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arXiv 2201.11539cs.ITmath.IT

具有私有需求和缓存的编码缓存

Coded Caching with Private Demands and Caches

Ali Gholami, Kai Wan, Hua Sun, Mingyue Ji, Giuseppe Caire

AI总结:

本文研究同时保护用户需求与缓存隐私的编码缓存,提出利用双服务器 PIR 构造私有方案,并反向由 MAN 方案构造阶最优 PIR,还给出放松缓存隐私时的负载阶增益方案。

摘要:

最近有研究表明,开创性的 Maddah-Ali and Niesen(MAN)编码缓存方案会将每个用户的需求信息泄露给其他用户。许多工作已经考虑了具有需求隐私的编码缓存,而现有的每一种具有私有需求的非平凡编码缓存方案,都建立在每个用户的缓存信息对其他用户保密这一事实之上。然而,这些方案中的大多数都会泄露用户的缓存信息。因此,在大多数现实场景中(例如视频流),系统会随时间被使用并经历多个连续传输轮次,这些方案在第一轮之后就会泄露需求隐私。这一观察促使我们提出同时具有私有需求和缓存的编码缓存新表述。本文的主要贡献是一种新构造,通过利用双服务器私有信息检索(PIR)方案来生成私有编码缓存方案。我们表明,如果在该 PIR 方案中需求在所有文件上均匀分布且查询相互独立,则所得缓存方案在需求和缓存两方面都具有隐私性。有趣的是,我们通过利用编码缓存方案,提出了这一类别中的一种新的双服务器 PIR 方案构造。通过将开创性的 MAN 编码缓存方案应用于我们的构造,所得双服务器 PIR 方案被证明是阶最优的。这是第二个新的结构性结果,在某种程度上闭合了编码缓存与 PIR 之间关系的环路。最后,为了探索缓存隐私与传输负载之间更广泛的权衡,我们放宽了缓存隐私约束,并引入了缓存信息泄露的定义。随后,同样作为我们新构造的副产品,我们提出了具有完美需求隐私和不完美缓存隐私的新方案;相对于在需求和缓存上都具有完美隐私的方案,这些方案在负载上实现了阶增益。

英文摘要:

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.

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