We investigate the demand-private coded caching problem, in whichKusers, each equipped with a cache of sizeM, access a library ofNfiles under a privacy constraint. This constraint requires that no user obtain any information about the demands of others. We first present a new virtual-user-based achievable scheme for arbitrary numbers of users and files, which yields tighter order-optimal guarantees whenN≤KandM≤ 1. Next, we further focus on the caseN≤K. On the achievability side, for cache sizeM∈ [0,N/(K+1)(N−1)], we propose a novel demand-private scheme based on the idea that each user’s decoding process should depend only on their own demand. In terms of converse, we derive a new converse bound that is applicable forN≤Kand arbitraryM. Comparing the proposed achievability and converse, we find the optimal memory-rate tradeoff of the demand-private coded caching problem forM∈ [0,N/(K+1)(N−1)] whereN≤K≤ 2N−2, and the optimal memory-rate tradeoff forM∈ [0,1/K+1] whereK> 2N− 2. Moreover, for the case of 2 files and arbitrary number of users, by deriving another new converse bound, the optimal memory-rate tradeoff is characterized forM∈ [0,2/K] ∪ [2(K-1)/K+1,2]. Finally, we provide the optimal memory-rate tradeoff of the demand-private coded caching problem for 2 files and 3 users under arbitrary cache sizeM.

This work addresses the secure multi-access coded caching (SMACC) problem involving$N$files,$K$users, and$K$caches, where each user can access$L$consecutive caches in a cyclic wrap-around manner. It is required that no user can obtain any information about the files other than the requested one. The optimal memory-rate tradeoff for the largest access number, i.e.,$L=K-1$, is found for the case of an arbitrary number of users and files. This is done by proposing two new optimal achievability schemes and providing tight converse results. As a special case, the optimal memory-rate tradeoff for the secure coded caching (SCC) problem [1] in the two-user case has been found.

We investigate the demand private coded caching problem, which is an$(N,\ K)$coded caching problem with$N$files,$K$users, each equipped with a cache of size$M$, and an additional privacy constraint on user demands. We first present a new virtual-user-based achievable scheme for arbitrary number of users and files. Then, for the case of 2 files and arbitrary number of users, we derive some new converse bounds. As a result, we obtain the exact memory-rate tradeoff of the demand private coded caching problem for 2 files and 3 users. As for the case of 2 files and arbitrary number of users, the exact memoryrate tradeoff is characterized for$M\in[0,\ \frac{2}{K}]\cup[\frac{2(K-1)}{K+1},\ 2]$.