Currently, a multimedia revolution of medical data in health information becomes part of our computing environment. However, the interchange of medical information is typically outsourced by third parties, which may affect the disclosure of confidentiality. To address this issue, we address high security and confidentiality through our proposed CHAN-PKC cryptomata. The proposed scheme uses a Diophantine equation to have the three stage of decryption for high security, but ESRKGS and RSA has one level of decryption. The results show that the proposed cryptomata has efficient encryption and decryption time when compared to the existing systems. At 10 K-bit moduli of key generation, CHAN-PKC consumes only 0.65 times of RSA, but ESRKGS takes 1.83 times of RSA. The timing similarity shows that both CHAN-PKC and RSA has a 100% correlation, but ESRKGS has only 90%. Hence our CHAN scheme is robust against side channel and also has a large key space than RSA. The security analysis confirms that our CHAN-PKC is very fast, secure against brute force and side channel attacks; therefore, it is feasible for real-time applications. © 2019, Springer Science+Business Media, LLC, part of Springer Nature.