云计算是一种新兴的计算模式,它为云用户提供了强大的计算环境,但同时也引起了用户安全性和隐私性问题的关注.模幂运算是大多数现行的密码系统的基本运算之一,也是公钥密码系统在计算资源限制型设备上的计算瓶颈所在.使用传统的平方-乘算法计算一个n比特的指数的模幂运算,平均需要1.5n个模乘,对于资源有限型用户(或设备,例如智能卡)来说,这个计算量是个很沉重的负载.外包计算是云计算模式的优点之一,它使得云用户的计算能力不再受限于各自的资源约束型设备,通过外包工作负载给云,云用户可以使用云提供的无限资源来完成高代价的计算.本文围绕“外包模幂运算”这个问题展开研究,为椭圆曲线的点的乘法的计算问题,提出了一个安全的外包计算方案,并且将本文的方案应用于加速椭圆曲线数字签名的验证. Cloud computing is an emerging computing paradigm that provides a powerful computing environment for cloud users but also raises concerns about user security and privacy.Module exponentiation is the basic operation of most current cryptosystems One is also the calculation bottleneck where public-key cryptosystems are used to compute resource-constrained devices.Using traditional squaring algorithms to compute exponentiation of an n-bit exponentiation requires an average of 1.5n modular multiplications, and for resource-limited users (Or device such as a smart card), this amount of computing is a heavy load.Outdoor computing is one of the advantages of the cloud computing model, which makes cloud computing users are no longer limited by their resource-constrained devices, by Outsourcing work load to the cloud, cloud users can use the unlimited resources provided by the cloud to complete the high-cost calculation.This paper focuses on the issue of “outsourcing modular exponentiation ”, and proposes the calculation of the multiplication of points of elliptic curve A secure outsourcing computation scheme, and the scheme of this paper is applied to verify the elliptic curve digital signature.