Robust and Secure Cache-aided Private Linear Function Retrieval from Coded Servers
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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.
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