Private Information Retrieval Using Circulant Permutation Matrices or the Zero Matrix

Private information retrieval (PIR) protocols allow a user to retrieve entries of a database without revealing the index of the desired item. Information-theoretical privacy can be achieved by the use of several servers and specific retrieval algorithms. In this paper, we investigate the problem of PIR under erasure-coded distributed storage systems and construct PIR protocols with optimal computational complexity for the servers, reasonable communication complexity, and low storage overhead. The proposed constructions also enjoy the advantages of low encoding complexity and low memory requirement for storing all possible queries for the user. More specifically, we concentrate on the study of using circulant permutation matrices or the zero matrix to construct PIR protocols for noncommunicating servers.