### Applications for Chaos-Based Secure Communications  
Some properties of chaos, such as complex behaviour, noise-like dynamics and spread spectrum can be used to encode data so that the transmitted message is inaccessible to possible eavesdroppers. To this purpose, a number of interesting papers have been published in the years 2018-2020. For example, in [5], new architectures of perturbed digital chaos for image permutation and diffusion have been proposed. The chaotic dynamics is perturbed at bit level using perturbation on state variables and/or on control parameters [5]. Under persistent perturbations, the dynamics of the chaotic map prove to be nonstationary, thus providing advantages in image permutation and diffusion based on cryptography. Simulation results using a logistic map have clearly demonstrated the effectiveness of the conceived approach [5].  
In [7], an encryption-based method for region of interest (ROI) security in high-efficiency video coding (HEVC) standards has been illustrated. The selective approach exploits a chaos-based stream cipher to encrypt some HEVC syntax elements. In particular, a standard HEVC decoder is used to decode the bit stream, whereas a secret key is necessary to decrypt the ROI [7]. The suggested chaos-based ROI encryption exploits the tile property of HEVC, which enables each video frame to be split into independent rectangular areas. Experimental measurements have highlighted that the conceived approach enables secure video encryption to be achieved in real-time, with satisfying bit rate and complexity overheads [7].  
In [6], the security of some steganagraphic methods (analysed in the spatial and frequency domain) has been improved by exploiting the properties of chaos. In particular, a statistical steganalysis system has been built in order to assess the robustness of three chaos-based steganographic methods [6]. Experimental results have shown that the conceived steganalysis system, which exploits multi-dimensional feature vectors, is able to effectively detect hidden information, regardless of the message size [6].  
In [3], a piecewise-linear function is exploited as a dynamic selector for dynamics editing. The approach, which is based on offset boosting, enables any chaotic dynamics from any nonlinear system to be extracted without modifying the system parameters. The authors of reference [3] suggest the use of dynamic selectors as novel keys for chaos-based secure communications, particularly when very complex dynamical systems are involved.  
In [4], two robust keyed hash functions comprising a chaotic system and a chaotic neural network have been proposed. The input message \(M\) is hashed to a hash value \(h\) with a fixed number of 256 or 512 bits. In particular, the chaotic system generates pseudo-chaotic samples, which become parameter values for the neural structure [4]. This combined architecture ensures that the generated hash functions possess excellent statistical properties, including high message and key sensitivity [4]. Thus, the proposed keyed chaos-based hash functions are suitable for digital signature, data integrity and message authentication [4].  
In [11], a matrix projective synchronization scheme for fractional-order maps is presented. A novel synchronization error is introduced, and a control algorithm is designed to stabilize the error dynamics at the origin. The synchronization of fractional maps is exploited for a secure communication application, which includes speech encryption over a public channel [11].  
In reference [12], S-boxes generated by using chaotic functions are analysed to measure their actual resistance to cryptanalysis. By using two heuristic methods and starting from pseudo-random S-boxes, the author of reference [12] has designed S-boxes that significantly outperform all previously published chaos-based S-boxes. Moreover, the approach in [12] enables to reach near-optimal average coordinate nonlinearity values, which are significantly greater than those known in literature.