可追溯性方案的界限
Bounds on Traceability Schemes
摘要：
Stinson-Wei可追溯性方案（称为可追溯性方案）是作为Chor-Fiat-Naor可追溯性方案（称为可追溯性码）的推广而提出的。无覆盖族是由Kautz和Singleton在二进制叠加代码的背景下引入的。本文发现了一种新的追踪方案与无覆盖族之间的关系，这种关系增强了从$t$到$t^2$的抗共谋强度，即$t$ -追踪方案是一个$t^2$ -无覆盖族.基于这个有趣的发现，我们得到新的上界的可追溯性计划。通过使用组合结构，我们构造了几个无限族的最优追踪方案，达到我们的新的上界。我们还提供了一个建设性的下界的可追溯性计划，其大小具有相同的顺序与我们的一般上界。同时，我们考虑了一个抗共谋的密钥分配方案--父识别集方案，该方案的条件比可追踪方案弱，但比无覆盖族强。对于父识别集系统，给出了一个新的上界。
英文摘要：
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 $t^2$, that is, 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 with our general upper bound. Meanwhile, we consider parent-identifying set system, 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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
