**1. Introduction**

Nowadays, rapid developments of Internet and digital technologies have led to tremendous digital multimedia contents transmitting over Internet networks. Thus, protection on the contents of digital data has attracted serious concern from medical, military, and many other areas. Various image encryption methods have emerged by using cryptographic techniques [1–4]. Although there exists a view that AES is not suitable for image encryption, Zhang recently refuted it by using AES of cipher block chaining mode to encryp<sup>t</sup> images [5].

The chaos-based encryption method has become one of the most ideal methods, since it has a lot of appropriate characteristics, e.g. high sensitivity on initial conditions, mixing property, ergodicity, complex behavior, etc. [6–8]. As a result, a lot of researchers have presented plenty of image encryption schemes with a chaotic system [9–13]. In [14], Askar et al. proposed a chaotic economic map based image encryption method, whose simulation results indicated that the proposed algorithm could successfully encryp<sup>t</sup> and decrypt the images, and it had a good performance on security tests, except noise attacks analysis. By using a single round based hyper-chaotic system, Shaikh et al. presented a color image encryption method with bi-directional pixel diffusion [15]. Additionally, Li et al. presented a "transforming-scrambling-diffusion" model based color image encryption method with a four-dimensional (4D) hyper-chaotic system, which could convert pixel values to gray format before scrambling [16]. There is no doubt that some of the encryption methods in these chaos-based schemes still have weaknesses to some extent. However, different chaotic systems are neither superior nor inferior each other. A high-dimensional chaotic system has complex chaotic behaviors with high time cost, while a low-dimensional

**Citation:** Zhang, D.; Chen, L.; Li, T. Hyper-Chaotic Color Image Encryption Based on Transformed Zigzag Diffusion and RNA Operation. *Entropy* **2021**, *23*, 361. https:// doi.org/10.3390/e23030361

Academic Editors: Amelia Carolina Sparavigna and Salim Lahmiri

Received: 27 January 2021 Accepted: 15 March 2021 Published: 17 March 2021

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**Copyright:** © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

chaotic system is opposite [17–19]. Hence, in this paper, a 6D hyper-chaotic system is employed as a pseudo-random numbers sequence generator for more complexity.

Zigzag is a common scrambling operation in image encryption [20,21]. In [22], Li et al. presented a 3D logistic map based color image encryption method with Zigzag scramble; the experiments showed that this method had brute-force attack and statistical attack resistance, but differential attacks analysis was missing. While, Wang et al. proposed a color encryption method with a Zigzag transformation, which could change the start pixel from upper left corner to the other three corners in an image [20]. Next year, Wang et al. [23] presented another image encryption method, which introduced an extended Zigzag confusion for a non-square image. Additionally, in [24], Zhao et al. proposed a novel color image encryption by combining Zigzag map and Hénon map together for permutation. However, these image encryption schemes implement Zigzag scramble on 2D images, which leads to some adjacent values in special positions of the image not being able to be scrambled, and different channels of a color image could not be scrambled, either. On the other hand, some image encryptions transformed 2D image to 3D cube [25], which gives out a new encryption inspiration on permutation, but most of them were focused on rotation, but not Zigzag. Therefore, Zigzag is utilized in diffusion on a 3D cube instead of scramble on 2D image to eliminate these drawbacks in this paper.

Deoxyribonucleic acid (DNA), a biological concept, has recently become a popular trend in the image encryption field [26,27]. By using DNA-based techniques, cipher images could obtain competitive entropy, correlation coefficients etc. [4,28–31]. In [29], Chai et al. presented a new diffusion mechanism that is based on the random numbers that are generated by plaintext image, and incorporated DNA encryption with four-wing hyper-chaotic system. Reference [32] proposed an image encryption method using a spatial map based DNA sequence matrix. In general, the DNA-based encryption mechanism includes two steps: use DNA operation rules to convert pixels of plaintext image to DNA codon matrix and change chaotic sequence to DNA keys to generate cipher image with DNA codon matrix.

While unlike the two strands structure of DNA sequences, Ribonucleic acid (RNA) is a single strand structure. RNA could form double helixes with complementary base pairing. By using this feature, some new image encryption methods have been proposed. In [33], Mahmud et al. presented an image encryption method by combining RNA with Genetic Algorithm (GA) through using a logistic map. In [34], Abbasi et al. employed Chen's chaotic system to encryp<sup>t</sup> an image with imperialist competition algorithm and RNA operations. Yadollahi et al. utilized the concepts of DNA and RNA to construct a two-phase image encryption method [35]. While an image encryption method is presented by Wang et al. through using an one-dimensional (1D) chaotic system combined from Logistic and Sine map, extended Zigzag confusion, and RNA operation [23]. However, all of these four schemes focus on gray image encryption. Although there is a color image experiment in [23], it is realized by running the scheme three times in three channels.

Being motivated by above discussions, a novel color image encryption method, called HCZRNA, is proposed in this paper. At the beginning, a 6D hyper-chaotic system is employed to generate three pseudo-random matrices. Subsequently, one of the pseudorandom matrices is used to permute plaintext color image. Additionally, 3D transformed Zigzag diffusion is implemented on initial cipher image with the second pseudo-random matrix. After diffusion, an RNA operation is used to convert the diffused image to RNA codons array, and update this array through RNA codons tables that are generated by the third pseudo-random matrix. Finally, a cipher image is obtained.

The main contributions of this work is listed as follows:


• Extensive experiments and analyses demonstrate that the proposed HCZRNA could resist various types of attacks.

The rest of this paper is structured as follows: Section 2 introduces the used 6D hyperchaotic system, 3D Zigzag and RNA. Section 3 presents the HCZRNA scheme and explains how initial values and pseudo-random matrix are generated in detail. Section 4 reports and analyzes the experimental results. Finally, Section 5 concludes this paper.
