Synchronization of Hidden Hyperchaotic Attractors in Fractional-Order Complex-Valued Systems with Application to Secure Communications

Shoreh, A.A.-H.; Kuznetsov, Nikolay V.; Mokaev, Timur N.; Tavazoei, Mohammad Saleh

doi:10.1109/elconrus51938.2021.9396284

Cited by 3 publications

(9 citation statements)

References 24 publications

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“…6. The scheme consists of the following elements: (a) The error between the derive (18) and the response (19) systems described by the solutions of system (10). • Hyperchaotic transmitter and receiver systems, which generate the pseudo-states variables x(t) ∈ C n and y(t) ∈ C n , respectively.…”

Section: Application To Secure Communicationsmentioning

confidence: 99%

“…[1][2][3][4]). Starting from the pioneering work of Pecora and Carroll [5], in which an effective technique to synchronize two identical chaotic systems with different starting points is proposed, diverse types of chaos synchronization methods have been discovered to synchronize chaotic systems, such as complete synchronization [6,7], active control [8][9][10], lag synchronization [11,12], sliding mode control [2], cluster synchronization [13], adaptive synchronization [14][15][16] and many more. Up to date, chaos synchronization has been studied in depth for dynamical systems described by real-valued variables.…”

Section: Introductionmentioning

confidence: 99%

“…The ideas of their techniques are follows: some schemes are designed to send the information signal between the transmitter and the receiver through one public channel, and the message by suitable encryption function is injected into the states of the transmitter (see e.g., [26][27][28][29]); other ones use the same algorithm, but instead of one public channel there are two channels: one to send the states of the transmitter system, and the second one to transmit the information-bearing signal. To get rapid synchronization and more security (see e.g., [10,12,30]). Further, rather than inserting the message into the states of the transmitter, another type of scheme is designed, where the message is injected into the parameters of the transmitter, and by the adaptive laws of parameters the message can be recovered (see e.g., [24,31]).…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

New adaptive synchronization algorithm for a general class of hyperchaotic complex-valued systems with unknown parameters and its application to secure communication

Shoreh,

Kuznetsov,

Mokaev

2021

Preprint

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This report aims to study adaptive synchronization between a general class of hyperchaotic complex-valued systems with unknown parameters, which is motivated by extensive application areas of this topic in nonlinear sciences (e.g., secure communications, encryption techniques, etc.). Based on the complexity of hyperchaotic dynamical systems, which may be beneficial in secure communications, a scheme to achieve adaptive synchronization of a general class of hyperchaotic complex-valued systems with unknown parameters is proposed. To verify scheme's consistency, the control functions based on adaptive laws of parameters are derived analytically, and the related numerical simulations are performed. The complex-valued Rabinovich system describing the parametric excitation of waves in a magneto-active plasma is considered as an interesting example to study this kind of synchronization. A scheme for secure communication and improving the cryptosystem is proposed; the sketch is constructed to split the message and inject some bit of information signal into parameters modulation and the other bit into the transmitter system's states, which, in turn, complicates decryption task by intruders. Meanwhile, the information signal can be accurately retrieved at the receiver side by adaptive techniques and decryption function. Different types of encrypted messages are considered for testing the robustness of the proposed scheme (e.g., plain text and gray images with diverse scales of white Gaussian noise).

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Section: Application To Secure Communicationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

New adaptive synchronization algorithm for a general class of hyperchaotic complex-valued systems with unknown parameters and its application to secure communication

Shoreh,

Kuznetsov,

Mokaev

2021

Preprint

View full text Add to dashboard Cite

show abstract

“…This means the error states between synchronized systems converge to zero. Inspired by the first method proposed by Pecora and Carroll to achieve synchronization of two identical systems [14], several techniques have been introduced for synchronizing chaotic systems with integer-order and fractional-order, including active control [15], adaptive control [16][17][18], sliding mode control [12,19], backstepping technique [20,21], nonlinear feedback control [22] and others (see e.g. [23][24][25]).…”

Section: Introductionmentioning

confidence: 99%

“…Fractional-order complex-valued systems have gained significant attention due to their ability to capture the complex dynamics observed in various real-world phenomena and their potential applications in diverse fields such as physics, engineering, image processing, neural networks, and communications [26,35,36]. In recent years, several techniques based on the theory of complex functions have been developed to investigate various synchronization phenomena in fractional-order complex-valued systems; e.g., finite-time synchronization [36], pinning synchronization [37], adaptive synchronization [38], and complete synchronization [15] are among the synchronization schemes that have been studied extensively.…”

Section: Introductionmentioning

confidence: 99%

A novel adaptive synchronization algorithm for a general class of fractional-order complex-valued systems with unknown parameters, and applications to circuit realization and color image encryption

Shoreh,

Mahmoud

2024

Phys. Scr.

