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Issue No. 05 - May (2013 vol. 25)
ISSN: 1041-4347
pp: 1125-1134
Xun Yi , Victoria University, Melbourne
Mohammed Golam Kaosar , Victoria University, Melbourne
Russell Paulet , Victoria University, Melbourne
Elisa Bertino , Purdue University, West Lafayette
Private Information Retrieval (PIR) allows a user to retrieve the $(i)$th bit of an $(n)$-bit database without revealing to the database server the value of $(i)$. In this paper, we present a PIR protocol with the communication complexity of $(O(\gamma \log n))$ bits, where $(\gamma)$ is the ciphertext size. Furthermore, we extend the PIR protocol to a private block retrieval (PBR) protocol, a natural and more practical extension of PIR in which the user retrieves a block of bits, instead of retrieving single bit. Our protocols are built on the state-of-the-art fully homomorphic encryption (FHE) techniques and provide privacy for the user if the underlying FHE scheme is semantically secure. The total communication complexity of our PBR is $(O(\gamma \log m+\gamma n/m))$ bits, where $(m)$ is the number of blocks. The total computation complexity of our PBR is $(O(m\log m))$ modular multiplications plus $(O(n/2))$ modular additions. In terms of total protocol execution time, our PBR protocol is more efficient than existing PBR protocols which usually require to compute $(O(n/2))$ modular multiplications when the size of a block in the database is large and a high-speed network is available.
Protocols, Encryption, Servers, Complexity theory, Indexes, fully homomorphic encryption, Private information retrieval, private block retrieval

R. Paulet, M. G. Kaosar, X. Yi and E. Bertino, "Single-Database Private Information Retrieval from Fully Homomorphic Encryption," in IEEE Transactions on Knowledge & Data Engineering, vol. 25, no. , pp. 1125-1134, 2013.
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