Medical image encryption could aid in preserving patient privacy. In this article, we provide a chaotic system-based medical picture encryption method. The diffusion and permutation architecture was used. The permutation based on plain image and chaotic keys is offered to shuffle the plain picture's pixels to other rows and columns, weakening the strong connections between neighboring pixels. Diffusion is suggested to spread small changes of plain images to all of the pixels in cipher images to enhance the encryption effect. We analyze the chaotic behavior of the proposed system using various techniques and tests such as bifurcation plots, Lyapunov exponents, MSE, PSNR tests, and histogram analysis.