Eur. Phys. J. Plus (2018) 133: 6
https://doi.org/10.1140/epjp/i2018-11834-2

Regular Article

A new hyperchaotic map and its application for image encryption

¹ Institute for Mathematical Research, Universiti Putra Malaysia, Serdang, Malaysia
² Malaysia-Italy Centre of Excellence for Mathematical Science, Universiti Putra Malaysia, Serdang, Malaysia
³ Department of Mathematics, Universiti Putra Malaysia, Serdang, Malaysia
⁴ The Branch of Applied Mathematics, Applied Science Department, University of Technology, Baghdad, Iraq

^* e-mail: haydernatiq86@ymail.com

Received: 21 August 2017
Accepted: 11 December 2017
Published online: 9 January 2018

Abstract

Based on the one-dimensional Sine map and the two-dimensional Hénon map, a new two-dimensional Sine-Hénon alteration model (2D-SHAM) is hereby proposed. Basic dynamic characteristics of 2D-SHAM are studied through the following aspects: equilibria, Jacobin eigenvalues, trajectory, bifurcation diagram, Lyapunov exponents and sensitivity dependence test. The complexity of 2D-SHAM is investigated using Sample Entropy algorithm. Simulation results show that 2D-SHAM is overall hyperchaotic with the high complexity, and high sensitivity to its initial values and control parameters. To investigate its performance in terms of security, a new 2D-SHAM-based image encryption algorithm (SHAM-IEA) is also proposed. In this algorithm, the essential requirements of confusion and diffusion are accomplished, and the stochastic 2D-SHAM is used to enhance the security of encrypted image. The stochastic 2D-SHAM generates random values, hence SHAM-IEA can produce different encrypted images even with the same secret key. Experimental results and security analysis show that SHAM-IEA has strong capability to withstand statistical analysis, differential attack, chosen-plaintext and chosen-ciphertext attacks.