Outsourcing paradigm is one of the most attractive benefits of cloud computing, where computation workloads can be outsourced to cloud servers by the resource-constrained devices, for example, RFID tags. With this paradigm, cloud clients can avoid setting up their own infrastructures. Accordingly, some new challenges, for example, security and checkability, are inevitably introduced. In this project, we address the issue of secure outsourcing algorithm for modular exponentiations in the one-malicious version of two untrusted program model. We demonstrate that our proposed algorithm is more effective than the state of the art algorithms. Then again, we call attention to in this project the primary outsource-secure algorithm for simultaneously modular exponentiations proposed recently is insecure, where the sensitive information can be leaked to the malicious servers. Therefore, we propose another also, the more efficient algorithm for concurrent secluded exponentiations. We likewise propose the developments for outsource-secure Cramer-Shoup encryptions and Schnorr signature which are likewise more efficient than the state of the art algorithms.