Hierarchy of Chaotic Maps with an Invariant Measure
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Behnia and Akhshani's mixture of the Logistic map with a coupled map has large key space and high-level security, although its speed is only acceptable.
“S. Behnia and A. Akhshani [55] were the first to mix the Logistic map with a coupled map based on [56,57] for image encryption.This mixture scheme has large key space and high-level security, although its speed is only acceptable.”
From Chaos-Based Image Encryption: Review, Application, and Challenges (2023) · cites this paper as [57]
The Introduction (p. 3) describes a family of chaotic maps constructed by composition, supporting the citation's use as a basis for a map-based scheme. It does not describe Behnia and Akhshani's Logistic-map image-encryption scheme or assess its key space, security, or speed. (LLM, conf=0.84)
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Research works printed but not linked: 6
- [1][1] M.A.Jafarizadeh, S.Behnia, S.Khorram and H.Naghshara nlin.cd/0003036. - · arXiv
- [2][2] I.P.Cornfeld, S.V.Fomin and Ya,G.Sinai. Ergodic Theory, Springer-Verlag, Berlin, (1982). -
- [4][4] S.Tasaki, Z.Suchanecki, I.Antoniou. Physics Letters A, 179 (1993) 103 -
- [7][7] G.Froyland. In proceedings of the 1997 International Symposium on Nonlinear Theory and its Applications, Hawaii, Volume 2(1997) 1129 -
- [9][9] Z.X.Wang, D.R.Guo. Special Functions, World Scientific Publishing, (1989). -
- [10][10] Robert L.Devancy, An Introduction to Chaotic Dynamical Systems, Addison Wesley, (1982). -
Cited by
Sorted by citations
Chaos-Based Image Encryption: Review, Application, and Challenges
Zhang, B., & Liu, L. (2023) · Mathematics · doi:10.3390/math11112585 · Cited by 328 · see citing works
“S. Behnia and A. Akhshani [55] were the first to mix the Logistic map with a coupled map based on [56,57] for image encryption.”
Background
- Authors
- Jafarizadeh, M. A., Behnia, S., Khorram, S., & Nagshara, H.
- Affiliations
- University of Tabriz (IR)
- Islamic Azad University, Tehran (IR)
- Corresponding author
- Jafarizadeh, M. A.
- Khorram, S.
- Nagshara, H.
- Venue
- Journal of Statistical Physics
- Published
- 2001-09
- Volume
- 104
- Issue
- 5-6
- Pages
- 1013-1028
- ISSN
- 0022-4715 (ISSN-L)
- 1572-9613
- OpenAlex
- W2096469007
- Cited by
- 56
- References
- 0
- Citations by year
- 2026: 1 · 2025: 1 · 2023: 1 · 2022: 4 · 2021: 1 · 2020: 2 · 2019: 2 · 2018: 1 · 2017: 2 · 2016: 1 · 2014: 3 · 2013: 4 · 2012: 7
- FWCI
- 1.55
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Licence
- Locations
- Journal of Statistical Physics (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- arXiv (Cornell University)
- Topics
- Physical Sciences › Mathematics › Mathematical Physics › Mathematical Dynamics and Fractals
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Chaos control and synchronization
- Physical Sciences › Mathematics › Mathematical Physics › advanced mathematical theories
- Keywords
- chaotic maps, invariant measures, interval maps, Kolmogorov-Sinai entropy, Lyapunov exponents, period-doubling cascade, fixed-point attractors, logistic map, tent map
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