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Single-Database Private Information Retrieval from Fully Homomorphic Encryption
May 2013 (vol. 25 no. 5)
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.
Index Terms:
Protocols,Encryption,Servers,Complexity theory,Indexes,fully homomorphic encryption,Private information retrieval,private block retrieval
Citation:
Xun Yi, Mohammed Golam Kaosar, Russell Paulet, Elisa Bertino, "Single-Database Private Information Retrieval from Fully Homomorphic Encryption," IEEE Transactions on Knowledge and Data Engineering, vol. 25, no. 5, pp. 1125-1134, May 2013, doi:10.1109/TKDE.2012.90
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