From chaos to encryption using fractional order Lorenz-Stenflo model with flux-controlled feedback memristor

Khan, Najeeb Alam; Qureshi, Muhammad Ali; Akbar, Saeed; Ara, Asmat

doi:10.1088/1402-4896/aca1e8

Cited by 13 publications

(8 citation statements)

References 39 publications

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“…The Lorenz-Stenflo mathematical model describes the dynamics and behaviors concerned with atmosphere. The next study in our special issue proposes a novel 5-dimensional fractional-order chaotic system reliant on the Lorenz-Stenflo model with a feedback memristor [18]. Through the analyses of the phase portraits, equilibrium points, bifurcation analysis and Poincaré maps, the system is stated to generate a two-wing attractor with symmetrical coexistence.…”

Section: Work In Progressmentioning

confidence: 99%

Advanced fractional calculus, differential equations and neural networks: analysis, modeling and numerical computations

Baleanu,

Karaca,

Vázquez

et al. 2023

Phys. Scr.

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Most physical systems in nature display inherently nonlinear and dynamical properties; hence, it would be difficult for nonlinear equations to be solved merely by analytical methods, which has given rise to the emerging of engrossing phenomena such as bifurcation and chaos. Conjointly, due to nonlinear systems’ exhibiting more exotic behavior than harmonic distortion, it becomes compelling to test, classify and interpret the results in an accurate way. For this reason, avoiding preconceived ideas of the way the system is likely to respond is of pivotal importance since this facet would have effect on the type of testing run and processing techniques used in nonlinear systems. Paradigms of nonlinear science may suggest that it is ‘the study of every single phenomenon’ due to its interdisciplinary nature, which is another challenge encountered and needs to be addressed by generating and designing a systematic mathematical framework where the complexity of natural phenomena hints the requirement of identifying their commonalties and classifying their various manifestations in different nonlinear systems. Studying such common properties, concepts or paradigms can enable one to gain insight into nonlinear problems, their essence and consequences in a broad range of disciplines all forthwith. Fractional differential equations associated with non-local phenomena in physics have arisen as a powerful mathematical tool within a multidisciplinary research framework. Fractional differential equations, as one extension of the fractional calculus theory, can yield the evolution of various systems properly, which reinforces its position in mathematics and science while setting stage for the description of dynamic, complicated and nonlinear events. Through the reflection of the systems’ actual properties, fractional calculus manifests unforeseeable and hidden variations, and thus, enables integration and differentiation, with the solutions to be approximated by numerical methods along with modeling and predicting the dynamics of multiphysics, multiscale and physical systems. Neural Networks (NNs), consisting of hidden layers with nonlinear functions that have vector inputs and outputs, are also considerably employed owing to their versatile and efficient characteristics in classification problems as well as their sophisticated neural network architectures, which make them capable of tackling complicated governing partial differential equation problems. Furthermore, partial differential equations are used to provide comprehensive and accurate models for many scientific phenomena owing to the advancements of data gathering and machine learning techniques which have raised opportunities for data-driven identification of governing equations derived from experimentally observed data. Given these considerations, while many problems are solvable and have been solved, efforts are still needed to be able to respond to the remaining open questions in the fields that have a broad range of spectrum ranging from mathematics, physics, biology, virology, epidemiology, chemistry, engineering, social sciences to applied sciences. With a view of different aspects of such questions, our special issue provides a collection of recent research focusing on the advances in the foundational theory, methodology and topical applications of fractals, fractional calculus, fractional differential equations, differential equations (PDEs, ODEs, to name some), delay differential equations (DDEs), chaos, bifurcation, stability, sensitivity, machine learning, quantum machine learning, and so forth in order to expound on advanced fractional calculus, differential equations and neural networks with detailed analyses, models, simulations, data-driven approaches as well as numerical computations.

