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.

A 3-Layer PSN for Image Encryption Utilizing Fractional-Order Chen Hyperchaotic Map and Cryptographically-Secure PRNGs

“…To that end, scientists and engineers have been making use of various mathematical constructs and ideas inspired by nature to design secure and robust image encryption algorithms. Recent literature shows the employment of cellular automata (CA) [20][21][22], DNA coding [8,[23][24][25], electric circuits [26,27], as well as heavy reliance on dynamical functions of chaotic behavior [6,[28][29][30][31][32]. The following paragraph highlights the utilization of various such ideas in the development of pseudo-random number generators (PRNGs) to build encryption keys and substitution boxes (S-boxes).…”

“…The Mersenne Twister is deployed by the researchers in [7] as one of the encryption keys in a multi-stage cryptosystem. An S-box is designed and utilized as the core stage in a 3-stage image cryptosystem in [8], where the Lorenz system is numerically solved and its solution is used to generate a PRNG, which is then employed to generate the S-box. In another multi-stage image cryptosystem, the authors of [39] employ a discretized version of the chaotic sine map to create an S-box and the hyperchaotic Lu system as a PRNG.…”

“…Furthermore, upon studying hyperchaotic functions, a wide number of control parameters are readily apparent [43]. This implies that their use in image cryptosystems results in a significantly wider key space, which reduces the likelihood of brute-force attacks ever succeeding [8]. Attempting to solve hyperchaotic systems at a fractional-order permits a further expansion of the number of control variables and, consequently, realizing an even wider key space.…”

“…The previous paragraphs aimed at describing the need for research on image cryptosystems, the reliance of scholars on PRNGs to generate encryption keys and robust S-boxes, as well as the emerging utilization of hyperchaotic functions of fractional-order in this field of research. While the literature shows the prevalence of image cryptosystems that involve the use of multiple stages, in most cases these are limited to only 3 stages that comprise a total of a permutation-substitution-permutation (as in [7][8][9]20,34]). In the rare case of employing more stages, execution times are not reported [46].…”

“…While some researchers have focused their efforts into advancing cryptographic algorithms [6][7][8][9], others have dedicated their efforts towards the field of steganography [10,11].…”