The DOI matches its Crossref record; 64 of the 65 references it cites were found in a registry or an index.
S-Box Based Image Encryption Application Using a Chaotic System without Equilibrium
Open accessAbstract
Chaotic systems without equilibrium are of interest because they are the systems with hidden attractors. A nonequilibrium system with chaos is introduced in this work. Chaotic behavior of the system is verified by phase portraits, Lyapunov exponents, and entropy. We have implemented a real electronic circuit of the system and reported experimental results. By using this new chaotic system, we have constructed S-boxes which are applied to propose a novel image encryption algorithm. In the designed encryption algorithm, three S-boxes with strong cryptographic properties are used for the sub-byte operation. Particularly, the S-box for the sub-byte process is selected randomly. In addition, performance analyses of S-boxes and security analyses of the encryption processes have been presented.
Overview
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
The check wasn’t confident either way, so it gives no verdict — never disputed.
In the citing paper
“In this sense, to solve the discrete logarithm problem when the solution set of the elliptic curve has a prime factor of 2 256 , is equivalent to factoring n with a 2 3072 size [9].”
From Cryptosystem Based on the Elliptic Curve With a High Degree of Resistance to Damage on the Encrypted Images (2020) · cites this paper as [9]
Experimental — accuracy not yet measured
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Citations
Cites
2 retracted
Khan, M., Shah, T., & Batool, S. I. (2015) · Neural Computing and Applications · doi:10.1007/s00521-015-1887-y · Cited by 147
RetractedKhan, M., & Shah, T. (2014) · Neural Computing and Applications · doi:10.1007/s00521-014-1663-4 · Cited by 68
RetractedDetermining Lyapunov exponents from a time series
Wolf, A., Swift, J. B., Swinney, H. L., & Vastano, J. A. (1985) · Physica D: Nonlinear Phenomena · doi:10.1016/0167-2789(85)90011-9 · Cited by 9,499
Communication Theory of Secrecy Systems
Shannon, C. E. (1949) · Bell System Technical Journal · doi:10.1002/j.1538-7305.1949.tb00928.x · Cited by 9,440
Approximate entropy as a measure of system complexity.
Pincus, S. M. (1991) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.88.6.2297 · Cited by 5,811
Ergodic theory of chaos and strange attractors
Eckmann, J., & Ruelle, D. P. (1985) · Reviews of Modern Physics · doi:10.1103/revmodphys.57.617 · Cited by 4,982
An equation for continuous chaos
Rössler, O. E. (1976) · Physics Letters A · doi:10.1016/0375-9601(76)90101-8 · Cited by 4,012
Differential cryptanalysis of DES-like cryptosystems
Biham, E., & Shamir, A. (1991) · Journal of Cryptology · doi:10.1007/bf00630563 · Cited by 2,914
SOME BASIC CRYPTOGRAPHIC REQUIREMENTS FOR CHAOS-BASED CRYPTOSYSTEMS
ALVAREZ, G., & LI, S. (2006) · International Journal of Bifurcation and Chaos · doi:10.1142/s0218127406015970 · Cited by 2,119
Sprott, J. C. (1994) · Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics · doi:10.1103/physreve.50.r647 · Cited by 1,299
Image encryption using chaotic logistic map
Pareek, N. K., Patidar, V., & Sud, K. K. (2006) · Image and Vision Computing · doi:10.1016/j.imavis.2006.02.021 · Cited by 1,261
(2011) · Cited by 904
Baptista, M. S. (1998) · Physics Letters A · doi:10.1016/s0375-9601(98)00086-3 · Cited by 885
Leonov, G. A., & Kuznetsov, N. V. (2013) · International Journal of Bifurcation and Chaos · doi:10.1142/s0218127413300024 · Cited by 854
Localization of hidden Chuaʼs attractors
Leonov, G. A., Kuznetsov, N. V., & Vagaitsev, V. I. (2011) · Physics Letters A · doi:10.1016/j.physleta.2011.04.037 · Cited by 709
Hidden attractors in dynamical systems
Dudkowski, D., Jafari, S., Kapitaniak, T., Kuznetsov, N. V., Leonov, G. A., & Prasad, A. (2016) · Physics Reports · doi:10.1016/j.physrep.2016.05.002 · Cited by 704
Self-citationChaos and cryptography: block encryption ciphers based on chaotic maps
