Title: Efficient fully homomorphic encryption with circularly secure key switching process

Authors: Tanping Zhou; Xiaoyuan Yang; Wei Zhang; Liqiang Wu

Addresses: Key Laboratory of Network and Information Security under the Chinese Armed Police Force, Electronic Department, Engineering College of the Armed Police Force, Xi'an, 710086, China ' Key Laboratory of Network and Information Security under the Chinese Armed Police Force, Electronic Department, Engineering College of the Armed Police Force, Xi'an, 710086, China ' Key Laboratory of Network and Information Security under the Chinese Armed Police Force, Electronic Department, Engineering College of the Armed Police Force, Xi'an, 710086, China ' Key Laboratory of Network and Information Security under the Chinese Armed Police Force, Electronic Department, Engineering College of the Armed Police Force, Xi'an, 710086, China

Abstract: Fully homomorphic encryption (FHE) has important applications in cloud computing. However, almost all fully homomorphic encryption schemes share two common flaws that they all use large-scale secret keys and some operations are inefficient. In this paper, the 'special b' variant of the learning with errors problem (bLWE) is presented, and helps us construct the first circularly secure key switching process which can replace the key switching process and similar re-linearisation process used by the existing FHE schemes. Then, we present an efficient FHE. Compared with Brakerski's scheme, our scheme reduces L secret keys to one and is more efficient. Finally, we prove the chosen-plaintext attack (CPA) security of the fully homomorphic scheme and the circular security of key switching process in standard model under the learning with errors problem (LWE) assumption.

Keywords: circular security; fully homomorphic encryption; FHE; LWE problem; learning with errors; cryptography; secure key switching; cloud computing; secret keys; chosen-plaintext attacks.

DOI: 10.1504/IJHPCN.2016.080414

International Journal of High Performance Computing and Networking, 2016 Vol.9 No.5/6, pp.417 - 422

Available online: 22 Nov 2016 *

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