Secure and Server-User Private Linear Function Retrieval in Multi-Server Multi-User Systems

摘要

This paper investigates the ultimate performance limits of distributed multi-server systems with cache-aided users, where the users aim to retrieve a linear function of the files of a library that are replicated at multiple non-colluding servers. In addition to correct decoding, the following conditions are imposed: (a) the content of the library must be kept secure from a wiretapper who obtains all the signals sent by the servers; (b) any subset of users together can not obtain any information about the demands of the remaining users; and (c) the users’ demands must be kept private against any individual server. A Distributed Key Superposition (DKS) scheme is proposed, which uses the idea of superposition of security and privacy keys to guarantee conditions (a) and (b) simultaneously, as in the single server setup. Condition (c) is guaranteed by the fact that each server is responsible for delivering a fraction of the requested linear function, and insuring that the privacy keys used by a server are generated and pushed to the user caches by another server. Interestingly, the achievable load-memory tradeoff with the additional constraint (c) is the same as the single server case if there are at least two servers.