Secure outsourcing of modular exponentiations under single untrusted programme model

Cloud computing gathers a lot of computing resources together, and provides cheap, efficient and convenient services. With the development of cloud computing, the importance of security issues is increasing. Modular exponentiations are one of the basic and expensive operations of public key cryptography. We consider the single untrusted programed model of modular exponentiations outsourcing algorithm in this paper. A new secure outsourcing of modular exponentiations scheme is proposed under this model. In this scheme, a new logical split method about modular exponentiation is put forward. The modular exponentiation is divided into several parts and a random value is kept for verification. The exponent and the base of modular exponentiations are keeping privacy in the process of outsourcing. The computational burden for users in the process of outsourcing is small, and the users can verify the results with high checkability.