### Abstract

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 $(O(mlog m))$ 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.

Original language | English |
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Pages (from-to) | 1125-1134 |

Number of pages | 10 |

Journal | IEEE Transactions on Knowledge and Data Engineering |

Volume | 25 |

Issue number | 5 |

DOIs | |

Publication status | Published - May 2013 |

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## Cite this

Xun, Y., Kaosar, M., Paulet, R., & Bertino, E. (2013). Single-Database Private Information Retrieval from Fully Homomorphic Encryption.

*IEEE Transactions on Knowledge and Data Engineering*,*25*(5), 1125-1134. https://doi.org/10.1109/TKDE.2012.90