Bounds on Traceability Schemes
Bounds on Traceability Schemes
复制标题
DOI：
10.1109/tit.2017.2766659
复制
发表时间：
2016-09
影响因子：
2.5
通讯作者：
Yujie Gu;Y. Miao
中科院分区：
文献类型：
--
作者：
Yujie Gu;Y. Miao
提出了Stinson – Wei的可追溯性方案（称为可追溯性方案），以作为Chor-Fiat-Noor可追溯性方案的概括（称为Traceability代码）作为广播加密。二进制叠加的代码。 $ t^{2} $，即，$ t $ - 跟踪方案是$ t^{2} $ - 基于这个有趣的发现，我们使用组合使用了新的上限结构，我们构建了几个无限的最佳可追溯性方案家族，这些家族达到了我们的新上限。同时，我们考虑了父母识别的设定系统，这是一种比可追溯性方案较弱的抗收集键分发方案，但与无覆盖家庭相比，还具有更强的条件。
The Stinson–Wei traceability scheme (known as traceability scheme) was proposed for broadcast encryption as a generalization of the Chor–Fiat–Naor traceability scheme (known as traceability code). Cover-free family was introduced by Kautz and Singleton in the context of binary superimposed code. In this paper, we find a new relationship between a traceability scheme and a cover-free family, which strengthens the anti-collusion strength from $t$ to $t^{2}$ , i.e., a $t$ -traceability scheme is a $t^{2}$ -cover-free family. Based on this interesting discovery, we derive new upper bounds for traceability schemes. By using combinatorial structures, we construct several infinite families of optimal traceability schemes, which attain our new upper bounds. We also provide a constructive lower bound for traceability schemes, the size of which has the same order of magnitude as our general upper bound. Meanwhile, we consider parent-identifying set systems, an anti-collusion key-distributing scheme requiring weaker conditions than traceability scheme but stronger conditions than cover-free family. A new upper bound is also given for parent-identifying set systems.