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The hierarchical caching system where a server connects with multiple mirrorsites, each connecting with a distinct set of users, and both the mirror sitesand users are equipped with caching memories has been widely studied. Howeverall the existing works focus on single file retrieval, i.e., each user requestsone file, and ignore the security and privacy threats in communications. Inthis paper we investigate the linear function retrieval problem forhierarchical caching systems with content security and demand privacy, i.e.,each user requests a linear combination of files, and meanwhile the files inthe library are protected against wiretappers and users' demands are keptunknown to other users and unconnected mirror sites. First we propose a newcombination structure named hierarchical placement delivery array (HPDA), whichcharacterizes the data placement and delivery strategy of a coded cachingscheme. Then we construct two classes of HPDAs. Consequently two classes ofschemes with or without security and privacy are obtained respectively wherethe first dedicates to minimizing the transmission load for the first hop andcan achieve the optimal transmission load for the first hop if ignoring thesecurity and privacy constraints; the second has more flexible parameters onthe memory sizes and a lower subpacketization compared with the first one, andachieves a tradeoff between subpacketization and transmission loads.

Hierarchical Cache-Aided Linear Function Retrieval with Security and Privacy Constraints