# Chaotic Image Encryption: State-of-the-Art, Ecosystem, and Future Roadmap
## 3 State-of-the-Art
### State-of-the-Art in Chaos Aspect
#### 3.1.3 Chaos Dimension  
The dimension of a chaos map refers to the number of functions (x(t), y(t), etc.) it is composed of. Many image encryption algorithms utilize chaotic functions of vary ing dimensions. Chaotic functions used in chaotic image encryption can be categorized as follows:  
* One-dimensional Work with one-dimensional chaos includes that by [PERSON] and [PERSON] [85], where the novel 1D Sine Chaotic System (1 DSCS) was proposed. This system exhibits a large parameter interval as compared to the standard sine map it was built upon. [PERSON] et al. [86] proposed an image encryption algorithm utilizing the 1D tent map. A similar algorithm also using the tent map was proposed by [PERSON] et al. [87]. Extensive testing proved both algorithms to be effective at resisting common cryptographic attacks. The former paper also elaborated on the low chaotic range for the tent map and suggested that future work use a variant with a larger range such as the tent-sine map.
* Two-dimensional An image encryption algorithm based on two-dimensional chaos was proposed by [PERSON] and [PERSON] [88]. This algorithm uses the 2D logistic chaotic system and a novel block image encryption procedure. Experimental results demonstrated the algorithm to have strong randomness, low pixel correlations, and high key sensitivity.
* Three-dimensional Many image encryption algorithms utilize three-dimensional chaos. One such algorithm was proposed by [PERSON] et al. [89], where they utilized the 3D logistic and cat maps. The novel usage of image reconstruction techniques also improved the effectiveness of the algorithm. In an algorithm proposed by [PERSON] et al. [90], the 2D image was converted into three-dimensional space by creating three streams from the red, green, and blue channels of the image. The 3D modular chaotic map was used as the chaos source for encryption. Two other algorithms using three-dimensional chaos systems were proposed by [PERSON] and [PERSON] [91] and [PERSON] and [PERSON] [92], respectively. In the former, the Rossler chaos system was used, whereas the latter study opted to use the Lorenz system.
* Four-dimensional [PERSON] et al. [93] proposed a novel four-dimensional chaos system based on concepts known as \"shape synchronization\" and \"driver-response\". The complex mathematical underpinnings make the algorithm very difficult to break, and experimental tests in the application of image encryption showed promising results for its effectiveness.
* Five-dimensional [PERSON] and [PERSON] [94] proposed a novel five-dimensional chaotic map composed of the 2D logistic map and 3D discrete Lorenz map. Experimental simulations of the system when applied to image encryption resulted in high scores in many common encryption strength tests.
* Multiple dimensional Work related to mixing maps of varying dimensions in image encryption has also been performed. For example, [PERSON] and [PERSON] [95] proposed an image encryption algorithm using both the 1D logistic map and 3D Lorenz system. Experimental results demonstrated that the algorithm has strong security. [PERSON] et al. [96] proposed a novel image encryption and transmission procedure based on Elliptic Curve Cryptography (ECC). Encryption is achieved using 3D and 4D Arnold cat maps as chaos sources, and the Elliptic Curve Diffie-Hellman (EDCH) key exchange algorithm is utilized to establish a shared key between parties. Digital signatures allow the algorithm to authenticate the encrypted message before decryption, and experimental results showed the method to be effective.