In todays world, Cloud computing has attracted research communities as it provides services in reduced cost due to virtualizing all the necessary resources. Even modern business architecture depends upon Cloud computing .As it is a internet based utility, which provides various services over a network, it is prone to network based attacks. Hence security in clouds is the most important in case of cloud computing. Cloud Security concerns the customer to fully rely on storing data on clouds. That is why Cloud security has attracted attention of the research community. This paper will discuss securing the data in clouds by implementing key agreement, encryption and signature verification/generation with hyperelliptic curve cryptography.