Journal
IEEE TRANSACTIONS ON INFORMATION FORENSICS AND SECURITY
Volume 15, Issue -, Pages 1248-1260Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TIFS.2019.2937634
Keywords
Private information retrieval; distributed storage system; file length; coded servers; capacity-achieving
Funding
- National Natural Science Foundation of China [61871331]
- Major Frontier Project of Sichuan Province [2015JY0282]
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In a distributed storage system, private information retrieval (PIR) guarantees that a user retrieves one file from the system without revealing any information about the identity of its interested file to any individual server. In this paper, we investigate an (N, K, M) coded server model of PIR, where each of M files is distributed to N servers in the form of (N, K) maximum distance separable (MDS) code for some N > K and M > 1. As a result, we propose a new capacity-achieving (N, K, M) coded linear PIR scheme such that it can be implemented with file length K(N-K)/gcd(N,K), which is much smaller than the previous best result K (N/gcd(N, K)(M-1). Notably, among all the capacity-achieving coded linear PIR schemes, we show that the file length is optimal if M > [K/gcd(N, K) - K/N-K] + 1 or min(K, N - K)vertical bar N, and within a multiplicative gap min(K, N-K)/ gcd(N,K) of a lower bound on the minimum file length otherwise.
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