In this paper, we report an effective cryptosystem aimed at securing the transmission of medical images in an Internet of Healthcare Things (IoHT) environment. This contribution investigates the dynamics of a 2-D trigonometric map designed using some well-known maps: Logistic-sine-cosine maps. Stability analysis reveals that the map has an infinite number of solutions. Lyapunov exponent, bifurcation diagram, and phase portrait are used to demonstrate the complex dynamic of the map. The sequences of the map are utilized to construct a robust cryptosystem. First, three sets of key streams are generated from the newly designed trigonometric map and are used jointly with the image components (R, G, B) for hamming distance calculation. The output distance-vector, corresponding to each component, is then Bit-XORed with each of the key streams. The output is saved for further processing. The decomposed components are again Bit-XORed with key streams to produce an output, which is then fed into the conditional shift algorithm. The Mandelbrot Set is used as the input to the conditional shift algorithm so that the algorithm efficiently applies confusion operation (complete shuffling of pixels). The resultant shuffled vectors are then Bit-XORed (Diffusion) with the saved outputs from the early stage, and eventually, the image vectors are combined to produce the encrypted image. Performance analyses of the proposed cryptosystem indicate high security and can be effectively incorporated in an IoHT framework for secure medical image transmission.

/pdf/a-new-chaotic-map-with-dynamic-analysis-and-encryption-4kvxgo1z4p.pdf

A New Chaotic Map With Dynamic Analysis and Encryption Application in Internet of Health Things

A new 3-D chaotic dynamical system with a peanut-shaped closed curve of equilibrium points is introduced in this work. Since the new chaotic system has infinite number of rest points, the new chaotic model exhibits hidden attractors. A detailed dynamic analysis of the new chaotic model using bifurcation diagrams and entropy analysis is described. The new nonlinear plant shows multi-stability and coexisting convergent attractors. A circuit model using MultiSim of the new 3-D chaotic model is designed for engineering applications. The new multi-stable chaotic system is simulated on a field-programmable gate array (FPGA) by applying two numerical methods, showing results in good agreement with numerical simulations. Consequently, we utilize the properties of our chaotic system in designing a new cipher colour image mechanism. Experimental results demonstrate the efficiency of the presented encryption mechanism, whose outcomes suggest promising applications for our chaotic system in various cryptographic applications.

/pdf/a-3-d-multi-stable-system-with-a-peanut-shaped-equilibrium-8v38ea6cif.pdf

A 3-D Multi-Stable System With a Peanut-Shaped Equilibrium Curve: Circuit Design, FPGA Realization, and an Application to Image Encryption

Color image encryption using non-dominated sorting genetic algorithm with local chaotic search based 5D chaotic map

A privacy image encryption algorithm based on piecewise coupled map lattice with multi dynamic coupling coefficient

Designing efficient and secure cryptosystems has been a preoccupation for many scientists and engineers for a long time wherein they use chaotic systems to design new cryptosystems. While one dimensional (1-D) chaotic maps possess powerful properties compared to higher dimension ones, they are vulnerable to various attacks due to their small key space, chaotic discontinuous ranges, and degradation in chaotic dynamical behaviours. Moreover, when simulated on a computer, every such chaotic system produces a periodic cycle. Meanwhile, quantum random walks exhibit the potential for deployment in efficient cryptosystem design, which makes it an excellent solution for this problem. In this context, we present a new method for constructing substitution boxes (S-boxes) based on cascaded quantum-inspired quantum walks and chaos inducement. The performance of the proposed S-box scheme is investigated via established S-box evaluation criterion and outcomes suggest that the constructed S-box has significant qualities for viable applications information security. Further, we present an efficient scheme for pseudo-random numbers generation (PRNG) whose sustainability over long periods remedies the periodicity problem associated with traditional cryptographic applications. Furthermore, by combining the two mechanisms, an atypical image encryption scheme is introduced. Simulation results and analysis validate that the proposed image encryption algorithm will offer gains in many cryptographic applications.

