# Chaotic Image Encryption: State-of-the-Art, Ecosystem, and Future Roadmap
## 3 State-of-the-Art
### State-of-the-Art in Chaos Aspect
#### 3.1.2 Chaos Sources
Using the map in this algorithm greatly improves CBC's performance when applied to images, and a visual comparison demonstrated massive improvements. * Tangent map [PERSON] et al. [66] proposed a Random Number Generation (RNG) algorithm based on the usage of the mathematical hyperbolic tangent function. When the RNG algorithm was applied to image encryption, the resulting procedure demonstrated strong cryptography
* Multiple maps Mixing multiple mapping functions in image encryption algorithms can serve multiple purposes. For example, [PERSON] et al. [67] employed a verity of different maps to achieve tasks such as more chaotic permutation, diffusion, and RNG. A similar technique employing various maps in different stages of the encryption procedure was also proposed by [PERSON] et al. [68]. [PERSON] et al. [69] proposed a novel keystream generation technique utilizing multiple chaotic maps that incorporates the plaintext itself into the stream. The algorithm was motivated by the need to defend against CPT and KPT attacks, and an analysis of the algorithm showed it is effective in achieving its goal. In terms of areas of application, stronger algorithms enforced by the use of multiple chaotic maps are important in numerous fields. For example, [PERSON] et al. [70] proposed an algorithm using multiple maps for encrypting colored medical images, which can be seen as unique in their size and sensitivity. Experimental and statistical analysis of the resulting procedure showed it is secure for use with healthcare images. * Other mathematical sources In addition to chaotic systems and maps, some researchers have used the following mathematical designs, which have not been originally defined for chaos creation:
* Space-filling curves Fractal geometry has several intriguing properties, such as self-similarity, composition by iterative methods, and a complex structure. [PERSON] et al. [71] utilized Hilbert curves and H-fractals, types of self-filling curves, in a novel image encryption algorithm. This algorithm alternates the use of both curves to efficiently scramble the pixels of the image. * Memory cellular automata Cellular Automata (CA) can best be described as a grid of cells with a finite set of states and a transition function that governs how cells change state over time. Whereas a standard CA only depends on the generation t-1, Memory Cellular
Automata (MCA) depend on more parameters. When the MCA's rules are defined by chaotic maps, the structure becomes a powerful tool for image encryption. Several algorithms using various-order MCAs have been proposed, for example a 4D MCA by [PERSON] et al. [72], a 2D MCA by [PERSON] et al. [73], and an indefinite CA by [PERSON] et al. [74]. - Transcendental numbers In mathematics, a transcendental number has the characteristic that digits to the right of the decimal have no pattern [75]. [PERSON] et al. [75] proposed an image encryption algorithm that uses chaos and the transcendental number Pi, dubbed Chaotic Pi Ciphering (CPC). The algorithm uses Pi and a chaos source created using differential equations to generate cipher keys and substitution boxes. Physical Sources In addition to mathematical sources, chaos can be created using physical phenomena and used in chaotic image encryption:  
* Optical Chaos Our physical world can provide many forms of chaos, with just one example being light. In studies by [PERSON] et al. [76] and [PERSON] et al. [77], they found success in producing a chaotic base for image encryption algorithms using lasers. Extensive security testing of both algorithms showed them to be highly secure and feasible for practical use. Other studies have also been carried out, such as those by [PERSON] et al. [78] and [PERSON] et al. [79], where optical chaos is utilized for encrypting and then transmitting images for storage in the cloud. Experimental results showed both procedures to be secure and safe for production use. * Chua circuit Some physical electronic circuits such as the Chua circuit can produce chaotic behavior. [PERSON] et al.