In this paper, we investigate a private information retrieval (PIR) problem for secure distributed storage systems in the presence of an eavesdropper. We design the secure distributed database and the corresponding PIR scheme, which protect not only user privacy (concealing the index of the desired message) from the databases, but also data security (concealing the messages themselves) from an eavesdropper. In our proposed scheme, we use a secret sharing scheme in storing the messages for data security at each of the databases. We consider two different scenarios on whether the databases are aware of the index sets of the secret shares stored in other databases. The key idea in designing an efficient PIR procedure is to exploit the secret shares of undesired messages as a side information by means of storing the secret shares at multiple databases. In particular, it is shown that the rates of the proposed PIR schemes are within a constant multiplicative factor from the derived upper-bound on the capacity of PIR problem.
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