Private Information Retrieval Over Random Linear Networks

In this paper, the problem of providing privacy to users requesting data over a network from a distributed storage system (DSS) is considered. The DSS, which is considered as the multi-terminal destination of the network from the user's perspective, is encoded by a maximum rank distance (MRD) code to store the data on these multiple servers. A private information retrieval (PIR) scheme ensures that a user can request a file without revealing any information on which file is being requested to any of the servers. In this paper, a novel PIR scheme is proposed, allowing the user to recover a file from a storage system with low communication cost, while allowing some servers in the system to collude in the quest of revealing the identity of the requested file. The network is modeled as a random linear network, i.e., all nodes of the network forward random (unknown) linear combinations of incoming packets. Both error-free and erroneous random linear networks are considered.