/pdf/quantum-inspired-cascaded-discrete-time-quantum-walks-with-5fgvzhukc2.pdf

Quantum-inspired cascaded discrete-time quantum walks with induced chaotic dynamics and cryptographic applications

A lightweight image encryption algorithm is presented based on chaos induction via a 5-dimensional hyperjerk oscillator (5DHO) network. First, the dynamics of our 5DHO network is investigated and shown to exhibit up to five coexisting hidden attractors in the state space that depend exclusively on the system’s initial values. Further, a simple implementation of the circuit was used to validate its ability to exhibit chaotic dynamical properties. Second, an Arduino UNO platform is used to confirm the usability of our oscillator in embedded system implementation. Finally, an efficient image encryption application is executed using the proposed chaotic networks based on the use of permutation-substitution sequences. The superior qualities of the proposed strategy are traced to the dynamic set of keys used in the substitution process which heralds the generation of the final ciphered image. Based on the average results obtained from the entropy analysis (7.9976), NPCR values (99.62), UACI tests (33.69) and encryption execution time for 512 × 512 images (0.1141 s), the proposed algorithm is adjudged to be fast and robust to differential and statistical attacks relative to similar approaches.

https://www.mdpi.com/1424-8220/20/1/83/pdf

A Multidimensional Hyperjerk Oscillator: Dynamics Analysis, Analogue and Embedded Systems Implementation, and Its Application as a Cryptosystem

One of the major challenges in chaos dynamics is the design of simple and realisable electronic circuits capable of complex dynamic behaviours. Our contribution studies the dynamics and implementation of a simple chaotic memristive RLC oscillator circuit of jerky type as well as its application in designing image cryptosystem. The proposed circuit consists of an operational amplifier and an RLC network, comprising a resistor, an inductor, and two capacitors. Considering the crucial role of symmetry in physical, chemical, biological, and mechanical systems, a voltage control memristor emulator is employed to induce symmetry in the proposed circuit. For the dynamic analysis, fourth-order differential equation with exponential nonlinearities is used. Furthermore, standard analysis tools such as Lyapunov spectrum, bifurcation analysis, and phase space trajectories are employed. The phase space is magnetized using four symmetric attractors coexisting for the same set of parameters and different initial conditions indicate the symmetricity of the proposed system. Meanwhile, asymmetric attractor is capable of merging into one symmetric attractor through an attractor-merging bifurcation. Extensive experimental validations of these properties via PSPICE simulations and by using real electronic components are reported. Finally, the chaotic sequences emanating from the proposed oscillator are exploited to design an encryption algorithm that is subsequently validated via simulations and standard image security analysis with prominent outcomes in terms of very low encryption time (0.0746s for 128  ×  128 colour image), mean entropy of 7.999 and mean NPCR of 99.62% just to name a few.

A memristive RLC oscillator dynamics applied to image encryption

In this paper, a new 4D hyperchaotic nonlinear dynamical system with two positive Lyapunov exponents is presented. Exhaustive dynamic analyses of the novel hyperchaotic model using several dynamical studies are described. The dynamics of the system considered are first investigated analytically and numerically to explore phenomena and the selection of hyperchaotic behavior utilized for designing image cryptosystem. Since the proposed hyperchaotic model has rich dynamics, it displays hidden attractors. It emerges from this dynamic the existence of a single unstable equilibrium point giving rise to self-excited attractors, hysteresis phenomenon, and hyperchaotic behavior strongly recommended for securing information by its character. Furthermore, the feasibility and synchronization of the proposed system are also presented by developing, respectively, Raspberry surveys and an adaptive synchronization approach of two identical hyperchaotic systems. By employing the hyperchaotic behavior of the 4D map, an image encryption scheme is proposed as well. It is one round of a pixel-based permutation and a bit-wise diffusion phase. The secret key of the 4D map is derived from the SHA-256 value of the input image. It acts as the signature of the input image. Hence, the secret key exhibits high sensitivity to single-bit alteration in the image, which makes the cryptosystem robust against chosen/known-plaintext attacks. Performance analyses prove that the proposed cryptosystem provides the best in terms of the performance/complexity trade-off, as compared to some recently published algorithms.

/pdf/a-new-4d-hyperchaotic-system-with-dynamics-analysis-24coc8zc.pdf

A New 4D Hyperchaotic System with Dynamics Analysis, Synchronization, and Application to Image Encryption

Dynamic analysis of a novel chaotic system with no linear terms and use for DNA-based image encryption

https://www.preprints.org/manuscript/201912.0110/v1/download

Nkapkop Jean De Dieu

Papers

A Multidimensional Hyperjerk Oscillator: Dynamics Analysis, Analogue and Embedded Systems Implementation, and Its Application as a Cryptosystem

A memristive RLC oscillator dynamics applied to image encryption

A New 4D Hyperchaotic System with Dynamics Analysis, Synchronization, and Application to Image Encryption

Dynamic analysis of a novel chaotic system with no linear terms and use for DNA-based image encryption

A Multidimensional Hyperjerk Oscillator: Dynamics Analysis, Analogue and Digital Implementation, and Its Application as a Cryptosystem