Cloud computing enables the access of the resources such as network hardware’s, storage, applications and services that are configurable based on the demand in a network especially specific to the operations on the data. The need for data security in the cloud is progressively higher as the abundant sensitive data in the cloud are transferred among various stakeholders for data operations leads to loss of data confidentiality. To maintain data confidentiality in the cloud, the data need to be encrypted with cryptographic algorithms. Existing cryptographic algorithms face the challenges of key management, dynamic encryption, and computational complexity. In this paper, a novel variant of DNA cryptosystem is proposed to secure the original data within the DNA nucleotides providing greater storage space, reduced overhead and dynamic operations. The significance of DNA is incorporated in the proposed Novel DNA cryptosystem, which encrypts the data transferred between the Data Owner and the Data User in the cloud. Enhanced ElGamal cryptosystem is the proposed asymmetric cryptosystem used to address key management issues in the cloud, by securely transferring the key file between the Data Owner and the Data User. Enhanced ElGamal cryptosystem provides better user authentication and performance with respect to the security accomplishment against attacks. At the same time, Novel DNA cryptosystem achieves better performance, reduced the complexity of implementing the properties of DNA and embarks upon a standardized algorithmic approach among the existing DNA cryptographic methodologies. The performance analysis, mathematical proof as well as security analysis forms the security metrics and it meets out the proposed objectives. Thus, on utilizing the proposed Novel DNA and Enhanced ElGamal cryptosystems (i.e) both symmetric and asymmetric cryptosystems, enhances the security and performance of data storage and retrieval in the cloud.