Cloud computing is a novel computing paradigm which provides powerful computing resources for cloud users. However, this paradigm also brings new challenges for security and privacy. The modular exponentiation is one of basic operations among most of current cryptosystems. It also presents the computational bottleneck in most public-key cryptography on computationally limited devices. Without outsourcing, a device using the traditional square-and-multiply algorithm need 1.5n modular multiplications on average to carry out a modular exponentiation for n-bit exponents. Thus, it is a very time-consuming operation for device with limited computational resources, such as smart card. Cloud computing has a great deal of computational resources and then the computation/storage intensive tasks can be performed through being delegated to resource-abundant cloud servers. A practically and securely outsourced scheme was present, which was used for computing point multiplication on elliptic curves, and was applied to speeding up signature verification of the ECDSA (Elliptic Curves Digital Signature Algorithm).