Jakimoski, G., & Kocarev, L. (2001) · IEEE Transactions on Circuits and Systems I Fundamental Theory and Applications · doi:10.1109/81.904880 · Cited by 680
Sprott, J. C. (2010) · WORLD SCIENTIFIC eBooks · doi:10.1142/7183 · Cited by 551
Simple chaotic flows with a line equilibrium
Jafari, S., & Sprott, J. C. (2013) · Chaos Solitons & Fractals · doi:10.1016/j.chaos.2013.08.018 · Cited by 545
Self-citationHidden attractor in smooth Chua systems
Leonov, G. A., Kuznetsov, N. V., & Vagaitsev, V. I. (2012) · Physica D Nonlinear Phenomena · doi:10.1016/j.physd.2012.05.016 · Cited by 529
Elementary quadratic chaotic flows with no equilibria
Jafari, S., Sprott, J. C., & Golpayegani, S. M. R. H. (2013) · Physics Letters A · doi:10.1016/j.physleta.2013.01.009 · Cited by 495
Self-citationA fast image encryption scheme based on chaotic standard map
Wong, K., Kwok, B. S.-H., & Law, W.-S. (2007) · Physics Letters A · doi:10.1016/j.physleta.2007.12.026 · Cited by 414
Dynamical behaviors of a chaotic system with no equilibria
Wei, Z. (2011) · Physics Letters A · doi:10.1016/j.physleta.2011.10.040 · Cited by 403
Image encryption using the two-dimensional logistic chaotic map
Wu, Y., Noonan, J. P., Yang, G., & Jin, H. (2012) · Journal of Electronic Imaging · doi:10.1117/1.jei.21.1.013014 · Cited by 318
Image scrambling encryption algorithm of pixel bit based on chaos map
Ye, G. (2010) · Pattern Recognition Letters · doi:10.1016/j.patrec.2009.11.008 · Cited by 302
Secure image encryption algorithm design using a novel chaos based S-box
Çavuşoğlu, Ü., Kaçar, S., Pehlivan, I., & Zengin, A. (2017) · Chaos, Solitons & Fractals · doi:10.1016/j.chaos.2016.12.018 · Cited by 291
Self-citationA PROPOSED STANDARD FOR THE PUBLICATION OF NEW CHAOTIC SYSTEMS
Sprott, J. C. (2011) · International Journal of Bifurcation and Chaos · doi:10.1142/s021812741103009x · Cited by 273
Constructing a chaotic system with any number of equilibria
Wang, X., & Chen, G. (2012) · Nonlinear Dynamics · doi:10.1007/s11071-012-0669-7 · Cited by 270
Self-citationImage encryption process based on chaotic synchronization phenomena
VOLOS, C. K., Kyprianidis, I. M., & Stouboulos, I. N. (2012) · Signal Processing · doi:10.1016/j.sigpro.2012.11.008 · Cited by 257
A novel method for designing S-boxes based on chaotic maps
Tang, G., Liao, X., & Chen, Y. (2004) · Chaos Solitons & Fractals · doi:10.1016/j.chaos.2004.04.023 · Cited by 249
A novel image encryption algorithm based on self-adaptive wave transmission
Liao, X., Lai, S., & Zhou, Q. (2010) · Signal Processing · doi:10.1016/j.sigpro.2010.03.022 · Cited by 235
A chaos-based robust wavelet-domain watermarking algorithm
Dawei, Z., Chen, G., & Wenbo, L. (2004) · Chaos Solitons & Fractals · doi:10.1016/j.chaos.2003.12.104 · Cited by 219
The structured design of cryptographically good s-boxes
Adams, C. M., & Tavares, S. E. (1990) · Journal of Cryptology · doi:10.1007/bf00203967 · Cited by 212
A combined chaotic cryptographic and hashing scheme
Wong, K. (2003) · Physics Letters A · doi:10.1016/s0375-9601(02)01770-x · Cited by 194
Image encryption using binary bitplane
Zhou, Y., Cao, W., & Chen, C. L. P. (2014) · Signal Processing · doi:10.1016/j.sigpro.2014.01.020 · Cited by 191
A new finding of the existence of hidden hyperchaotic attractors with no equilibria
Wei, Z., Wang, R., & Liu, A. (2014) · Mathematics and Computers in Simulation · doi:10.1016/j.matcom.2014.01.001 · Cited by 184
Çavuşoğlu, Ü., Zengi̇n, A., Pehli̇van, İ., & Kaçar, S. (2016) · Nonlinear Dynamics · doi:10.1007/s11071-016-3099-0 · Cited by 180
Self-citationA chaotic path planning generator for autonomous mobile robots
VOLOS, C. K., Kyprianidis, I. M., & Stouboulos, I. N. (2012) · Robotics and Autonomous Systems · doi:10.1016/j.robot.2012.01.001 · Cited by 179
A novel technique for the construction of strong S-boxes based on chaotic Lorenz systems
Khan, M., Shah, T., Mahmood, H., Gondal, M. A., & Hussain, I. (2012) · Nonlinear Dynamics · doi:10.1007/s11071-012-0621-x · Cited by 164
New class of chaotic systems with circular equilibrium
Götthans, T., & Petržela, J. (2015) · Nonlinear Dynamics · doi:10.1007/s11071-015-2056-7 · Cited by 159
