The growth of local data annually implies extra charges for the customers, which makes their business slowing down. Cloud computing paradigm comes with new technologies that offer a very economic and cost-effective solution, but the organizations are slow in accepting it due to security issues and challenges associated with it. Security is one of the major issues which hamper the growth of cloud and it is highly crucial to protect the sensitive data and systems in the cloud setting in order to ensure the privacy of its users. This work explores the new directions in cloud computing security, while highlighting the correct selection of these fundamental technologies from cryptographic point of view.