Security, Privacy and Linear Function Retrieval in Multi-Access Combinatorial Topology with Private Cache
Mallikharjuna Chinnapadamala, Balaji Sundar Rajan · 2024
In this work, the problem setup consists of a server with$N$files connected to$K$users through an error-free shared link. Also, it consists of$C$caches of size$M_{M}\mathbf{files}$called multi-access caches and$K$caches of size$M_{P}$files called private caches. Each user is connected to a private cache and to a unique set of$r$multi-access caches. For every set of$r$multi-access caches, there is a user. For this setup a scheme is proposed that satisfies the following simultaneously: a) Linear Function Retrieval (LFR), b) content-security from an eavesdropper, and c) demand-privacy against a colluding set of users. It is shown that the private caches included in this work, enables the proposed scheme to provide privacy against colliding users. Also it is shown that to achieve the same rate both in [17] and in the proposed scheme, the total memory accessed by each user is less in the proposed scheme. Moreover, it turns out that the total cache memory requirement is also less for the system considered in this work compared to that in [17]. When$r=1$, the proposed scheme recovers one of the schemes given by Yan and Tuninetti (“Key Superposition Simultaneously Achieves Security and Privacy in Cache-Aided Linear Function Retrieval,” in Trans. Inf. Forensics and Security, 2021).