Cloud storage service is one of the services provided by cloud computing where data is stored on a remote group of public storage severs. Despite the various benefits of cloud storage service, the service suffers from various security problems. This paper introduces a new cryptographic and pairing-based security solution to overcome the security issues/concerns found in cloud storage. In addition to confidentiality and privacy, the proposed solution provides a mechanism that eliminates the need for a trusted third-party entity for the purpose of cipher key management, private key distribution and user revocation. Besides, the solution is concerned with providing protection for the cipher key and its derived sub-keys against different security threats.