## 1 Introduction  
Nowadays, in an online environment where tons of personal data are shared and instantaneously stored in servers or clouds that are distributed all over the globe, it is very difficult for people to maintain control over sensitive information when necessary. Here, we refer to different types of information, such as emails, photos, videos, and audio that are an essential part of our lives. If we cannot control or take care of our data, they can be accessed, stolen, altered, or copied by alien entities in seconds, without our consent. Thus, data protection has become important to every member of society. Large companies have been caught up in the conflict due to server data leakages that exposes all of a user's stored information. Even though information is processed and protected in many ways in order to prevent attacks and protect digital assets from being compromised, these processes are often inadequate in keeping them secure. This reality poses an enormous challenge both for privacy and cybersecurity. This is where data encryption comes in. Encryption helps to protect information by turning readable data into unreadable results. Nowadays, the most popular globally used applications are based on sharing and storing images online. Image encryption has become one of the most critical tools in today's cyberworld. A digital image is characterized by intrinsic features such as bulk data, high pixel correlation, and redundancy. Therefore, image encryption is an extremely important technology to ensure the security of sensitive information. Different image encryption schemes are outlined in this paper, such as optical transformation [1; 2; 3; 4], cellular automata [5; 6; 7], DNA coding [8; 9; 10; 11; 12], data encryption standard (DES) [13; 14; 15], advanced encryption standard (AES) [16; 17; 18; 19; 20], and Blowfish [21]. However, the last three were mainly designed for textual information rather than digital image information. In 1989, the British mathematician [PERSON] introduced the first chaos-based encryption algorithm, where a logistic map was used as a key generator [22]. In fact, chaotic behaviors can be determined by nonlinear dynamic systems, where any tiny initial deviation will be exponentially amplified. Intrinsic properties of chaotic systems, such as ergodicity, sensitive dependence on initial conditions, random like behavior, and the mixing effect, lead to a natural relationship and structural similarity between chaos and cryptography. This is an important milestone for chaos-based encryption technology. Later, in 1998, [PERSON] introduced the first general architecture for a chaos-based image cipher [23] consisting of permutation and diffusion. In the first stage, pixels were permutated by a two-dimensional area-preserving chaotic map. Then, pixel values were modified using a discretized chaotic map in the diffusion procedure. This architecture became the most popular structure and has been adopted in many chaos-based image encryption algorithms. For instance, [PERSON] et al. [24] used a 3D Arnold's cat map for substitution and employed [PERSON]'s chaotic system for the diffusion process. In [25], an image encryption algorithm with a permutation-diffusion structure was introduced and a tent map used to shuffle the positions of image pixels, and delayed coupled map lattices (DCML) were then employed to confuse the relationship between the plain and cipher image. Some researchers improved the two-stage structure, presenting a one-stage structure. [PERSON] et al. [26] proposed an image encryption algorithm that combined the permutation and diffusion stages into one stage, where the plain image was divided into blocks that could be permutated as a unit, and another algorithm that could simultaneously perform confusion and diffusion was proposed in [27], but the pixel of the image was the unit in confusion. In addition, a three-stage image encryption structure was developed and introduced; [PERSON] et al.