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Cited by 270Chaos-based Image/Signal EncryptionMathematical Dynamics and FractalsChaos control and synchronization

Dynamic Analysis of Digital Chaotic Maps via State-Mapping Networks

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Li, Chengqing, Feng, Bingbing, Li, Shujun, Kurths, Juergen, Chen, Guanrong·2019·IEEE Transactions on Circuits and Systems I: Regular Papers
DOI 10.1109/tcsi.2018.2888688
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Abstract

Chaotic dynamics is widely used to design pseudo-random number generators and for other applications, such as secure communications and encryption. This paper aims to study the dynamics of the discrete-time chaotic maps in the digital (i.e., finite-precision) domain. Differing from the traditional approaches treating a digital chaotic map as a black box with different explanations according to the test results of the output, the dynamical properties of such chaotic maps are first explored with a fixed-point arithmetic, using the Logistic map and the Tent map as two representative examples, from a new perspective with the corresponding state-mapping networks (SMNs). In an SMN, every possible value in the digital domain is considered as a node and the mapping relationship between any pair of nodes is a directed edge. The scale-free properties of the Logistic map's SMN are proved. The analytic results are further extended to the scenario of floating-point arithmetic and for other chaotic maps. Understanding the network structure of a chaotic map's SMN in digital computers can facilitate counteracting the undesirable degeneration of chaotic dynamics in finite-precision domains, also helping to classify and improve the randomness of pseudo-random number sequences generated by iterating the chaotic maps.

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  • The periods of PRNS obtained by iterating Logistic map and skew tent map in a digital computer are rigorously analyzed in [48].

    “The periods of PRNS obtained by iterating Logistic map and skew tent map in digital computer are rigorously analyzed in [48].”

    From When an attacker meets a cipher-image in 2018: A year in review (2019) · cites this paper as [48]

    The Introduction (p. 1) says finite-state chaotic-map orbits eventually enter periodic loops, and Section II (p. 2) analyzes the Logistic and Tent maps in digital arithmetic. But the cited paper studies their state-mapping networks rather than rigorously deriving the periods of pseudorandom sequences from both maps; its Tent-map analysis (p. 6) concerns the ordinary Tent map, not a skew tent map. (LLM, conf=0.84)

    Experimental — accuracy not yet measured

  • The underlying weak randomness of chaos-based PRNG is widely omitted in image encryption schemes.

    “The underlying weak randomness of chaos-based PRNG is widely omitted.”

    From When an attacker meets a cipher-image in 2018: A year in review (2019) · cites this paper as [48]

    The Introduction (p. 2) says finite-precision chaotic maps cannot reach an ideal chaotic state and that degraded dynamics may weaken encryption schemes. This supports concern about chaos-based PRNGs, but the paper does not say that image-encryption schemes widely omit or overlook weak randomness. (LLM, conf=0.82)

    Experimental — accuracy not yet measured

  • In [94], PWLCM is adopted as the source producing PRNS, whose randomness is seriously compromised in a digital computer.

    “Interestingly, [94] adopts PWLCM as the source producing pseudo-random number sequence, whose randomness is seriously comprised in a digital computer [48].”

    From When an attacker meets a cipher-image in 2018: A year in review (2019) · cites this paper as [48]

    The Introduction (p. 2) says the paper studies the Logistic and Tent maps as examples and discusses using state-mapping networks to evaluate chaos-based pseudorandom generators. It does not say that the authors adopt PWLCM specifically as a source of pseudorandom number sequences. The statement about compromised randomness is attached to [48] in the citing sentence, not to this source. (LLM, conf=0.78)

    Experimental — accuracy not yet measured

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Cited by

Sorted by citations

Authors
Li, C., Feng, B., Li, S., Kurths, J., & Chen, G.
Affiliations
  • Hunan University (CN)
  • Xiangtan University (CN)
  • University of Kent (GB)
  • City University of Hong Kong (HK)
ORCID
Venue
IEEE Transactions on Circuits and Systems I: Regular Papers
Publisher
Institute of Electrical and Electronics Engineers (IEEE)
Published
2019-06
Volume
66
Issue
6
Pages
2322-2335
ISSN
  • 1549-8328 (ISSN-L)
  • 1558-0806
DOI
10.1109/tcsi.2018.2888688
OpenAlex
W2905420870
Cited by
270
References
3
Citations by year
2026: 15 · 2025: 24 · 2024: 29 · 2023: 26 · 2022: 44 · 2021: 42 · 2020: 46 · 2019: 44
FWCI
19.67
Type
journal article
Language
en
Open access
Licence
Locations
  • IEEE Transactions on Circuits and Systems I Regular Papers (publishedVersion)
  • arXiv (Cornell University) (submittedVersion)
  • Kent Academic Repository (University of Kent) (submittedVersion)
  • Publication Database PIK (Potsdam Institute for Climate Impact Research (PIK)) (submittedVersion)
  • arXiv (Cornell University)
Funders
  • National Natural Science Foundation of China (61772447, 61532020)
  • DAAD/K.C. Wong Fellowship (91664078)
  • Royal Society (IE111186)
  • Hong Kong Research Grants Council (CityU 11234916)
Topics
  • Physical Sciences › Computer Science › Computer Vision and Pattern Recognition › Chaos-based Image/Signal Encryption
  • Physical Sciences › Mathematics › Mathematical Physics › Mathematical Dynamics and Fractals
  • Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Chaos control and synchronization
Keywords
logistic map, tent map, fixed-point arithmetic, floating-point arithmetic, scale-free networks, pseudorandom number generators, directed graphs

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