The complex dynamics of a simple memristive tabu learning neuron (MTLN) are considered in this article. The analysis of the stability of its equilibria revealed that it displays self-excited dynamics. The investigation of the dynamics of the considered model highlighted that it is extremely sensitive to the initial conditions. That sensitivity to the initial conditions is supported by the coexistence of an infinite number of stable states for the same set of system parameters but using different initial states. Among the infinity of coexisting stable states, there are periodic, quasiperiodic, and chaotic ones. The coexistence of an infinite number of chaotic attractors found in this work and not yet reported in such a model represents the first important contribution of this work. The circuit of the coupled neuron is also realized in the PSPICE simulation environment to further support the obtained result in extreme multistability. Therefore, the revealed chaotic dynamics of the MTLN is applied to compress and encrypt digital medical images. The compressed sensing (CS) approach is combined with deoxyribonucleic acid (DNA) coding/decoding to achieve high compression/encryption performances, including very low computational cost (encryption time t = 0.162 ms, encryption throughput ET = 1618.1 MB/s, number of CPU cycles NC = 1.8) useful for real-time compression. The compression/encryption method developed in this work represents the second main contribution based on the results of the analysis metrics.

The nonlinear ion-acoustic waves (IAWs) in a space plasma are capable of exhibiting chaotic dynamics which can be applied to cryptography. Dynamical properties of IAWs are examined using the direct method in plasmas composed of positive and negative ions and nonextensive distributed electrons. Applying the wave transformation, the governing equations are deduced into a dynamical system (DS). Supernonlinear and nonlinear periodic IAWs are presented through phase plane analysis. The analytical periodic wave solution for IAW is obtained. Under the influence of an external periodic force, the DS is transformed to a perturbed system. The perturbed DS describes multistability property of IAWs with change of initial conditions. The multistability behavior features coexisting trajectories such as, quasiperiodic, multiperiodic and chaotic trajectories of the perturbed DS. The chaotic feature in the perturbed DS is supported by Lyapunov exponents. This interesting behavior in the windows of chaotic dynamics is exploited to design efficient encryption algorithm. First SHA-512 is used to compute the hash digest of the plain image which is then used to update the initial seed of the chaotic IAWs system. Note that SHA-512 uses one-way function to map input data to the output, consequently it is quite impossible to break the proposed encryption technique. Second DNA coding is used to confuse and diffuse the DNA version of the plain image. The diffused image follows DNA decoding process leading to the cipher image. The security performance is evaluated using some well-known metrics and results indicate that the proposed cryptosystem can resist most of existing cryptanalysis techniques. In addition complexity analysis shows the possibility of practical implementation of the proposed algorithm.

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.

Wireless Body Area Network (WBAN) is a crucial tool in modern medical areas. This refers to the intelligent interconnection of wireless sensor nodes installed outside or inside the human body to recover some human vital signs. The security and bandwidth saturation remain crucial problems of this technology. In this work, a cross-ring based neural network model (CRNN) is obtained from the HNN definition and its complex dynamics is deeply analyzed. The steady state study shows that the model has a unique equilibrium point and its analysis shows that the model’s dynamics is self-excited. Based on the two-parameter Lyapunov spectrum, the set of synaptic weights has been quickly identified to illustrate hyperchaotic behavior of the CRNN. With the help of bifurcation plots, graphs of the Lyapunov spectrum, and phase portraits, we have characterized periodic, chaotic, and hyperchaotic patterns in the model. Furthermore, an experimental setup has been built using microcontroller technology to further support the results of the numerical simulations. A parallel compressive sensing algorithm combined with a nonlinear congruent generator has been used to show the application of the newly designed CRNN to medical image compression and security. Security and compression performances indicate an efficient scheme with the capability to resist various attacks and the capability to produce low size data image from large size data image. For instant from 256×256 image size, an encrypted and compressed output image is obtained at the compression rate of 0.5, processing time of 0.147ms, encryption throughput of 1783.3MBits/s, for a 2.9GHz processor, the number of cycle to process the algorithm is 1.62. Consequently, the proposal can be applied to Wireless Body Area Networks (WBANs).

Considering a nonlinear dynamic oscillator, a high Lyapunov exponent indicates a high degree of randomness useful in many applications, including cryptography. Most existing oscillators yield very low Lyapunov exponents. The proposed work presents a general strategy to derive an n-D hyperchaotic map with a high Lyapunov exponent. A 2D case study was analyzed using some well-known nonlinear dynamic metrics including phase portraits, bifurcation diagrams, finite time Lyapunov exponents, and dimension. These metrics indicated that the state of the novel map was more scattered in the phase plane than in the case of some traditional maps. Consequently, the novel map could produce output sequences with a high degree of randomness. Another important observation was that the first and second Lyapunov exponents of the proposed 2D map were both positive for the whole parameter space. Consequently, the attractors of the map could be classified as hyperchaotic attractors. Finally, these hyperchaotic sequences were exploited for image encryption/decryption. Various validation metrics were exploited to illustrate the security of the presented methodology against cryptanalysts. Comparative analysis indicated the superiority of the proposed encryption/decryption protocol over some recent state-of-the-art methods.