Title: Secure outsourcing of modular inverses and scalar multiplications on elliptic curves

Authors: Yuan Ping; Xuyang Guo; Baocang Wang; Jingxian Zhou

Addresses: School of Information Engineering, Xuchang University, Xuchang, He'nan, China; Information Technology Research Base of Civil Aviation Administration of China, Civil Aviation University of China, Tianjin, China ' No. 1 Middle School of Zhengzhou, Zhengzhou, He'nan, China ' School of Information Engineering, Xuchang University, Xuchang, He'nan, China; Key Laboratory of Computer Networks and Information Security, Ministry of Education, Xidian University, Xi'an, Shanxi, China ' Information Technology Research Base of Civil Aviation Administration of China, Civil Aviation University of China, Tianjin, China

Abstract: Currently, pricey data analysis urges outsourcing computations, such as modular inverse and point multiplication in elliptic curve cryptosystem. However, it raises security concerns on the untrusted cloud. Thus, we propose two outsourcing protocols for these two operations, respectively. For efficiency, in the first protocol, only three modular multiplications required by the client to outsource a modular inverse operation. In the second protocol, a point multiplication operation can be carried out just by doing two addition operations on elliptic curves. For security, in both protocols, the input is randomly split into two parts to meet both input and output privacy. The security is theoretically proved under a single server and two non-colluding servers' models, respectively. Furthermore, the cheating behaviours of the servers can be detected by probabilities of 100% and 75%, respectively. Besides the achieved security goal, experiments confirm the significant improvement on efficiency in comparison with the traditional ones.

Keywords: cloud computing; secure outsourcing; modular inverse; point multiplication; elliptic curve; public key cryptography.

DOI: 10.1504/IJSN.2020.106832

International Journal of Security and Networks, 2020 Vol.15 No.2, pp.101 - 110

Received: 07 Feb 2019
Accepted: 04 Aug 2019

Published online: 17 Apr 2020 *

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