Quadratic Function Chaotic System and its Application on Digital Image Encryption

To obtain chaotic systems with good properties to help chaos based image encryption, this paper first study the condition under which quadratic functions can be used as pseudo-random sequence generator. We give a necessary and sufficient condition for quadratic functions topologically conjugate with...

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Vydáno v:IEEE access Ročník 8; s. 55540 - 55549
Hlavní autoři: Guo, Hongfeng, Zhang, Xin, Zhao, Xinyao, Yu, Hang, Zhang, Li
Médium: Journal Article
Jazyk:angličtina
Vydáno: Piscataway IEEE 2020
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Témata:
Algorithms
Chaos theory
Chaotic communication
chaotic image encryption
Digital images
Digital imaging
Encryption
Generators
logistic map
Logistics
Pseudorandom sequences
Quadratic equations
Quadratic function
topological conjugacy
ISSN:2169-3536, 2169-3536
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Abstract To obtain chaotic systems with good properties to help chaos based image encryption, this paper first study the condition under which quadratic functions can be used as pseudo-random sequence generator. We give a necessary and sufficient condition for quadratic functions topologically conjugate with the most frequently used Logistic map and Tent map. Since topological conjugacy maintains chaotic characteristics, more quadratic functions can be used as pseudo-random sequence generators in the digital image encryption. Then, it analyzes a diffusion algorithm with a good effect but poor in resisting the chosen plaintext attack. It is also verified by simulation. The quadratic function chaotic system is applied in the improvement of the diffusion algorithm. Furthermore, the improved algorithm contains plaintext related and cyclic shift operations. Finally, the performance analysis shows that the improved scheme has good security and high efficiency.
AbstractList To obtain chaotic systems with good properties to help chaos based image encryption, this paper first study the condition under which quadratic functions can be used as pseudo-random sequence generator. We give a necessary and sufficient condition for quadratic functions topologically conjugate with the most frequently used Logistic map and Tent map. Since topological conjugacy maintains chaotic characteristics, more quadratic functions can be used as pseudo-random sequence generators in the digital image encryption. Then, it analyzes a diffusion algorithm with a good effect but poor in resisting the chosen plaintext attack. It is also verified by simulation. The quadratic function chaotic system is applied in the improvement of the diffusion algorithm. Furthermore, the improved algorithm contains plaintext related and cyclic shift operations. Finally, the performance analysis shows that the improved scheme has good security and high efficiency.
Author Zhang, Xin
Guo, Hongfeng
Yu, Hang
Zhao, Xinyao
Zhang, Li
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SubjectTerms Algorithms
Chaos theory
Chaotic communication
chaotic image encryption
Digital images
Digital imaging
Encryption
Generators
logistic map
Logistics
Pseudorandom sequences
Quadratic equations
Quadratic function
topological conjugacy
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Title Quadratic Function Chaotic System and its Application on Digital Image Encryption
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