Towards Practical Private Information Retrieval From MDS Array Codes

Private information retrieval (PIR) is the problem of privately retrieving one out of <inline-formula> <tex-math notation="LaTeX">$M$ </tex-math></inline-formula> original files from <inline-formula> <tex-math notation="LaTeX">$N$ </tex-math></inline-formula> severs, <italic>i.e.</italic>, each individual server gains no information on the identity of the file that the user is requesting. Usually, the <inline-formula> <tex-math notation="LaTeX">$M$ </tex-math></inline-formula> files are replicated or encoded by a maximum distance separable (MDS) code and then stored across the <inline-formula> <tex-math notation="LaTeX">$N$ </tex-math></inline-formula> servers. Compared to mere replication, MDS-coded servers can significantly reduce the storage overhead. Particularly, PIR from minimum storage regenerating (MSR) coded servers can simultaneously reduce the repair bandwidth when repairing failed servers. Existing PIR protocols from MSR-coded servers either require large sub-packetization levels or are not capacity-achieving. In this paper, a PIR protocol from MDS array codes is proposed, subsuming PIR from MSR-coded servers as a special case. Particularly, only the case of non-colluding, honest-but-curious servers is considered. The retrieval rate of the new PIR protocol achieves the capacity of PIR from MDS-/MSR-coded servers. By choosing different MDS array codes, the new PIR protocol can have varying advantages when compared with existing protocols, <italic>e.g.</italic>, 1) small sub-packetization, 2) (near-)optimal repair bandwidth, 3) implementable over the binary field <inline-formula> <tex-math notation="LaTeX">$\mathbf {F}_{2}$ </tex-math></inline-formula>.

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