Security, Privacy and Linear Function Retrieval in Multi-Access Combinatorial Topology with Private Cache

In this work, the problem setup consists of a server with <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$N$</tex> files connected to <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$K$</tex> users through an error-free shared link. Also, it consists of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$C$</tex> caches of size <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$M_{M}\mathbf{files}$</tex> called multi-access caches and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$K$</tex> caches of size <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$M_{P}$</tex> files called private caches. Each user is connected to a private cache and to a unique set of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$r$</tex> multi-access caches. For every set of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$r$</tex> 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 <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$r=1$</tex>, 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).