Theory and practice of chaotic cryptography
Amigó, J. M., Kocarev, L., & Szczepański, J. (2007) · Physics Letters A · doi:10.1016/j.physleta.2007.02.021 · Cited by 157
A hyperchaotic system without equilibrium
Wang, Z., Cang, S., Ochola, E. O., & Sun, Y. (2011) · Nonlinear Dynamics · doi:10.1007/s11071-011-0284-z · Cited by 148
A block cipher with dynamic S-boxes based on tent map
Wang, Y., Wong, K., Liao, X., & Xiang, T. (2008) · Communications in Nonlinear Science and Numerical Simulation · doi:10.1016/j.cnsns.2008.12.005 · Cited by 146
Rajagopal, K., Karthikeyan, A., & Srinivasan, A. (2016) · Nonlinear Dynamics · doi:10.1007/s11071-016-3189-z · Cited by 143
Designing chaotic S-boxes based on time-delay chaotic system
Özkaynak, F., & Yavuz, S. (2013) · Nonlinear Dynamics · doi:10.1007/s11071-013-0987-4 · Cited by 141
A system theory approach for designing cryptosystems based on hyperchaos
Grassi, G., & Mascolo, S. (1999) · IEEE Transactions on Circuits and Systems I Fundamental Theory and Applications · doi:10.1109/81.788815 · Cited by 134
A novel heuristic method for obtaining S-boxes
Chen, G. (2006) · Chaos Solitons & Fractals · doi:10.1016/j.chaos.2006.08.003 · Cited by 126
Simple Chaotic Flow with Circle and Square Equilibrium
Götthans, T., Sprott, J. C., & Petržela, J. (2016) · International Journal of Bifurcation and Chaos · doi:10.1142/s0218127416501376 · Cited by 116
Chaos-based color image block encryption scheme using S-box
Liu, H., Kadir, A., & Niu, Y. (2014) · AEU - International Journal of Electronics and Communications · doi:10.1016/j.aeue.2014.02.002 · Cited by 115
A robust chaotic algorithm for digital image steganography
Ghebleh, M., & Kanso, A. A. (2013) · Communications in Nonlinear Science and Numerical Simulation · doi:10.1016/j.cnsns.2013.10.014 · Cited by 114
A novel approach for designing substitution-boxes based on nonlinear chaotic algorithm
Hussain, I., Shah, T., & Gondal, M. A. (2012) · Nonlinear Dynamics · doi:10.1007/s11071-012-0573-1 · Cited by 96
Xu, G., Shekofteh, Y., Akgül, A., Li, C., & Panahi, S. (2018) · Entropy · doi:10.3390/e20020086 · Cited by 89
Emulating complex business cycles by using an electronic analogue
Bouali, S., Buscarino, A., Fortuna, L., Frasca, M., & Gambuzza, L. V. (2012) · Nonlinear Analysis Real World Applications · doi:10.1016/j.nonrwa.2012.02.010 · Cited by 72
A novel image encryption algorithm based on chaos maps with Markov properties
Liu, Q., Li, P., Zhang, M., Sui, Y., & Yang, H. (2014) · Communications in Nonlinear Science and Numerical Simulation · doi:10.1016/j.cnsns.2014.06.005 · Cited by 63
Digital watermarking based on chaotic map and reference register
Wu, Y., & Shih, F. Y. (2007) · Pattern Recognition · doi:10.1016/j.patcog.2007.04.013 · Cited by 55
A novel chaos‐based encryption algorithm over TCP data packet for secure communication
Çavuşoğlu, Ü., Akgül, A., Kaçar, S., Pehli̇van, İ., & Zengi̇n, A. (2016) · Security and Communication Networks · doi:10.1002/sec.1414 · Cited by 51
Self-citationA New Two-Dimensional Map with Hidden Attractors
Wang, C., & Ding, Q. (2018) · Entropy · doi:10.3390/e20050322 · Cited by 47
Lai, Q., & Wang, L. (2016) · Optik · doi:10.1016/j.ijleo.2016.03.014 · Cited by 45
SKIPJACK review: interim report
Brickell, E. F., Denning, D. E., Kent, S., Maher, D. P., & Tuchman, W. (1995) · Springer eBooks · Cited by 27
Dynamics analysis and circuit implementation of a new three-dimensional chaotic system
Zhou, W., Wang, Z., Wu, M., Zheng, W., & Weng, J.-F. (2015) · Optik · doi:10.1016/j.ijleo.2015.02.029 · Cited by 26
Study of chaos functions for their suitability in generating Message Authentication Codes
Arumugam, G., Praba, V. L., & Radhakrishnan, S. (2006) · Applied Soft Computing · doi:10.1016/j.asoc.2006.05.005 · Cited by 22
A Novel Digital Image Encryption Algorithm Based on Orbit Variation of Phase Diagram
Shen, Q., & Liu, W. (2017) · International Journal of Bifurcation and Chaos · doi:10.1142/s0218127417502042 · Cited by 15
Approximate entropy (ApEn) as a complexity measure.
