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Hierarchical Cache-Aided Linear Function Retrieval with Security and Privacy Constraints
The hierarchical caching system where a server connects with multiple mirror
sites, each connecting with a distinct set of users, and both the mirror sites
and users are equipped with caching memories has been widely studied. However
all the existing works focus on single file retrieval, i.e., each user requests
one file, and ignore the security and privacy threats in communications. In
this paper we investigate the linear function retrieval problem for
hierarchical caching systems with content security and demand privacy, i.e.,
each user requests a linear combination of files, and meanwhile the files in
the library are protected against wiretappers and users' demands are kept
unknown to other users and unconnected mirror sites. First we propose a new
combination structure named hierarchical placement delivery array (HPDA), which
characterizes the data placement and delivery strategy of a coded caching
scheme. Then we construct two classes of HPDAs. Consequently two classes of
schemes with or without security and privacy are obtained respectively where
the first dedicates to minimizing the transmission load for the first hop and
can achieve the optimal transmission load for the first hop if ignoring the
security and privacy constraints; the second has more flexible parameters on
the memory sizes and a lower subpacketization compared with the first one, and
achieves a tradeoff between subpacketization and transmission loads.Comment: arXiv admin note: substantial text overlap with arXiv:2205.0023
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