Electronic Health Records (EHR) security ensures the confidentiality of patients' information and guarantees healthcare providers' accountability. Sharing such medical records with third party through an unsecure channel may be abused or disclosed to other unauthorized parties. Therefore, there is a rising need for a novel technology, which allows for outsourcing the data through an unsecure channel while preserving the privacy of EHR. In this paper, a novel Block chain Assisted Cloud based Key exchange (BACK) technique has been introduced, that uses blockchain technology for secure data transmission. The proposed method uses the novel secure Quantum Diffie Hellman key exchange (QDHKE) system for sharing the key in an unsecure environment. The BACK methodology helps in sharing the medical data through unsecure channel while maintaining the confidentiality and privacy of health information. The proposed method has been evaluated using CloudSim simulator. The efficiency of the technique has been assessed in terms of particulars like the time it takes to encrypt, decode, and execute and computational cost. According to the experimental results, the proposed BACK method achieves less encryption time of 12.5%, 7.4%, and 4.65% than existing techniques such as Healthchain, Blockchain integrated with IPFS, and Blockchain-based FL respectively.