<p>Nowadays, in telemedicine and medicinal applications, digital images are widely used to transform information for remote diagnosis and first aid response. Digital images significantly contribute to transmitting data/information over a public network with high redundancy and correlation. A large image provides a better way to support crypto graphical algorithms for encryption. Chaotic map approaches enhance the security of digital images by supporting such qualities and being extremely sensitive to the initial conditions. To strengthen data protection, we suggested a new hybrid double encryption technique that combines the Tinkerbell map and Arnold’s Cat map in this research. Here, we use the Tinkerbell map to encrypt the image first, followed by the Arnold cat map, and then we reverse the procedure to obtain the decrypted image; this suggested method provides us with large number of control parameters for increased safety and uncertainty, as well as good correlation coefficient, entropy, MSE and PSNR values. Many metrics, including NPCR and UACI, are used to monitor minute pixel changes to evaluate the efficacy of image encryption.</p>