Volume 10 - Issue 2
Secure Computation Outsourcing for Inversion in Finite Field
- Qianqian Su
College of Computer Science and Technology, Qingdao University, Qingdao 266071, China, State Key Laboratory of Information Security, Institute of Information Engineering Chinese Academy of Sciences, Beijing 100093, China
suqianqian@iie.ac.cn
- Rong Hao
College of Computer Science and Technology, Qingdao University, Qingdao 266071, China
hr@qdu.edu.cn
- Shaoxia Duan
College of Computer Science and Technology, Qingdao University, Qingdao 266071, China
shaoxiaduan@163.com
- Fanyu Kong
School of Software, Shandong University, Jinan 250101, China
fanyukong@sdu.edu.cn
- Xiaodong Liu
School of Software, Shandong University, Jinan 250101, China
liuxiaodong@sdu.edu.cn
- Jia Yu
College of Computer Science and Technology, Qingdao University, Qingdao 266071, China
qduyujia@gmail.com
Keywords: Secure computation outsourcing, Inversion, Verifiability, Privacy
Abstract
With the widespread of cloud service and the popularity of mobile devices, more and more researchers
are working on the technologies that can securely outsource expensive computation tasks
to a single semi-trusted cloud server. Inversion has always been considered one of the most basic and
prohibitively expensive arithmetic operations in cryptographic system based on finite field or elliptic
curve. In this paper, we construct two algorithms for secure outsourcing inversion operation with
the help of single and untrusted cloud server. The first algorithm, named Inv, is designed for secure
outsourcing single element’s inversion. The second algorithm, named MInv is designed for secure
outsourcing multiple elements’ inversion. Compared with using the extended Euclidean algorithm,
the client can achieve higher efficacy by using the first proposed algorithm Inv. The efficiency of
the second proposed algorithm on the cloud side is superior to invoking the first algorithm multiple
times. At the same time, there is no increase in computational burden on the client side. The formal
security analysis shows that our algorithms satisfy the security of verifiability, input-privacy, and
output-privacy. Furthermore, we simulate our proposed algorithms to evaluate its performance. The
simulation results demonstrate that our proposed algorithms are valid and practical.