Cryptography is the art and science of achieving security by encoding the message or data to make them unreadable. It is related to the aspects of network security such as privacy, reliability and accessibility of the data. A cryptosystem or cryptographic system is only the authenticated way in which user can access the encrypted data and decrypt it. The authenticated messages are shared between the authorized users. Security in cloud computing is a major concern. There are some cryptosystem techniques introduced in this security. First, Attribute Based Encryption is a public key encryption technique which is used to enable the access control over the encrypted data using qualified attributes. Second, Identity Based Encryption allows for a sender can encrypt a message to an identity without access to a public key certificate. Third, a new public key cryptosystem encrypt a message not only a public key but also under an identifier of the ciphertext classes.