A New Algorithm for Secure Outsourcing Composite Modular Exponentiation

Modular exponentiations are widely used in discrete-log based cryptographic protocols. Most researches have been done for outsourcing exponentiation modular a prime, while less work has been done for outsourcing exponentiation modular a composite. In this paper, we first raise a new secure outsourcing algorithm for exponentiation modular a composite in the one malicious model. Then, we prove that this algorithm is secure in the one-malicious model and give efficiency analysis later. Comparing with other algorithms, ours is more efficient for composite modular exponentiation. Finally, we use this algorithm to realize a outsource-secure algorithm for Shamir´s Identitybased Signature scheme.