ExpSOS: Secure and Verifiable Outsourcing of Exponentiation Operations for Mobile Cloud Computing

Discrete exponential operation, such as modular exponentiation and scalar multiplication on elliptic curves, is a basic operation of many public-key cryptosystems. However, the exponential operations are considered prohibitively expensive for resource-constrained mobile devices. In this paper, we address the problem of secure outsourcing of exponentiation operations to one single untrusted server. Our proposed secure outsourcing scheme for general exponential (ExpSOS) only requires a very limited number of modular multiplications at local mobile environment, and thus it can achieve significant computational performance gain. ExpSOS also provides a secure verification scheme with probability approximately 1 to ensure that the mobile end users can always receive valid results. The comprehensive analysis as well as the simulation results in real mobile device demonstrates that our proposed ExpSOS can significantly improve the existing schemes in efficiency, security, and result verifiability. We apply ExpSOS to securely outsource several cryptographic protocols to show that ExpSOS can be widely applied to many computation-intensive applications and achieve significant performance improvement.