Recently it was shown that the seminal Maddah-Ali and Niesen (MAN) coded caching scheme leaks the demand information of each user to the others. Many works have considered coded caching with demand privacy, while each non-trivial existing coded caching scheme with private demands was built on the fact that the cache information of each user is private to the others. However, most of these schemes leak the users' cache information. Consequently, in most realistic settings (e.g., video streaming), where the system is used over time with multiple sequential transmission rounds, these schemes leak demand privacy beyond the first round. This observation motivates our new formulation of coded caching with simultaneously private demands and caches. The main contribution of this paper is a new construction that generates private coded caching schemes by leveraging two-server private information retrieval (PIR) schemes. We show that if in the PIR scheme the demand is uniform over all files and the queries are independent, the resulting caching scheme is private on both the demands and on the caches. Interestingly, we propose a new construction of two-server PIR schemes in this class by leveraging coded caching schemes. By applying the seminal MAN coded caching scheme into our construction, the resulting two-server PIR scheme is proved to be order optimal. This is a second new structural result, somehow closing the loop in the relation between coded caching and PIR. Finally, to explore a broader tradeoff between cache privacy and transmission load, we relax the cache privacy constraint and introduce the definition of leakage on cache information. Then, again as a by-product of our new construction, we propose new schemes with perfect demand privacy and imperfect cache privacy that achieve an order-gain in load with respect to the scheme with perfect privacy on both demands and caches.

翻译：最近研究表明，经典的Maddah-Ali与Niesen（MAN）编码缓存方案会泄露每个用户的需求信息给其他用户。许多工作已研究具有需求隐私性的编码缓存，而现有每个非平凡的需求私有编码缓存方案都建立在每个用户的缓存信息对他人私密这一基础上。然而，这些方案大多泄露了用户的缓存信息。因此，在大多数现实场景（如视频流）中，当系统随时间运行多轮连续传输时，此类方案会在第一轮后泄露需求隐私。这一观察促使我们提出同时保护需求与缓存隐私的编码缓存新框架。本文的主要贡献在于通过利用双服务器私有信息检索（PIR）方案构建了一种生成私有编码缓存方案的新方法。我们证明，若PIR方案中需求在所有文件上均匀分布且查询相互独立，则生成的缓存方案在需求与缓存两方面均保持私密。有趣的是，我们通过利用编码缓存方案，提出了一类新型双服务器PIR方案。将经典的MAN编码缓存方案应用于我们的构造后，所得双服务器PIR方案被证明是最优阶的。这是第二个结构性新成果，某种程度上闭合了编码缓存与PIR之间的关联循环。最后，为探索缓存隐私与传输负载间更广泛的权衡，我们放宽缓存隐私约束并引入缓存信息泄漏的定义。再次作为新构造的副产品，我们提出了具有完美需求隐私与非完美缓存隐私的新方案，与同时实现需求与缓存完美隐私的方案相比，其在负载上取得了阶数增益。