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 (Formula presented.) and (Formula presented.), entropy values between (Formula presented.) and (Formula presented.), PSNR values (in the original and encrypted images) between (Formula presented.) and (Formula presented.), the number of pixel change rate (NPCR) values between (Formula presented.) and (Formula presented.), unified average changing intensity (UACI) values between (Formula presented.) and (Formula presented.), and a vast range of possible keys (Formula presented.). 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.