A Novel Image Encryption Algorithm Based on the Delayed Maps and Permutation-Confusion-Diffusion Architecture

Abstract

To improve the dynamical behaviors of 1D chaotic maps, a new linear-delay-modulation method (LDM) is proposed. Derived from the Sine map, a delayed Sine map (DSM) is proposed based on the LDM. Then, we substitute the Sine map in the SIMM system with DSM and obtained a delayed SIMM system (DSIMM). Its chaotic performance is analyzed through the phase diagram, Lyapunov exponent spectrum, and complexity. The results show that the delayed chaotic map can generate more complex dynamical behaviors and more random sequences. Hence, we apply the two delayed systems to a novel image encryption algorithm with the permutation-confusion-diffusion architecture. Firstly, to permutate the pixel of the image efficiently, the plain-image is scrambled by using a multilayer of the nonlinear index. Secondly, the image is confused by using the chaotic matrix generated with two chaotic sequences, and then, the ciphertext is transformed into a 1D sequence. Finally, to improve the plaintext sensitivity and facilitate key management, we enhance the sensitivity by applying a novel diffusion algorithm instead of using plaintext-related keystream. The diffusion equation contains the sum of undiffused pixels and the operation of cyclic bit-shift. Simulation results for the gray image illustrate the effectiveness of the proposed encryption algorithm.