# 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
The resulting S-boxes were found to satisfy the five criteria (bijective, non-linearity, strict avalanche, bit independence, input/output XOR distribution) required for acceptable use in cryptographic algorithms. * Henon map The Henon map was first discovered in 1978 and can be described as a 2D mapping function with two control parameters, which, when chosen strategically, enable the map to behave chaotically. [PERSON] et al. [54] proposed an image encryption algorithm utilizing Henon maps for shuffling the pixels of the image and 4D Qi hyper-chaos to generate keys for encryption. Experimental analysis of the algorithm demonstrates strong cryptographic properties and resistance against common attacks. * Logistic-sine system A Logistic-Sine System (LSS) is a discrete combination of the logistic and sine maps, both of which exhibit chaotic behavior under particular initial conditions. [PERSON] and [PERSON] [55] referred to such a combination of the two maps as a _compound chaotic map_ and utilized it in a novel encryption algorithm using XOR and modulus operations. [PERSON] et al. [56] investigated the inefficiencies with single chaos systems and proposed a novel algorithm utilizing LSS and cascade chaos to improve upon said inefficiencies. Experimental analysis through simulation has proven the new algorithm to be highly resilient In another study, [PERSON] et al. [57] conducted cryptanalysis on an existing algorithm based on multiple S-boxes, but were able to break it using CPT attacks. A new algorithm was proposed to improve upon the old one and involved only a single S-box constructed utilizing LSS. Further cryptanalysis of the new algorithm showed improvement over the original and was also quite fast. Variants of LSS have also been employed in encryption algorithms, such as a 2D Logistic Modulated Sine Coupling Logistic (LSMCL) map proposed by [PERSON] et al. [58], a Logistic Sine Modulation Map (LSIMM) proposed by [PERSON] et al. [59], and a 2D Logistic Adjusted Sine Chaotic Map (LASCM) proposed by [PERSON] and [PERSON] [60]. In all cases, theoretical analysis and simulations determined the algorithms to be both secure and efficient. * Baker map The baker map is a bijective permutation function that operates on an MxM matrix by randomizing its cells according to a secret key and is well respected in the image encryption community. [PERSON] et al. [61] utilized the baker map in an image encryption algorithm to improve upon a classic technique known as Double Random Phase Encoding (DRPE). The proposed algorithm uses the map to pre-process the image before applying DRPE, and experimental analysis showed significant increases in security as opposed to using DRPE alone. Another algorithm utilizing the baker map was proposed by [PERSON] et al. [62], where high-dimensional dynamical multiple chaos was paired with the baker map to achieve a larger avalanche effect. Experimental results again showed significant increases in security when
* Tinkerbell map [PERSON] [63] proposed an encryption algorithm utilizing Tinkerbell maps, a pair of chaotic functions, to inject strong pseudo-random numbers in multiple points during the encryption and decryption process. Differential and correlational analysis of the algorithm showed the proposed method to be highly efficient. * Cubic map A cubic map is a single-dimensional chaotic function that produces values on the interval [0, 1] and can be controlled by a single mapping parameter. [PERSON] et al. [64] proposed an encryption technique that employs a hybrid chaos source composed of the cubic and tent maps, as well as the Iterative Chaotic Map with Infinite Collapses (ICMICs). The resulting hybrid map is used with the XOR operation to achieve encryption, and an analysis of the algorithm showed that it is suitable for repeated use and is resilient against attacks. * Gingerbreadman map [PERSON] et al. [65] used the Gingerbreadman map, a 2D chaotic map, to generate encrypted keys for use with the well-known Cipher Block Chain (CBC) encryption algorithm.