Image Encryption Technology Based on Fractional Two-Dimensional Triangle Function Combination Discrete Chaotic Map Coupled with Menezes-Vanstone Elliptic Curve Cryptosystem

Liu, Zeyu; Xia, Tiecheng; Wang, Jinbo

doi:10.1155/2018/4585083

Cited by 9 publications

(4 citation statements)

References 33 publications

(35 reference statements)

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“…e evolution of chaotic dynamics such as periodic, quasi periodic and chaotic attractors in this system can be obtained by varying control parameter [0, 25] by xing all other parameters constant. When ∈ [13,25] the system generates hyperchaotic attractor and this region is utilized for encryption purpose. e encryption process in higher dimensional space eliminates periodic window problems such as limited chaotic range and nonuniform distribution.…”

Section: Hadamard Gatementioning

confidence: 99%

“…It is one of the subtle behaviours associated with the evolution of a nonlinear physical system with signi cant properties such as topological transitivity, aperiodicity, deterministic pseudo randomness, and sensitive dependence on initial conditions [11]. e complex chaos theory have been utilized in many conventional cryptographic approaches like RC5 stream cipher and elliptical curve cryptography to strengthen the security of encryption processes [12,13]. Cryptographic algorithms based on chaos theory consist of two operations such as permutation and di usion.…”

Section: Introductionmentioning

confidence: 99%

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Speech Encryption Algorithm Based on Nonorthogonal Quantum State with Hyperchaotic Keystreams

Farsana

Gopakumar²

2020

Advances in Mathematical Physics

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With the advancement in modern computational technologies like cloud computing, there has been tremendous growth in the field of data processing and encryption technologies. In this contest there is an increasing demand for successful storage of the data in the encrypted domain to avoid the possibility of data breach in shared networks. In this paper, a novel approach for speech encryption algorithm based on quantum chaotic system is designed. In the proposed method, classical bits of the speech samples are initially encoded in nonorthogonal quantum state by the secret polarizing angle. In the quantum domain, encoded speech samples are subjected to bit-flip operation according to the Controlled–NOT gate followed by Hadamard transform. Complete superposition of the quantum state in both Hadamard and standard basis is achieved through Hadamard transform. Control bits for C-NOT gate as well as Hadamard gate are generated with a modified Lu˙-hyperchaotic system. Secret nonorthogonal rotation angles and initial conditions of the hyperchaotic system are the keys used to ensure the security of the proposed algorithm. The computational complexity of the proposed algorithm has been analysed both in quantum domain and classical domain. Numerical simulation carried out based on the above principle showed that the proposed speech encryption algorithm has wider keyspace, higher key sensitivity and robust against various differential and statistical cryptographic attacks.

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Section: Hadamard Gatementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Speech Encryption Algorithm Based on Nonorthogonal Quantum State with Hyperchaotic Keystreams

Farsana

Gopakumar²

2020

Advances in Mathematical Physics

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“…Hence, Fractional difference is suitable for the complicated images. 19,20 For an energy function (or signalÞ sðtÞ2L 2 ðRÞ , its v-order fractional differential is…”

Section: Fractional Differential Operatormentioning

confidence: 99%

Image segmentation by improved minimum spanning tree with fractional differential and Canny detector

Lin

Guo

Yan

et al. 2019

Journal of Algorithms & Computational Technology

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In this study, we propose an algorithm that uses an improved Minimum Spanning Tree algorithm and a modified Canny edge detector to segment images that contain a considerable amount of noises. First, we use our modified Canny operator to pre-process an image, and record the obtained object boundary information; then, we apply the improved Minimum Spanning Tree algorithm to associate the above information with boundary points in order to separate edges into two classes in the image, namely the inner and boundary regions. In particular, Minimum Spanning Tree algorithm is improved by using Fractional differential and combining the functions of the intra-regional and interregional differences with a function for edge weights. Based on the experimental results, compared with the other four exiting algorithms, the new algorithm has the higher accuracy and the better effect for noised image segmentation.

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“…The definition of fractional derivative contains convolution, which can well express the memory effect and show the cumulative effect over time. Compared with the traditional integer-order calculus, fractional calculus has more advantages and is a suitable mathematical tool for describing the memory characteristics [1][2][3][4][5][6][7][8][9][10][11] and in recent years, it has become the powerful mathematical tool in many disciplines, especially in the study of viscoelastic materials.…”

Section: Introductionmentioning

confidence: 99%

Stochastic P-Bifurcation of a Bistable Viscoelastic Beam with Fractional Constitutive Relation under Gaussian White Noise

Zhang

et al. 2018

Discrete Dynamics in Nature and Society

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In this paper, we study the stochastic P-bifurcation problem for axially moving of a bistable viscoelastic beam with fractional derivatives of high order nonlinear terms under Gaussian white noise excitation. First, using the principle for minimum mean square error, we show that the fractional derivative term is equivalent to a linear combination of the damping force and restoring force, so that the original system can be simplified to an equivalent system. Second, we obtain the stationary Probability Density Function (PDF) of the system’s amplitude by stochastic averaging, and using singularity theory, we find the critical parametric condition for stochastic P-bifurcation of amplitude of the system. Finally, we analyze the types of the stationary PDF curves of the system qualitatively by choosing parameters corresponding to each region within the transition set curve. We verify the theoretical analysis and calculation of the transition set by showing the consistency of the numerical results obtained by Monte Carlo simulation with the analytical results. The method used in this paper directly guides the design of the fractional order viscoelastic material model to adjust the response of the system.

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Image Encryption Technology Based on Fractional Two-Dimensional Triangle Function Combination Discrete Chaotic Map Coupled with Menezes-Vanstone Elliptic Curve Cryptosystem

Cited by 9 publications

References 33 publications

Speech Encryption Algorithm Based on Nonorthogonal Quantum State with Hyperchaotic Keystreams

Speech Encryption Algorithm Based on Nonorthogonal Quantum State with Hyperchaotic Keystreams

Image segmentation by improved minimum spanning tree with fractional differential and Canny detector

Stochastic P-Bifurcation of a Bistable Viscoelastic Beam with Fractional Constitutive Relation under Gaussian White Noise

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