Transmission and storage of medical data using cloud-based Internet-of-health-systems (IoHS) necessitate important prerequisites, such as secrecy, legitimacy, and integrity. This paper recommends a novel hybrid encryption/decryption scheme that can be applied in e-healthcare, or IoHS, for the protection of medical images. The proposed system explores innovative perturbation algorithms that utilize novel chaotic maps. The new maps parameters and chaotic sequences are used to control the permutation and diffusion properties of the scheme. The derived properties control pixel shuffling and operations of substitution. Chaotic behaviors of the proposed system are analyzed using bifurcation diagram, Lyapunov exponents, and NIST and DIEHARD tests. Moreover, evaluation using various test images indicated that the proposed maps have high efficiency and showed high robustness and protection of medical images. Experiments and security review also documented the good ability of the developed cryptosystem to withstand a variety of cyber-attacks. Furthermore, quantitative results using benchmark color and greyscale images prove the high security levels, sensitivity, and low residual intelligibility with high quality recovered data of our technique than several typical and state-of-the-art encryption schemes. This has been documented using statistical and security analysis metrics, such as number of pixels change rate (NPCR, 99.814%), unified average changing intensity (UACI, 33.694%), peak signal-to-noise-ratio (PSNR, 7.723), and entropy (7.9991).