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This article proposes an adaptive synchronization (AS) algorithm to synchronize a general class of fractional-order complex-valued systems with completely unknown parameters, which may appear in physical and engineering problems. The analytical and theoretical concepts of the algorithm rely on the mathematical framework of the Mittag-Leffler global stability of fractional-order systems. A specific control system is established analytically based on the fractional-order adaptive laws of parameters, and the corresponding numerical results are executed to verify the accuracy of the AS algorithm. The proposed synchronization method is evaluated using the fractional-order complex Rabinovich system as an attractive example. The electronic circuits of the new system with different fractional-order are designed. By utilizing the Multisim electronic workbench software, various chaotic/hyperchaotic behaviors have been observed, and a good agreement is found between the numerical results and experimental simulation. In addition, the approximation of the transfer function for different fractional-order are presented. And the corresponding resistor and capacitor values in the chain ship model (CSM) are estimated, which can be utilized in designing electronic circuits for other fractional-order systems. Furthermore, two strategies for encrypting color images are proposed using the AS algorithm and fractional-order adaptive laws of parameters. In the first strategy, the color image is treated as a single package and divided into two vectors. The first vector is embedded into transmitter parameters, while the second vector is injected into the transmitter state signals. In the second strategy, the primary RGB channel components of the original color image are extracted and separated into two vectors, and the same process is followed as in the first strategy. These strategies complicate the decryption task for intruders. Different scales of white Gaussian noise are added to color images to examine the robustness of the proposed color images encryption strategies.

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Hybrid synchronisation method based on inverse generalised and inverse projected high dimensional discrete chaotic systems

Xing,

Zeng,

Dong

et al. 2024

Phys. Scr.

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High-dimensional discrete chaotic systems have a wide range of engineering applications, while the chaotic synchronization method is the key to confidential communication applications. Based on the proposed discriminant theorem for high-order polynomial chaotic mapping, in this paper, a hybrid inverse generalization and inverse projection synchronization method for high-dimensional discrete chaotic systems is constructed. The method increases the flexibility of synchronization control by designing to enable the coexistence of inverse projection synchronization and inverse generalized synchronization in chaotic systems, by specifically using an invertible and adjustable constant diagonal matrix to extend the control capability of the error system. Meanwhile, this paper proposed the validity of this hybrid synchronization scheme based on the multi-stationary chaotic system for the first time, through comparison, it is certified that the multi-stationary discrete chaotic synchronization system introduced in this paper not only has complex dynamics behavior but also has a faster synchronization speed. Meanwhile, this paper proposed the validity of this hybrid synchronization scheme based on the multi-stationary chaotic system for the first time, through comparison, it is certified that the multi-stationary discrete chaotic synchronization system introduced in this paper not only has complex dynamics behavior but also has a faster synchronization speed. Finally, a transmission system based on hybrid synchronization is also designed in this paper, where experiments and analyses of cryptographic transmission of pictures are carried out, and the results of the analyses show that the system has higher security and a larger key space.

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Synchronization of Hidden Hyperchaotic Attractors in Fractional-Order Complex-Valued Systems with Application to Secure Communications

Cited by 3 publications

References 24 publications

New adaptive synchronization algorithm for a general class of hyperchaotic complex-valued systems with unknown parameters and its application to secure communication

New adaptive synchronization algorithm for a general class of hyperchaotic complex-valued systems with unknown parameters and its application to secure communication

A novel adaptive synchronization algorithm for a general class of fractional-order complex-valued systems with unknown parameters, and applications to circuit realization and color image encryption

Hybrid synchronisation method based on inverse generalised and inverse projected high dimensional discrete chaotic systems

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