In this work, a new medical image encryption/decryption algorithm was proposed. It is based on three main parts: the Jigsaw transform, Langton’s ant, and a novel way to add deterministic noise. The Jigsaw transform was used to hide visual information effectively, whereas Langton’s ant and the deterministic noise algorithm give a reliable and secure approach. As a case study, the proposal was applied to high-resolution retinal fundus images, where a zero mean square error was obtained between the original and decrypted image. The method performance has been proven through several testing methods, such as statistical analysis (histograms and correlation distributions), entropy computation, keyspace assessment, robustness to differential attack, and key sensitivity analysis, showing in each one a high security level. In addition, the method was compared against other works showing a competitive performance and highlighting with a large keyspace (>1×101,134,190.38). Besides, the method has demonstrated adequate handling of high-resolution images, obtaining entropy values between 7.999988 and 7.999989, an average Number of Pixel Change Rate (NPCR) of 99.5796%±0.000674, and a mean Uniform Average Change Intensity (UACI) of 33.4469%±0.00229. In addition, when there is a small change in the key, the method does not give additional information to decrypt the image