  This work investigates the problem of cache-aided content Secure and demand
Private Linear Function Retrieval (SP-LFR), where three constraints are imposed
on the system:(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) no colluding subset of users together obtain information about
the demands of the remaining users. A procedure is proposed to derive an SP-LFR
scheme from a given Placement Delivery Array (PDA), which is known to give
coded caching schemes with low subpacketization for systems with neither
security nor privacy constraints. This procedure uses the superposition of
security keys and privacy keys in both the cache placement and transmitted
signal to guarantee content security and demand privacy, respectively. In
particular, among all PDA-based SP-LFR schemes, the memory-load pairs achieved
by the PDA describing the Maddah-Ali and Niesen's scheme are Pareto-optimal and
have the lowest subpacketization. Moreover, the achieved load-memory tradeoff
is optimal to within a constant multiplicative gap except for the small memory
regime (i.e., when the cache size is between 1 and 2) and the number of files
is smaller than the number of users. Remarkably, the memory-load tradeoff does
not increase compared to the best known schemes that guarantee either only
content security in all regimes or only demand privacy in regime mentioned
above.
