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Cited by 11Chaos-based Image/Signal EncryptionComputer Science and EngineeringAdvanced Steganography and Watermarking Techniques

An algorithm based on 6D fractional order hyperchaotic system and knight tour algorithm to encrypt image

Open access
He, Chenchen, Chen, Zhong, Wang, Lujie, Wu, Ximei, Liu, Tongzhe, Long, Bofeng·2024·Physica Scripta
DOI 10.1088/1402-4896/ad3409
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Abstract

The security guarantee of data transmission is becoming more crucial as the frequency of information interchange rises. Ensuring the security of images is essential since they serve as a vital transmission medium. This research suggests an image encryption method that combines the knight tour algorithm with a 6D fractional order hyperchaotic system. First, chaotic sequences are produced using a fractional order hyperchaotic system, which is then utilized to index order and jumble the entire image. To retrieve the image after the second scrambling, choose the knight tour beginning point and run ten rounds of knight tour algorithms on the scrambled image. Thirdly, to maximize the efficiency of picture encryption, employ diffusion methods. The outcomes of the imaging experiment were lastly tested and assessed. The security of the image can be successfully guaranteed by a high-dimensional fractional order hyperchaotic system. This is because its high dimensionality gives it a larger key space than the low dimensional system. This is why it can resist attacks more effectively. After a series of evaluation experiments, it is obvious that this encryption scheme has good encryption performance.

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  • The 6D hyperchaotic Vaidyanathan fractional-order system exhibits four positive Lyapunov exponents, indicating hyperchaotic dynamics, with a Kaplan-Yorke dimension equal to 4.105.

    “For the specified parameter set, the system exhibits four positive Lyapunov exponents, indicating the presence of hyperchaotic dynamics, as discussed in 26, where the Kaplan-Yorke dimesion equals to 4.105.”

    From Hyperchaotic fractional-order image encryption with Knight’s tour scrambling for satellite imagery (2026) · cites this paper as [26]

    Section 2.2 states that the 6D Vaidyanathan system has four positive Lyapunov exponents for the specified parameters and initial values, then describes converting it to a fractional-order system. The copy does not state that the fractional-order system has four positive exponents or give a Kaplan–Yorke dimension of 4.105 (searched: “Kaplan Yorke,” “Lyapunov dimension,” and “4.105”). (LLM, conf=0.88)

    Experimental — accuracy not yet measured

  • The combination of local algebraic mixing, channel-specific dynamic substitution, and knight-guided bit-level diffusion yields a tightly coupled architecture that is structurally distinct from existing chaos+chess scrambling frameworks.

    “This combination of local algebraic mixing, channel-specific dynamic substitution, and knight-guided bit-level diffusion yields a tightly coupled architecture that is structurally distinct from existing chaos+chess scrambling frameworks16,26.”

    From Hyperchaotic fractional-order image encryption with Knight’s tour scrambling for satellite imagery (2026) · cites this paper as [26]

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Cited by

Sorted by citations

Authors
He, C., Chen, Z., Wang, L., Wu, X., Liu, T., & Long, B.
Affiliations
Hengyang Normal University (CN)
Corresponding author
  • He, Chenchen
  • Chen, Zhong
ORCID
Venue
Physica Scripta
Publisher
IOP Publishing
Published
2024-04-01
Volume
99
Issue
5
Pages
055205
ISSN
  • 0031-8949 (ISSN-L)
  • 1402-4896
DOI
10.1088/1402-4896/ad3409
OpenAlex
W4392792017
Cited by
11
References
2
Citations by year
2026: 3 · 2025: 2 · 2024: 6
FWCI
1.40
Type
journal article
Language
en
Open access
Licence
Locations
Physica Scripta (publishedVersion)
Funders
  • Scientific Research Fund of Hunan Provincial Education Department (19A066)
  • Science and Technology Innovation Program of Hunan Province (2016TP1020)
Topics
  • Physical Sciences › Computer Science › Computer Vision and Pattern Recognition › Chaos-based Image/Signal Encryption
  • Physical Sciences › Computer Science › Artificial Intelligence › Computer Science and Engineering
  • Physical Sciences › Computer Science › Computer Vision and Pattern Recognition › Advanced Steganography and Watermarking Techniques
Keywords
image encryption, fractional-order hyperchaotic system, chaotic sequences, image scrambling, diffusion, key space, secure data transmission

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