New algorithms for secure outsourcing of modular exponentiations

Abstract

Modular exponentiations have been considered the most expensive operation in discrete-logarithm based cryptographic protocols. In this paper, we propose a new secure outsourcing algorithm for exponentiation modular a prime in the one-malicious model. Compared with the state-of-the-art algorithm [33], the proposed algorithm is superior in both efficiency and checkability. We then utilize this algorithm as a subroutine to achieve outsource-secure Cramer-Shoup encryptions and Schnorr signatures. Besides, we propose the first outsource-secure and efficient algorithm for simultaneous modular exponentiations. Moreover, we prove that both the algorithms can achieve the desired security notions. © 2012 Springer-Verlag.