Single-Database Private Information Retrieval from Fully Homomorphic Encryption

2013 ◽  
Vol 25 (5) ◽  
pp. 1125-1134 ◽  
Author(s):  
Xun Yi ◽  
Mohammed Golam Kaosar ◽  
Russell Paulet ◽  
Elisa Bertino
Keyword(s):  
Information Retrieval ◽  
Private Information ◽  
Homomorphic Encryption ◽  
Private Information Retrieval ◽  
Fully Homomorphic Encryption

An Efficient Fully Homomorphic Encryption Scheme for Private Information Retrieval in the Cloud

2019 ◽  
Vol 34 (04) ◽  
pp. 2055008
Author(s):  
Xun Wang ◽  
Tao Luo ◽  
Jianfeng Li
Keyword(s):  
Information Retrieval ◽  
Theoretical Analysis ◽  
Private Information ◽  
Homomorphic Encryption ◽  
Private Information Retrieval ◽  
Encryption Scheme ◽  
Fully Homomorphic Encryption ◽  
Encrypted Data ◽  
Privacy Concerns ◽  
Simulation Results

Information retrieval in the cloud is common and convenient. Nevertheless, privacy concerns should not be ignored as the cloud is not fully trustable. Fully Homomorphic Encryption (FHE) allows arbitrary operations to be performed on encrypted data, where the decryption of the result of ciphertext operation equals that of the corresponding plaintext operation. Thus, FHE schemes can be utilized for private information retrieval (PIR) on encrypted data. In the FHE scheme proposed by Ducas and Micciancio (DM), only a single homomorphic NOT AND (NAND) operation is allowed between consecutive ciphertext refreshings. Aiming at this problem, an improved FHE scheme is proposed for efficient PIR where homomorphic additions and multiplications are based on linear operations on ciphertext vectors. Theoretical analysis shows that when compared with the DM scheme, the proposed scheme allows multiple homomorphic additions and a single homomorphic multiplication to be performed. The number of allowed homomorphic additions is determined by the ratio of the ciphertext modulus to the upper bound of initial ciphertext noise. Moreover, simulation results show that the proposed scheme is significantly faster than the DM scheme in the homomorphic evaluation for a series of algorithms.

scholarly journals Optimal Rate Private Information Retrieval from Homomorphic Encryption

2015 ◽  
Vol 2015 (2) ◽  
pp. 222-243 ◽  
Author(s):  
Aggelos Kiayias ◽  
Nikos Leonardos ◽  
Helger Lipmaa ◽  
Kateryna Pavlyk ◽  
Qiang Tang
Keyword(s):  
Information Retrieval ◽  
Private Information ◽  
Galois Theory ◽  
Homomorphic Encryption ◽  
Positive Root ◽  
Time Algorithm ◽  
Oblivious Transfer ◽  
Optimal Rate ◽  
Private Information Retrieval ◽  
Polynomial Size

Abstract We consider the problem of minimizing the communication in single-database private information retrieval protocols in the case where the length of the data to be transmitted is large. We present first rate-optimal protocols for 1-out-of-n computationallyprivate information retrieval (CPIR), oblivious transfer (OT), and strong conditional oblivious transfer (SCOT). These protocols are based on a new optimalrate leveled homomorphic encryption scheme for large-output polynomial-size branching programs, that might be of independent interest. The analysis of the new scheme is intricate: the optimal rate is achieved if a certain parameter s is set equal to the only positive root of a degree-(m + 1) polynomial, where m is the length of the branching program. We show, by using Galois theory, that even when m = 4, this polynomial cannot be solved in radicals. We employ the Newton-Puiseux algorithm to find a Puiseux series for s, and based on this, propose a Θ (logm)-time algorithm to find an integer approximation to s.

scholarly journals Efficient Private Information Retrieval Protocol with Homomorphically Computing Univariate Polynomials

2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Wenju Xu ◽  
Baocang Wang ◽  
Rongxing Lu ◽  
Quanbo Qu ◽  
Yange Chen ◽  
...  
Keyword(s):  
Information Retrieval ◽  
Open Problem ◽  
Private Information ◽  
Homomorphic Encryption ◽  
Communication Overhead ◽  
Private Information Retrieval ◽  
Secret Key ◽  
Communication Efficiency ◽  
Database Size ◽  
Univariate Polynomials

Private information retrieval (PIR) protocol is a powerful cryptographic tool and has received considerable attention in recent years as it can not only help users to retrieve the needed data from database servers but also protect them from being known by the servers. Although many PIR protocols have been proposed, it remains an open problem to design an efficient PIR protocol whose communication overhead is irrelevant to the database size N . In this paper, to answer this open problem, we present a new communication-efficient PIR protocol based on our proposed single-ciphertext fully homomorphic encryption (FHE) scheme, which supports unlimited computations with single variable over a single ciphertext even without access to the secret key. Specifically, our proposed PIR protocol is characterized by combining our single-ciphertext FHE with Lagrange interpolating polynomial technique to achieve better communication efficiency. Security analyses show that the proposed PIR protocol can efficiently protect the privacy of the user and the data in the database. In addition, both theoretical analyses and experimental evaluations are conducted, and the results indicate that our proposed PIR protocol is also more efficient and practical than previously reported ones. To the best of our knowledge, our proposed protocol is the first PIR protocol achieving O 1 communication efficiency on the user side, irrelevant to the database size N .

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