Key Superposition Simultaneously Achieves Security and Privacy in Cache-Aided Linear Function Retrieval

A coded caching scheme, referred to as key superposition, is proposed in the cache-aided content Secure and demand Private Linear Function Retrieval (SP-LFR) setup, where the following conditions are imposed: (a) each user is interested in retrieving an arbitrary linear combination of the files in the server’s library; (b) the content of the library must be kept secure from a wiretapper who obtains the signal sent by the server; and (c) any subset of users together can not obtain any information about the demands of the remaining users. The scheme uses the superposition of security keys and privacy keys in both the placement and delivery phases to guarantee content security and demand privacy, respectively. The achieved load-memory tradeoff is optimal to within a constant multiplicative gap, except for the small memory regime when there are less file than users. The memory-load tradeoff does not increase compared to the best known schemes that only guarantee content security in all regimes or only demand privacy in some regime.