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Security and Communication Networks
Volume 2018, Article ID 2363928, 14 pages
https://doi.org/10.1155/2018/2363928
Research Article

Privacy-Preserving Oriented Floating-Point Number Fully Homomorphic Encryption Scheme

1College of Computer Science, Nanjing University of Posts and Telecommunication, Nanjing 210003, China
2Key Laboratory of Broadband Wireless Communication & Sensor Networks Technology of Ministry of Education, Nanjing University of Posts and Telecommunications, Nanjing 210003, China
3Jiangsu Key Laboratory of Big Data Security & Intelligent Processing, Nanjing, Jiangsu 210023, China

Correspondence should be addressed to Geng Yang; nc.ude.tpujn@ggnay

Received 29 January 2018; Revised 19 May 2018; Accepted 5 June 2018; Published 24 July 2018

Academic Editor: Roberto Di Pietro

Copyright © 2018 Shuangjie Bai et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The issue of the privacy-preserving of information has become more prominent, especially regarding the privacy-preserving problem in a cloud environment. Homomorphic encryption can be operated directly on the ciphertext; this encryption provides a new method for privacy-preserving. However, we face a challenge in understanding how to construct a practical fully homomorphic encryption on non-integer data types. This paper proposes a revised floating-point fully homomorphic encryption scheme (FFHE) that achieves the goal of floating-point numbers operation without privacy leakage to unauthorized parties. We encrypt a matrix of plaintext bits as a single ciphertext to reduce the ciphertext expansion ratio and reduce the public key size by encrypting with a quadratic form in three types of public key elements and pseudo-random number generators. Additionally, we make the FFHE scheme more applicable by generalizing the homomorphism of addition and multiplication of floating-point numbers to analytic functions using the Taylor formula. We prove that the FFHE scheme for ciphertext operation may limit an additional loss of accuracy. Specifically, the precision of the ciphertext operation’s result is similar to unencrypted floating-point number computation. Compared to other schemes, our FFHE scheme is more practical for privacy-preserving in the cloud environment with its low ciphertext expansion ratio and public key size, supporting multiple operation types and high precision.