Private Information Retrieval Schemes with With Product-Matrix MBR Codes

Julien Lavauzelle (1, 2) , Razane Tajeddine (3) , Ragnar Freij-Hollanti (3) , Camilla Hollanti (3)

1 GRACE - Geometry, arithmetic, algorithms, codes and encryption
2 IRMAR - Institut de Recherche Mathématique de Rennes
3 Aalto University

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.

Mots clés: Private Information Retrieval; Regenerating codes

Domaines: Théorie de l'information [cs.IT]

Julien Lavauzelle, Razane Tajeddine, Ragnar Freij-Hollanti, Camilla Hollanti. Private Information Retrieval Schemes with With Product-Matrix MBR Codes. 2020. ⟨hal-01951956v1⟩