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Cloud computing is an Internet-based computing. In cloud computing, the service is fully served by the provider. Users need nothing but personal devices and Internet access. Computing services, such as data, storage, software, computing, and application, can be delivered to local devices through Internet. The major security issue of cloud computing is that cloud providers must ensure that their infrastructure is secure, and prevent illegal data accesses from outsiders, other clients, or even the unauthorized cloud employees. In this paper, we deal with key agreement and authentication for cloud computing. By using Elliptic Curve Diffie Hellman (ECDH) and symmetric bivariate polynomial based secret sharing, we design a secure cloud computing (SCC). Two types of SCC are proposed. One requires a trusted third party (TTP), and the other does not need a TTP. Additionally, via the homomorphism property of polynomial based secret sharing, our SCC can be extended to multi-server SCC (MSCC) to fit an environment where a multi-server system contains multiple servers to collaborate for serving applications.