  This paper investigates the ultimate performance limits of Linear Function
Retrieval (LFR) by cache-aided users from distributed coded servers. Each user
aims to retrieve a linear function of the files of a library, which are Maximum
Distance Separable (MDS) coded and stored at multiple servers.The system needs
to guarantee robust decoding in the sense that each user must decode its
demanded function with signals from any subset of servers whose cardinality
exceeds a threshold. In addition, the following conditions must be met:(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 all the servers even if they collude. A
scheme that uses the superposition of security and privacy keys is proposed to
meet all those conditions.The achieved load-memory tradeoff is the same as that
achieved in single-server case scaled by the inverse of the MDS code rate used
to encode the files, and the same optimality guarantees as in single-server
setup are obtained.
