Fractional two-dimensional discrete chaotic map and its applications to the information security with elliptic-curve public key cryptography

Liu, Zeyu; Xia, Tiecheng; Wang, Jinbo

doi:10.1177/1077546317734712

Cited by 21 publications

(13 citation statements)

References 43 publications

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“…Since the birth of elliptic curve public key cryptosystem, people have made a lot of achievements in the research of elliptic curve cryptography. There are not only theoretical research on elliptic curve cryptography [10][11][12], but also application research on elliptic curve cryptography [13][14][15][16][17][18][19]. The security of this cryptosystem is based on the difficulty of the elliptic curve discrete logarithm problem.…”

Section: Discussionmentioning

confidence: 99%

Group Structure of Special Parabola and Its Application in Cryptography

Li¹

2019

ACM

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Public key cryptography is one of the most important research contents in modern cryptography. Curve-based public key cryptosystems have attracted widespread attention in recent years because they have more obvious advantages in speed and key length than general public key cryptosystems. People have done a lot of research on elliptic cryptosystem, among which the realization of elliptic cryptosystem is a key content. In this paper, the definition of special parabola in algebraic closed domain is proposed, the group structure of special parabola in finite field is studied, and several forms of public key cryptosystem based on this parabola are given. The results show that the parabola, together with the additive operations defined above, form an Abelian group. The radix of this parabola can be easily determined, so that the factors it contains can be large prime. The security of its public key cryptosystem is based on the difficulty of solving the discrete logarithm problem on this parabola. Moreover, these parabolic public key cryptosystems are easy to code and decode in plaintext, and easier to design and implement than elliptic curve public key cryptosystems.

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Section: Discussionmentioning

confidence: 99%

Group Structure of Special Parabola and Its Application in Cryptography

Li¹

2019

ACM

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“…(3) can be achieved by utilizing the control laws in equation (5), if the state dependent coefficient matrix Φ(t) = Φ 1 (t) + Φ 2 satisfies the hypotheses…”

Section: Theorem 1 Synchronization Of Bidirectional N -Coupled Fractimentioning

confidence: 99%

“…In recent years, more and more attention has been diverted towards the study of fractionalorder chaotic systems due to their potential applications in the fields of secure communication, encryption, signal and control processing [1][2][3][4][5]. Various fractional-order dynamical systems, such as the fractional-order Lorenz system [6], the fractional-order Lü system [7], the fractional-order financial system [8], the fractional-order permanent magnet synchronous motor (PMSM) system [9], the fractional-order Rabinovich system [10], the fractional-order microscopic chemical system [11], the fractional-order hyperchaotic PWC system [12], have chaotic or hyperchaotic behavior.…”

Section: Introductionmentioning

confidence: 99%

Synchronization of bidirectional N-coupled fractional-order chaotic systems with ring connection based on antisymmetric structure

et al. 2019

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This paper discusses the synchronization problem of N-coupled fractional-order chaotic systems with ring connection via bidirectional coupling. On the basis of the direct design method, we design the appropriate controllers to transform the fractional-order error dynamical system into a nonlinear system with antisymmetric structure. By choosing appropriate fractional-order Lyapunov functions and employing the fractional-order Lyapunov-based stability theory, several sufficient conditions are obtained to ensure the asymptotical stabilization of the fractional-order error system at the origin. The proposed method is universal, simple, and theoretically rigorous. Finally, some numerical examples are presented to illustrate the validity of theoretical results.

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“…Some of the researches on integer-order dynamical systems can be generalized to fractional-order dynamical systems. Fractional-order dynamical systems have been widely investigated, such as synchronization [4], identification [5], stabilization [6] and approximate entropy analysis [7,8]. Time-delay is a frequently encountered phenomenon in real applications, such as physical, communication, economical, pneumatic and biological systems [9].…”

Section: Introductionmentioning

confidence: 99%

Multi-Switching Combination Synchronization of Three Fractional-Order Delayed Systems

Wang

Zhou

2019

Applied Sciences

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Multi-switching combination synchronization of three fractional-order delayed systems is investigated. This is a generalization of previous multi-switching combination synchronization of fractional-order systems by introducing time-delays. Based on the stability theory of linear fractional-order systems with multiple time-delays, we propose appropriate controllers to obtain multi-switching combination synchronization of three non-identical fractional-order delayed systems. In addition, the results of our numerical simulations show that they are in accordance with the theoretical analysis. Appl. Sci. 2019, 9, 4348 2 of 17 anti-decode and anti-attack abilities in image encryption and secure communication, in which origin messages are split into two parts and each part can be embedded into two separate drive systems. There are many works on combination synchronization [23][24][25][26]. To further strengthen the security in secure communication, Vincent et al. [27] proposed multi-switching combination synchronization scheme, in which the two drive systems are synchronized with the response system in different states. Based on the nonlinear control technique, Zheng [28] studied multi-switching combination synchronization of three non-identical chaotic systems. Khan [29] investigated adaptive multi-switching combination synchronization among three non-identical chaotic systems. In [30], Ahmad et al. proposed globally exponential multi-switching combination synchronization scheme, and applied it to secure communications. Multi-switching combination synchronization was applied in encrypted audio communication in [31]. The previous work on multi-switching combination synchronization schemes are based on integral-order chaotic systems. To improve the security in these synchronization schemes, based on fractional-order chaotic systems, Bhat et al. [32] extended the work in [27] to study multi-switching combination synchronization among three non-identical fractional-order chaotic systems. Khan et al. [33] investigated multi-switching combination-combination synchronization among a class of four non-identical fractional-order chaotic systems. In multi-switching combination-combination synchronization scheme, the state variables of two drive systems synchronize with different state variables of two response systems simultaneously, which makes the security of this scheme higher than that in [32].Since time-delay is a frequently encountered phenomenon in real applications, and the time-delay can be used as an additional parameter in synchronization to increase security in secure communication, we consider the work in [32] to investigate multi-switching combination synchronization scheme for non-identical fractional-order delayed systems by introducing time-delays in fractional-order systems.The rest of this paper is organized as follows. In Section 2, the concept of fractional calculus and the stability theory of linear fractional-order systems with multiple time-delays are briefly introduced. The multi-switching combinati...

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Fractional two-dimensional discrete chaotic map and its applications to the information security with elliptic-curve public key cryptography

Cited by 21 publications

References 43 publications

Group Structure of Special Parabola and Its Application in Cryptography

Group Structure of Special Parabola and Its Application in Cryptography

Synchronization of bidirectional N-coupled fractional-order chaotic systems with ring connection based on antisymmetric structure

Multi-Switching Combination Synchronization of Three Fractional-Order Delayed Systems

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