This paper presents a generalization of chaotic systems using two-dimensional affine transformations with six introduced parameters to achieve scaling, reflection, rotation, translation and/or shearing. Hence, the location of the strange attractor in space can be controlled without changing its chaotic dynamics. In addition, the embedded parameters enhance the randomness and sensitivity of the system and control its response. This approach overpasses performing the transformations as post-processing stages by applying them on the resulting time series. Trajectory control through dynamic parameters is demonstrated. Simulation results validate the proposed analysis for both the simplest and Lorenz chaotic systems. An image encryption scheme is implemented using transformed Lorenz system resulting in a more secure encryption scheme in comparison to Lorenz and other recent related works. The scheme exhibits good performance when assessed using the PRNG properties, encrypted image histogram and its uniformity through chi square test, pixel correlation, Mean Squared Error (MSE), entropy, Peak Signal-to-Noise Ratio (PSNR), the National Institute of Standards & Technology (NIST) test, key space, key sensitivity, resistance to differential, ciphertext-only, known plaintext, and chosen plaintext attacks, robustness against noise and computation time. © 2021
Sayed W.S., Radwan A.G., Fahmy H.A.H., Elsedeek A.
Affine transformations; Chaos; Dynamic translation; Image encryption; Lorenz system; Trajectory control
Egyptian Informatics Journal, Vol. 22, PP. 155 to 166, Doi: 10.1016/j.eij.2020.07.002