There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

Dynamical systems: stability, symbolic dynamics and chaos

This paper proposes a new hybrid chaotic map and a different way of using optimization technique to improve the performance of encryption algorithms. Compared to other chaotic functions, the proposed chaotic map establishes an excellent randomness performance and sensitivity. Based on its Lyapunov exponents and entropy measure, the characteristics of the new mathematical function are better than those of classical maps. We propose a new image cipher based on confusion/diffusion Shannon properties. The substitution phase of the proposed encryption algorithm, which depends on a new optimized substitution box, was carried out by chaotic Jaya optimization algorithm to generate S-boxes according to their nonlinearity score. The goal of the optimization process is to have a bijective matrix with high nonlinearity score. Furthermore, a dynamic key depending on the output of encrypted image is proposed. Security analysis indicates that the proposed encryption scheme can withstand different crypt analytics attacks.

An image encryption scheme based on a new hybrid chaotic map and optimized substitution box

The unmanned aerial vehicle (UAV) route planning problem mainly centralizes on the process of calculating the best route between the departure point and target point as well as avoiding obstructions on route to avoid collisions within a given flight area A highly efficient route planning approach is required for this complex high dimensional optimization problem However, many algorithms are infeasible or have low efficiency, particularly in the complex three-dimensional (3d) flight environment In this paper, a modified sparrow search algorithm named CASSA has been presented to deal with this problem Firstly, the 3d task space model and the UAV route planning cost functions are established, and the problem of route planning is transformed into a multi-dimensional function optimization problem Secondly, the chaotic strategy is introduced to enhance the diversity of the population of the algorithm, and an adaptive inertia weight is used to balance the convergence rate and exploration capabilities of the algorithm Finally, the Cauchy-Gaussian mutation strategy is adopted to enhance the capability of the algorithm to get rid of stagnation The results of simulation demonstrate that the routes generated by CASSA are preferable to the sparrow search algorithm (SSA), particle swarm optimization (PSO), artificial bee colony (ABC), and whale optimization algorithm (WOA) under the identical environment, which means that CASSA is more efficient for solving UAV route planning problem when taking all kinds of constraints into consideration

https://www.mdpi.com/1424-8220/21/4/1224/pdf

A Modified Sparrow Search Algorithm with Application in 3d Route Planning for UAV.

Encryption of data with high correlation, such as images, is a challenge for block ciphers, since patterns of the original image may remain after encryption. This is due to the deterministic mapping performed by the cipher. To overcome this limitation, a block cipher is used in an adequate mode of operation, such as cipher block chaining, counter mode. It is presented in this work randomized block ciphers inspired by the Rijndael architecture employing chaotic maps as an entropy source. It is shown that the proposal achieves good security and robustness indicators with fewer rounds compared to that obtained with the Rijndael algorithm.

Image encryption using block cipher and chaotic sequences

Finite-state Markov channels (FSMCs) are commonly used to characterize the memory of binary (binary-input, binary-output) discrete fading channels (DFCs). This paper proposes a new FSMC model, called the ternary Markov channel (TMC), to characterize ternary (binary-input, ternary-output) discrete channels with memory and soft-information. The TMC is used to model a DFC with the simplest soft-decision quantizer that labels low reliable received symbols as erasure symbols. This paper also proposes an enumerative technique to analytically evaluate the performance of a linear block code over the TMC. A new recurrence expression is developed for calculating the probability of codeword error for bounded distance error and erasure decoding.

Modeling Fading Channels With Binary Erasure Finite-State Markov Channels

An emitter-coupled pair chaotic generator is proposed with a control parameter that can be tuned for distinct chaotic behaviors. The proposed circuit is a compact, high-speed implementation of the chaotic map based on the hyperbolic tangent function. It is demonstrated that the circuit and map parameters are analytically related. As an application, we design a random number generator that passes all NIST statistical tests by applying a post-processing to the balanced bit sequence generated by a quantization of the circuit output.

Emitter-coupled pair chaotic generator circuit

We introduce in this paper a new chaotic map with dynamical properties controlled by two free parameters. The map definition is based on the hyperbolic tangent function, so it is called the tanh map. We demonstrate that the Lyapunov exponent of the tanh map is robust, remaining practically unaltered with the variation of its parameters. As the main application, we consider a chaotic communication system based on symbolic dynamics with advantages over current approaches that use piecewise linear maps. In this context, we propose a new measure, namely, the spread rate, to study the local structure of the chaotic dynamics of a one-dimensional chaotic map.

/pdf/a-smooth-chaotic-map-with-parameterized-shape-and-symmetry-44qselpguk.pdf

A smooth chaotic map with parameterized shape and symmetry

In this paper, we propose a methodology to design chaos-based communication systems, which exploits the topological structure of 3-D chaotic attractors. The first step consists in defining a proper partition of a Poincare section of the attractor and the subsequent encoding of the chaotic trajectories. Then, the evolution mechanism of the chaotic attractor, according to the dynamical restrictions imposed by the chaotic flow, is represented by a state diagram, where each state represents a region of the Poincare section or a branch in the template of the chaotic attractor. The state transitions are associated with segments of chaotic trajectories that connect the corresponding regions of the Poincare section. The chaotic signals are transmitted over both additive white Gaussian noise and Rayleigh flat fading channels, and a trellis structure derived from the state diagram is used at the decoder to estimate the transmitted information sequence. Finally, the bit error rate performance of the system is analyzed.

Daniel P. B. Chaves

Papers

Image encryption using block cipher and chaotic sequences

Modeling Fading Channels With Binary Erasure Finite-State Markov Channels

Emitter-coupled pair chaotic generator circuit

A smooth chaotic map with parameterized shape and symmetry

Digital Communication Systems Based on Three-Dimensional Chaotic Attractors