This paper proposes an encryption method based on multiple chaotic maps and differential encoding method to secure the medical images. The proposed method uses a permutation-based image scrambling method in the confusion phase. In the diffusion phase, Piecewise Linear Chaotic Map (PWLCM), Piecewise Chaotic Map (PWCM), and tent map with differential encoding method have been employed at different levels of the phase to secure the medical images. The model has been tested on Digital Imaging and Communications in Medicine (DICOM) images. The proposed encryption method demonstrates robust security against statistical and entropy attacks, with encrypted images exhibiting a correlation close to zero and achieving a maximum entropy value of 7.9993. The low SSIM value between the original and encrypted images confirms their dissimilarity. Higher Mean Square Error (MSE) values and lower Peak Signal-to-Noise Ratio (PSNR) values for encrypted images prove a negligible presence of original pixel values. Additionally, the encryption approach showcases resilience against differential attacks, with a Number of Pixel Change Rate (NPCR) value of 99.6% and a Unified Averaged Changed Intensity (UACI) value of 33.4%, both within acceptable standard ranges. The effectiveness of the proposed method demonstrates that these encrypted DICOM images are safe against various forms of attacks.