Dynamic analysis of a novel chaotic system with no linear terms and use for DNA-based image encryption

The present paper proposes the design of a new image encryption scheme based jointly on DNA coding and the chaotic sequence generated by a new 3D chaotic system without linear terms. The mathematical model of the proposed system is built from Sprott B system by introducing a quadratic nonlinearity in each linear term of the system except the constant term. This modification is done with the aim to build a very simple chaotic system without linear terms and with stylish mathematical expression. The system is analyzed in-depth to show its complex dynamics. This contribution also shows the possibility of the sequences of such types of oscillators without linear term to efficiently encrypt images. Thus, based jointly on the special randomness generated by this system with no linear terms and DNA encoding, a robust cryptosystem is proposed. The feasibility and robustness of the proposed image encryption scheme are evaluated by several security tests such as statistical and differential analysis, occlusion, and data loss attack as well as brute force attack. Thus, the technique achieved correlations close to zero, entropy values greater than 7.99, and key space greater than 2100. Besides, differential analysis shows that NPCR and UACI are greater than 99.60% and 33%, respectively. Furthermore, the quantitative analyzes of occlusion and data loss attacks as well as the results of comparison with some benchmark algorithms prove the efficiency and security of the proposed cryptosystem. To the best of author’s knowledge, none of the chaotic systems above mentioned without linear terms has been applied in the field of image encryption. Therefore, this contribution promotes the evolution of nonlinear science and its applications in image encryption using DNA coding.