In the current digitalized world, cloud computing becomes a feasible solution for the virtualization of cloud computing resources.  Though cloud computing has many advantages to outsourcing an organization’s information, but the strong security is the main aspect of cloud computing. Identity authentication theft becomes a vital part of the protection of cloud computing data. In this process, the intruders violate the security protocols and perform attacks on the organizations or user’s data. The situation of cloud data disclosure leads to the cloud user feeling insecure while using the cloud platform. The different traditional cryptographic techniques are not able to stop such kinds of attacks. BB84 protocol is the first quantum cryptography protocol developed by Bennett and Brassard in the year 1984. In the present work, three ways BB84GA security systems have been demonstrated using trusted cryptographic techniques like an attribute-based authentication system, BB84 protocol, and genetic algorithm. Firstly, attribute-based authentication is used for identity-based access control and thereafter BB84 protocol is used for quantum key distribution between both parties and later the concept of genetic algorithm is applied for encryption/decryption of sensitive information across the private/public clouds. The proposed concept of involvement of hybrid algorithms is highly secure and technologically feasible. It is a unique algorithm which may be used to minimize the security threats over the clouds. The computed results are presented in the form of tables and graphs.