Pincus, S. (1995) · PubMed · doi:10.1063/1.166092 · Cited by 2
Charney (1963) · doi:10.1175/1520-0469(1963)020
Flagged first, then by citations
1 of the 65 references couldn’t be matched to a known paper.
Research works printed but not linked: 4
- Stinson, D.R. (1995). Cryptography: Theory and Practice, CRC Press.
- Schneier, B. (1996). Applied Cryptography: Protocols, Algorithms, and Source Code in C, Wiley. [2nd ed.].
- Webster, A., and Tavares, S.E. (1985). On the design of S-boxes. Conference on the Theory and Application of Cryptographic Techniques, Springer.
- Rijmen, V., and Daemen, J. (2001). Advanced encryption standard. Proceedings of Federal Information Processing Standards Publications, National Institute of Standards and Technology, NIST.
Cited by
Sorted by citations
An Efficient Image Encryption Scheme Based on the LSS Chaotic Map and Single S-Box
Lu, Q., Zhu, C., & Deng, X. (2020) · IEEE Access · doi:10.1109/access.2020.2970806 · Cited by 281
A New Chaotic Map With Dynamic Analysis and Encryption Application in Internet of Health Things
Tsafack, N., Sankar, S., Abd-El-Atty, B., Kengne, J., Jithin, K. C., Belazi, A., Mehmood, I., Bashir, A. K., Song, O.-Y., & El‐Latif, A. A. A. (2020) · IEEE Access · doi:10.1109/access.2020.3010794 · Cited by 155
Remote sensing image compression and encryption based on block compressive sensing and 2D-LCCCM
Nan, S.-X., Feng, X., Wu, Y., & Zhang, H. (2022) · Nonlinear Dynamics · doi:10.1007/s11071-022-07335-4 · Cited by 133
A Secure and Fast Image Encryption Scheme Based on Double Chaotic S-Boxes
Zhu, S., Wang, G., & Zhu, C. (2019) · Entropy · doi:10.3390/e21080790 · Cited by 131
Jahanshahi, H., Yousefpour, A., Munoz-Pacheco, J. M., Kaçar, S., Pham, V., & Alsaadi, F. E. (2020) · Applied Mathematics and Computation · doi:10.1016/j.amc.2020.125310 · Cited by 122
Self-citation
Metadata
- Authors
- Wang, X., Çavuşoğlu, Ü., Kacar, S., Akgul, A., Pham, V.-T., Jafari, S., Alsaadi, F. E., & Nguyen, X. Q.
- Affiliations
- Shenzhen University (CN)
- Sakarya University (TR)
- Department of Electrical and Electronics Engineering, Faculty of Technology, Sakarya University, 54187 Serdivan, Turkey
- Department of Electrical and Electronics Engineering, Faculty of Technology, Sakarya University of Applied Sciences, 54187 Serdivan, Turkey
- Ton Duc Thang University (VN)
- Amirkabir University of Technology (IR)
- King Abdulaziz University (SA)
- National Council for Science and Technology Policy (VN)
- Corresponding author
- Pham, Viet-Thanh
- Venue
- Applied Sciences
- Publisher
- MDPI AG
- Published
- 2019-02-22
- Volume
- 9
- Issue
- 4
- Pages
- 781
- ISSN
- 2076-3417 (ISSN-L)
- OpenAlex
- W2916974458
- Cited by
- 125
- References
- 65
- Citations by year
- 2026: 3 · 2025: 4 · 2024: 19 · 2023: 17 · 2022: 25 · 2021: 26 · 2020: 26 · 2019: 5
- FWCI
- 9.16
- Type
- journal article
- Language
- en
- Open access
- gold
- dx.doi.org
- Licence
- Locations
- Applied Sciences (publishedVersion, cc-by)
- Sakarya Üniversitesi Kurumsal Açık Akademik Arşivi (submittedVersion)
- Sakarya University of Applied Sciences Institutional Repository (submittedVersion, other-oa)
- DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion, cc-by-sa)
- Funders
- National Natural Science Foundation of China (No. 61601306)
- and Shenzhen Overseas High Level Talent Peacock Project Fund (No. 20150215145C)
- Topics
- Physical Sciences › Computer Science › Computer Vision and Pattern Recognition › Chaos-based Image/Signal Encryption
- Physical Sciences › Computer Science › Artificial Intelligence › Cryptographic Implementations and Security
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Chaos control and synchronization
- Keywords
- image encryption, S-box, hidden attractors, circuit implementation, Lyapunov exponents, entropy analysis, encryption security analysis
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
