Application of Arnold’s Cat Map and Bülban Map for Image Encryption in Chaotic Cryptography

Abstract

This study examines the use of chaos theory to image encryption by proposing a unique algorithm for image encryption based on two chaotic maps: Arnold’s CatMap and Bülban Map. The main objectives of this work areto propose an algorithm that encrypts images using chaotic maps efficiently and effectively and in addition, to comprehend the mathematical features of the two chaotic maps. The encryption algorithm was created using version 2017b of MATLAB. The effectiveness of the map was then calculating by evaluating the cross-correlation, vertical, horizontal, and diagonal correlations, entropy, PSNR, and elapsed encryption time of the encrypted image. Further, a key sensitivity investigation was conducted to determine the key’s force resistance. The correlation values that were significantly closer to 0 confirmed the effectiveness of the encryption algorithm for each image format. Higher entropy levelsand lower PSNR values indicate that the encryption algorithm is effective. In addition, the trial-and-error method was used to determine the parameter range in which the Bülban map will display chaotic features. Based on the findings obtained for encryption using the two maps independently and the suggested hybrid map, the optimal algorithm has been proposed. Utilizing both Arnold’s cat and Bülban maps with iteration number 170 for Arnold’s Cat Map increases the reliability of image encryption compared to using only one of them.