Secure outsourcing of modular inverses and scalar multiplications on elliptic curves

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.