Private Information Retrieval Schemes With Product-Matrix MBR Codes

Abstract

A private information retrieval (PIR) scheme allows a user to retrieve a file from a database without revealing any information on the file being requested. As of now, PIR schemes have been proposed for several kinds of storage systems, including replicated and MDS-coded systems. However, the problem of constructing PIR schemes on regenerating codes has been sparsely considered. A regenerating code is a storage code whose codewords are distributed among nodes, enabling efficient storage of files, as well as low-bandwidth retrieval of files and repair of nodes. Minimum-bandwidth regenerating (MBR) codes define a family of regenerating codes allowing a node repair with optimal bandwidth. Rashmi, Shah, and Kumar obtained a large family of MBR codes using the product-matrix (PM) construction. In this work, a new PIR scheme over PM-MBR codes is designed. The inherent redundancy of the PM structure is used to reduce the download communication complexity of the scheme. A lower bound on the PIR capacity of MBR-coded PIR schemes is derived, showing an interesting storage space vs. PIR rate trade-off compared to existing PIR schemes with the same reconstruction capability. The present scheme also outperforms a recent PM-MBR PIR construction of Dorkson and Ng.

Design of Regenerating Code Based on Security Level in Cloud Storage System

“…This FR code can be represented by a set containing six subsets, as {N1-N6} = {6,1}, {1,2}, {2,3}, {3,4}, {4,5}, {5,6}. By mapping each subset into a storage node, this defined (6,2,2) FR can be applied to a distributed storage system. That is, the i-th node Vi corresponds to the i-th subset Ni, and stores the encoded symbols indexed by the points in Ni.…”

“…This blocking mechanism belongs to an information-theory-based data security protection scheme, which assumes that the eavesdropper is familiar with coding design principles and has infinite computing power. A way to use regenerating code technology to resist eavesdropping and ensure the data security of DSSs has become a challenging problem in the research of cloud storage systems in recent years [2].…”

Single-Server Private Information Retrieval with Side Information Under Arbitrary Popularity Profiles

“…where (a) holds since conditioning does not increase the entropy; (b) follows because U 1 = ∅; (c), (d), and (e) follow from (9) for the cases of i = 1, i = 2, and i = N, respectively; and (f) follows from the non-negativity of the entropy.…”

Private Information Retrieval from Colluding and Byzantine Servers with Binary Reed-Muller Codes

“…It was first introduced in [18] for coded storage and t-collusion and the best rate was shown to be achievable with generalized Reed-Solomon (GRS) codes. It has been extended to, e.g., binary and non-MDS codes [21], regenerating codes [22], unresponsive and Byzantine servers [23], streaming [24], random linear networks [25], and quantum PIR [26], [27]. Here, encouraged by the versatility of star product schemes and the computational efficiency of the binary field, we aim at constructing a robust binary scheme that is resistant toward colluding, non-responsive, and erroneous (Byzantine) servers.…”