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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.
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Submitted on : Monday, September 21, 2020 - 4:05:12 PM
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Julien Lavauzelle, Razane Tajeddine, Ragnar Freij-Hollanti, Camilla Hollanti. Private Information Retrieval Schemes with Product-Matrix MBR Codes. IEEE Transactions on Information Forensics and Security, Institute of Electrical and Electronics Engineers, 2021, 16, pp.441-450. ⟨10.1109/TIFS.2020.3003572⟩. ⟨hal-01951956v2⟩

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