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.