Cloud computing is a popular subject across the IT industry, but many risks associated with this relatively new delivery model is not yet fully understood. Cloud computing is an budding information technology of data storage, of local networks (infrastructure) as well as software and has its advantages of scalability, reliability, high performance and comparatively low cost feasible solution contrast to committed infrastructures. Here, initially the data owner will encrypt the searchable index with ElGamal cryptosystem utilizing Hyper Elliptical Curve Cryptography for double encryption. The ElGamal cryptosystem is utilized for security analysis where in sharing of multiple keys between two parties are performed aiming for better security. The random integer selection in the ElGamal cryptosystem is modified based on optimization process using Modified cuckoo search (MCS). Further Hyper elliptical curve cryptography is incorporated with ElGamal cryptosystem which is utilized for encryption and decryption. Also, the hyper elliptic curve cryptography is modified using auxiliary input in the divisor calculation in order to improve security. For selecting keys, we have used Gravitational search algorithm (GSO). The retrieval process will take a two-round communication between the cloud server and the data user. The experimental results shown that, the recommended technique attains minimum storage cost and minimum computation time when compared to the existing technique.