Eur. Phys. J. Special Topics 228, 1951-1967 (2019)
https://doi.org/10.1140/epjst/e2019-800209-3

Regular Article

Image encryption algorithm based on discrete logarithm and memristive chaotic system

¹ College of Physics and Electronics, Hunan Institute of Science and Technology, Yueyang 414006, P.R. China
² School of Electrical Engineering and Automation, Wuhan University, Wuhan 430072, P.R. China

^a e-mail: hnistlichl@163.com

Received: 23 November 2018
Received in final form: 31 January 2019
Published online: 14 October 2019

Abstract

In order to effectively resist the plaintext attacks introduced in recent cryptanalysis literatures, a reformative image encryption algorithm based on discrete logarithm and a memristive chaotic system is proposed in this paper. Firstly, we realize the permutation and confusion of a plain image by employing the discrete logarithms of memristive chaotic sequences. Then the discrete logarithms of intermediate cipher pixels and memristive chaotic sequences are used in the forward diffusion and backward diffusion of the permuated and confused image. Since the finite multiplication group adopted in this paper has up to 128 generators, we can expand the secret key space and enhance the ability of the proposed image encryption algorithm to resist plaintext attacks, by obtaining the generators through the secret key and the SHA256 hash value of the plain image. Finally, Simulation results and comparative analyses show that the proposed image encryption algorithm is not only secure and efficient, but also has very high practical value.