Heart disease is considered one of the complex and global-wide diseases, and its early detection plays a vital role in healthcare and cardiology. The Big-data requires a cloud that provides expandable data storage that is accessed via the internet. Moreover, the out-sourcing data in the cloud for storage makes it easier to the management of user data and also decreases the maintenance cost of data. However, some organizations do not trust to store the data in the cloud due to privacy and security concerns. Though the existing encryption techniques can confidentially protect the data, it has few drawbacks, like the access pattern can leak sensitive data. In this paper, an efficient framework for heart disease prediction was developed using deep learning methods using heart disease datasets from University of California, Irvine (UCI) repository. The proposed method utilizes Optimized Encryption based Elliptical Curve Diffie-Hellman (OEECDH) approach for key generation. Elliptic Curve Cryptography (ECC) with Diffie-Hellman algorithm utilized for decryption and encryption of data for enhancing the security and privacy in the cloud. Additionally, this algorithm reduces the complexity in computations and also encrypts the data more efficiently. This system is followed by the classification using a deep convolution network performed in experimental analysis. The performance of the proposed method is calculated from the parameters like decryption time, key generation time and encryption time. The proposed method shows better performance compared with existing techniques like Methicillin-Resistant Staphylococcus Aureus (MRSA), Rivest, Shamir, Adleman (RSA), MRSA-Colonized (MRSAC) and Elliptic Curve with Diffie–Hellman (ECDH) on the basis of performance metrics. Additionally, the proposed algorithm can be applied in health care systems to identify cardiac disease effectively.