Discrete exponential operation, such as modular exponentiation and scalarmultiplication on elliptic curves, is a basic operation of many public-keycryptosystems. However, the exponential operations are considered prohibitivelyexpensive for resource-constrained mobile devices. In this paper, we addressthe problem of secure outsourcing of exponentiation operations to one singleuntrusted server. Our proposed scheme (ExpSOS) only requires very limitednumber of modular multiplications at local mobile environment thus it canachieve impressive computational gain. ExpSOS also provides a secureverification scheme with probability approximately 1 to ensure that the mobileend-users can always receive valid results. The comprehensive analysis as wellas the simulation results in real mobile device demonstrates that our proposedExpSOS can significantly improve the existing schemes in efficiency, securityand result verifiability. We apply ExpSOS to securely outsource severalcryptographic protocols to show that ExpSOS is widely applicable to manycryptographic computations.
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