Application of DNA Coding, the Lorenz Differential Equations and a Variation of the Logistic Map in a Multi-Stage Cryptosystem

Abstract

The need for information security has become urgent due to the constantly changing nature of the Internet and wireless communications, as well as the daily generation of enormous volumes of multimedia. In this paper, a 3-stage image cryptosystem is developed and proposed. A tan variation of the logistic map is utilized to carry out deoxyribonucleic acid (DNA) encoding in the first stage. For the second encryption stage, the numerical solution of the Lorenz differential equations and a linear descent algorithm are jointly employed to build a robust S-box. The logistic map in its original form is utilized in the third stage. Diffusion is guaranteed through the first and third encryption stages, while confusion is guaranteed through the application of the S-box in the second encryption stage. Carrying out both confusion- and diffusion-inducing stages results in encrypted images that are completely asymmetric to their original (plain) counterparts. An extensive numerical analysis is carried out and discussed, showcasing the robustness and efficacy of the proposed algorithm in terms of resistance to visual, statistical, entropy, differential, known plaint text and brute-force attacks. Average values for the computed metrics are: Information entropy of 7.99, MSE of 9704, PSNR of 8.3 dB, MAE of 80.8, NPCR of 99.6 and UACI of 33. The proposed algorithm is shown to exhibit low computational complexity, encrypting images at an average rate of 1.015 Mbps. Moreover, it possesses a large key space of 2372, and is demonstratd to successfully pass all the tests of the NIST SP 800 suite. In order to demonstrate the superior performance of the proposed algorithm, a comparison with competing image encryption schemes from the literature is also provided.

Keywords

• chaotic maps
• cryptography
• image encryption
• logistic map
• Lorenz differential equations
• S-box