Color Image Encryption Algorithm Based on a Chaotic Model Using the Modular Discrete Derivative and Langton’s Ant

Abstract

In this work, a color image encryption and decryption algorithm for digital images is presented. It is based on the modular discrete derivative (MDD), a novel technique to encrypt images and efficiently hide visual information. In addition, Langton’s ant, which is a two-dimensional universal Turing machine with a high key space, is used. Moreover, a deterministic noise technique that adds security to the MDD is utilized. The proposed hybrid scheme exploits the advantages of MDD and Langton’s ant, generating a very secure and reliable encryption algorithm. In this proposal, if the key is known, the original image is recovered without loss. The method has demonstrated high performance through various tests, including statistical analysis (histograms and correlation distributions), entropy, texture analysis, encryption quality, key space assessment, key sensitivity analysis, and robustness to differential attack. The proposed method highlights obtaining chi-square values between 233.951 and 281.687, entropy values between 7.9999225223 and 7.9999355791, PSNR values (in the original and encrypted images) between 8.134 and 9.957, the number of pixel change rate (NPCR) values between 99.60851796% and 99.61054611%, unified average changing intensity (UACI) values between 33.44672377% and 33.47430379%, and a vast range of possible keys >5.8459×1072. On the other hand, an analysis of the sensitivity of the key shows that slight changes to the key do not generate any additional information to decrypt the image. In addition, the proposed method shows a competitive performance against recent works found in the literature.