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Section: Work In Progressmentioning

confidence: 99%

Advanced fractional calculus, differential equations and neural networks: analysis, modeling and numerical computations

Baleanu,

Karaca,

Vázquez

et al. 2023

Phys. Scr.

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“…By replacing certain fixed parameters with chaotic sequences generated from well-studied chaotic maps, we introduce an additional layer of randomness and complexity, making the enhanced cipher more resistant to differential and linear cryptanalysis attacks. The sensitive dependence on initial conditions exhibited by chaotic systems ensures that even a slight perturbation in the encryption process leads to drastic changes in the cipher output, thwarting the efforts of attackers to gain insights into the underlying structure of the cipher [5]. Furthermore, the efficiency aspect of our enhanced chaos-based PRESENT cipher remains a focal point of our research.…”

Section: Introductionmentioning

confidence: 99%

A novel enhanced chaos based present lightweight cipher scheme

Abdelli,

El hadj Youssef,

Kharroubi

et al. 2024

Phys. Scr.

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Lightweight ciphers have been developed to meet the rising need for secure communication in environments with limited resources. These ciphers provide robust encryption while ensuring efficient computation. Our paper introduces a new enhanced PRESENT lightweight cipher that utilizes chaotic systems to enhance its robustness and randomness while retaining the simplicity and compactness of the original cipher. By integrating chaotic maps into the cipher's core components, we improve its resistance against advanced cryptanalysis, such as differential, Salt and Peppers Noise (SPN), and loss data attacks. We also optimize the design for computational efficiency, making it suitable for deployment in devices with limited resources. Through extensive simulations and comparative analyses, we demonstrate the superiority of our enhanced cipher in terms of security and efficiency compared to other state-of-the-art lightweight ciphers. Our research contributes to the advancement of lightweight cryptography and provides a promising solution for secure communication in resource-constrained environments.

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“…where x, y, and z are state variables, a is constant parameter, and dots represent time derivatives. There exist many dynamical models in various fields [16][17][18][19][20][21][22][23]. Huang and Bae [16] presented the chaotic FO love model.…”

Section: Introductionmentioning

confidence: 99%

“…The chaotic FO Romeo and Juliet with an external force or external environment was studied [17]. Different cases of image encryption for chaotic dynamical systems were investigated [18][19][20][21][22][23].…”

Section: Introductionmentioning

confidence: 99%

On real and complex dynamical models with hidden attractors and their synchronization

2023

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In this work, we propose three chaotic (or hyperchaotic) models. These models are real or complex with one stable equilibrium point (hidden attractor). Based on a modified Sprott E model, three versions were introduced: the complex integer order, the real fractional order, and the complex fractional order. The basic properties of these models have been studied. We discover that the complex integer-order version has chaotic and hyperchaotic multi-scroll hidden attractors (MSHAs) by computing Lyapunov exponents (LEs). By making a small change to a model parameter, different MSHA values can be produced for this version. Our complex version's dynamics are richer than the integer version in [1]. The dynamics of the real fractional version are investigated through a bifurcation diagram and LEs. It has chaotic hidden attractors for various fractional-order q values. Through varying the model parameters of the complex fractional-order (FO) version, different numbers of chaotic MSHAs can be generated. Due to the complex dynamic behaviours of the MSHAs, these models may have several applications in physics, secure communications and image encryption. A new kind of combination synchronization (CS) between one integer-order drive model and two FO response models with different dimensions is proposed. The tracking control method is used to investigate a scheme for this type of synchronization. As an example, we used our three models to test the validity of this scheme, and an agreement between the analytical and numerical results was found.

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From chaos to encryption using fractional order Lorenz-Stenflo model with flux-controlled feedback memristor

Cited by 13 publications

References 39 publications

Advanced fractional calculus, differential equations and neural networks: analysis, modeling and numerical computations

Advanced fractional calculus, differential equations and neural networks: analysis, modeling and numerical computations

A novel enhanced chaos based present lightweight cipher scheme

On real and complex dynamical models with hidden attractors and their synchronization

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