利用概率方法推导了sdd最大码率的界；3)建立了一种两步译码算法，其译码效率优于已知的可分离码；4)提出了一种两阶段动态框架，用于动态跟踪叛逆者；5)建立了二进制多媒体IPP码的最大码率的新界限。

Traitor tracing is a mathematical approach of protecting copyright of digital content against collusion attacks. This project studies combinatorial secure codes for traitor tracing, with particular focus on exploring their maximum code rate and identifying algorithms. The obtained results are as follows. 1) A new unified concept of secure codes with list decoding (SCLDs) is proposed by integrating the idea of list decoding into secure codes with complete traceability; 2) Bounds on the maximum code rate of SCLDs are derived via the probabilistic method; 3) A two-step decoding algorithm is established for SCLDs, whose efficiency outperforms the known separable codes; 4) A two-stage dynamic framework is proposed for dynamic traitor tracing; 5) New bounds on the maximum code rate of binary multimedia IPP codes are established.