Security and Privacy in Cache-Aided Linear Function Retrieval for Multi-Access Coded Caching

A multi-access network consisting of C caches, K users with each user having access to unique set of r caches has been introduced recently. It considers Single File Retrieval (SFR) i.e, each user demands an arbitrary file from the server. It proposes a coded caching scheme which was shown to be optimal under the assumption of uncoded placement by Brunero and Elia ("Fundamental Limits of Combinatorial Multi-Access Caching" in arXiv:2110.07426 ). The above multi-access network is referred to as combinatorial topology which was considered in our work by imposing three additional constraints : a) Linear Function Retrieval (LFR) i.e., each user is interested in retrieving an arbitrary linear combination of the files in the server’s library; b) Security i.e., the content of the library must be kept secure from an eavesdropper who obtains the signal sent by the server; c) Privacy i.e., each user can only get its required file and can not get any information about the demands of other users. An achievable Secure, Private LFR (SP-LFR) scheme from which Private LFR (P-LFR), LFR schemes can be derived was proposed and also an achievable Secure LFR (S-LFR) scheme was proposed. In the higher memory region, rate achieved by SP-LFR scheme and P-LFR scheme will be same. When the access ratio (number of caches each user having access to) is 1, our SP-LFR scheme and P-LFR scheme reduces to MAN-PDA based SP-LFR scheme and MAN-PDA based P-LFR scheme respectively by Yan and Tuninetti ("Key Superposition Simultaneously Achieves Security and Privacy in Cache-Aided Linear Function Retrieval", in Trans. Inf. Forensics and Security, 2021) and our SP-LFR scheme, S-LFR and security key scheme for SFR by Sengupta et al. ("Fundamental limits of caching with secure delivery", in Trans. Inf. Forensics and Security, 2015 ) will have same performance.