This work investigates the problem of demand privacy against colluding users for shared-link coded caching systems, where no subset of users can learn any information about the demands of the remaining users. The notion of privacy used here is stronger than similar notions adopted in past work and is motivated by the practical need to insure privacy regardless of the file distribution. Two scenarios are considered: Single File Retrieval (SFR) and Linear Function Retrieval (LFR), where in the latter case each user demands an arbitrary linear combination of the files at the server. The main contributions of this paper are a novel achievable scheme for LFR, referred as privacy key scheme, and a new information theoretic converse bound for SFR. Clearly, being SFR a special case of LFR, an achievable scheme for LFR works for SFR as well, and a converse for SFR is a valid converse for LFR as well. By comparing the performance of the achievable scheme with the converse bound derived in this paper (for the small cache size regime) and existing converse bounds without privacy constraints (in the remaining memory regime), the communication load of the privacy key scheme turns out to be optimal to within a constant multiplicative gap in all parameter regimes. Numerical results show that the new privacy key scheme outperforms in some regime known schemes based on the idea of virtual users, which also satisfy the stronger notion of user privacy against colluding users adopted here. Moreover, the privacy key scheme enjoys much lower subpacketization than known schemes based on virtual users.

翻译：这项工作调查了对共享链接编码缓存系统串通用户的需求隐私问题, 用户中没有一个子集能够了解关于剩余用户需求的任何信息。 这里使用的隐私概念比过去工作中采用的类似概念更强, 其动机是实际需要确保隐私, 不论文件的分发情况如何。 考虑了两种设想: 单一文件检索val( SFR) 和 Linearinear 函数检索val (LFR) 。 在后一种情况下, 每个用户都要求将服务器的文档任意线性组合。 本文的主要贡献是对LFR 来说一个新颖的可实现方案, 被称为隐私关键方案, 以及一个新的信息对 SFR 的理论。 显然, SRFR 是LFR 的特殊案例, 一个LFR 的可实现计划, 一个为SFR( LFR) 和 SFR( Linearneal Don) 的可实现方案。 通过将可实现计划的业绩与本文中得出的相近线性组合( 小缓存系统) 和现有的反向无隐私限制的虚拟虚拟机制( ), 最接近的用户的内存式关键机制, 最深的通信系统 将已知的关键系统 向已知的关键系统 向已知的关键系统 显示一个已知的关键系统 。