Towards Practical Private Information Retrieval from MDS Array Codes

TL;DR

This paper introduces a practical PIR protocol from MDS array codes that achieves capacity, reduces sub-packetization, and supports efficient repair, improving over existing schemes especially in binary fields.

Contribution

The paper proposes a new PIR protocol from MDS array codes that is capacity-achieving, supports small sub-packetization, and is implementable over binary fields, enhancing practicality.

Findings

Achieves capacity for PIR from MDS/MSR coded servers.

Supports small sub-packetization levels.

Enables PIR over binary fields.

Abstract

Private information retrieval (PIR) is the problem of privately retrieving one out of $M$ original files from $N$ severs, i.e., each individual server learns nothing about the file that the user is requesting. Usually, the $M$ files are replicated or encoded by a maximum distance separable (MDS) code and then stored across the $N$ 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 schemes 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, 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 some advantages when compared with existing protocols, e.g., 1) small sub-packetization, 2) (near-) optimal repair bandwidth, 3) implementable over the binary field $\mathbf{F}_2$.