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Journal articles on the topic '3D chaotic map'

Author: Grafiati

Published: 5 June 2025

Last updated: 1 August 2025

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1

Yan, Wenhao, Zijing Jiang, Xin Huang, and Qun Ding. "A Three-Dimensional Infinite Collapse Map with Image Encryption." Entropy 23, no. 9 (2021): 1221. http://dx.doi.org/10.3390/e23091221.

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Chaos is considered as a natural candidate for encryption systems owing to its sensitivity to initial values and unpredictability of its orbit. However, some encryption schemes based on low-dimensional chaotic systems exhibit various security defects due to their relatively simple dynamic characteristics. In order to enhance the dynamic behaviors of chaotic maps, a novel 3D infinite collapse map (3D-ICM) is proposed, and the performance of the chaotic system is analyzed from three aspects: a phase diagram, the Lyapunov exponent, and Sample Entropy. The results show that the chaotic system has

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2

Mandangan, Arif, and Irene Lim Jin Ying. "Chaotic Encryption Scheme for Colour Image using 3D Lorenz Chaotic Map and 3D Chen System." International Journal of Computational Thinking and Data Science 1, no. 1 (2024): 10–24. http://dx.doi.org/10.37934/ctds.1.1.1024.

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Chaos-based image encryption system is an encryption method that uses chaotic systems in encrypting digital images for the purpose of enhancing security. Chaos theory exhibits some distinctive characteristics, which include butterfly-like patterns, unpredictable behavior, and sensitive dependence to initial conditions. . In the past few decades, image encryption based on a single chaotic map has been a common technique in encrypting images. However, there are still unauthorized interceptors who illegally access and obtain the private information of the image. With that being the case, an encry

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Irene Lim Jin Ying and Arif Mandangan. "Chaotic Encryption Scheme for Colour Image using 3D Lorenz Chaotic Map and 3D Chen System." International Journal of Advanced Research in Computational Thinking and Data Science 1, no. 1 (2025): 10–24. https://doi.org/10.37934/ctds.1.1.1024a.

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Chaos-based image encryption system is an encryption method that uses chaotic systems in encrypting digital images for the purpose of enhancing security. Chaos theory exhibits some distinctive characteristics, which include butterfly-like patterns, unpredictable behavior, and sensitive dependence to initial conditions. . In the past few decades, image encryption based on a single chaotic map has been a common technique in encrypting images. However, there are still unauthorized interceptors who illegally access and obtain the private information of the image. With that being the case, an encry

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4

Belozyorov, Vasiliy Ye. "Exponential-Algebraic Maps and Chaos in 3D Autonomous Quadratic Systems." International Journal of Bifurcation and Chaos 25, no. 04 (2015): 1550048. http://dx.doi.org/10.1142/s0218127415500480.

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For some 3D autonomous quadratic dynamical systems an explicit autonomous exponential-algebraic 1D map, generating chaos in mentioned systems, is designed. Examples of the systems, where chaos is generated by such discrete maps, are given. New results about an existence of chaotic dynamics in the quadratic 3D systems are also derived. Besides, for the Lanford system (it is 3D autonomous quadratic dynamical system) the value of some parameter at which the system shows increased chaotic behavior is indicated. This assertion is based on the construction for the Lanford system of 2D exponential-al

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5

Abdul-Kareem, Ali Akram, and Waleed Ameen Mahmoud Al-Jawher. "WAM 3D Discrete Chaotic Map for Secure Communication Applications." International Journal of Innovative Computing 13, no. 1-2 (2023): 45–54. http://dx.doi.org/10.11113/ijic.v13n1-2.419.

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Chaotic systems have become widely adopted as an effective way for secure data communications, because of its simple mathematical complexity and good security. The relationship between encryption algorithms and chaos systems has gained a lot of attention in the past few years, since it avoids the data spreading as well as lower the transmission delay and costs. In this paper a novel 3D discrete chaotic map is proposed for data encryption and secure communication and named as WAM. For secure communication, the Pecora and Carroll (P-C) method was utilized to achieve synchronization between the m

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6

Alsalam Ali, Nashwan, Abdul Monem S. Rahma, and Shaimaa H. Shaker. "3D Polygon Mesh Encryption Based on 3D Lorenz Chaotic Map." International Journal of Interactive Mobile Technologies (iJIM) 15, no. 15 (2021): 103. http://dx.doi.org/10.3991/ijim.v15i15.24177.

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<p class="0abstract">The multimedia application developments in recent years lead to the widespread of 3D model applications. It becomes more popular in various fields as well as exchanging it over the internet. The security of the 3D models is a very important issue now a day, so the scheme for encrypting the 3D model will be proposed in this work. In this proposed scheme, the 3D polygon mesh model will be protected through the encrypting process based on a 3D Lorenz Chaotic map where the vertices value of the 3D polygon mesh model will be modified using 3D keys generated by 3D Lorenz C

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Salunke, Sharad, Ashok Kumar Shrivastava, Mohammad Farukh Hashmi, Bharti Ahuja, and Neeraj Dhanraj Bokde. "Quad Key-Secured 3D Gauss Encryption Compression System with Lyapunov Exponent Validation for Digital Images." Applied Sciences 13, no. 3 (2023): 1616. http://dx.doi.org/10.3390/app13031616.

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High-dimensional systems are more secure than their lower-order counterparts. However, high security with these complex sets of equations and parameters reduces the transmission system’s processing speed, necessitating the development of an algorithm that secures and makes the system lightweight, ensuring that the processing speed is not compromised. This study provides a digital image compression–encryption technique based on the idea of a novel quad key-secured 3D Gauss chaotic map with singular value decomposition (SVD) and hybrid chaos, which employs SVD to compress the digital image and a

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8

Dridi, Fethi, Safwan El Assad, Wajih El Hadj Youssef, Mohsen Machhout, and René Lozi. "The Design and FPGA-Based Implementation of a Stream Cipher Based on a Secure Chaotic Generator." Applied Sciences 11, no. 2 (2021): 625. http://dx.doi.org/10.3390/app11020625.

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In this study, with an FPGA-board using VHDL, we designed a secure chaos-based stream cipher (SCbSC), and we evaluated its hardware implementation performance in terms of computational complexity and its security. The fundamental element of the system is the proposed secure pseudo-chaotic number generator (SPCNG). The architecture of the proposed SPCNG includes three first-order recursive filters, each containing a discrete chaotic map and a mixing technique using an internal pseudo-random number (PRN). The three discrete chaotic maps, namely, the 3D Chebyshev map (3D Ch), the 1D logistic map

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9

Dridi, Fethi, Safwan El Assad, Wajih El Hadj Youssef, Mohsen Machhout, and René Lozi. "The Design and FPGA-Based Implementation of a Stream Cipher Based on a Secure Chaotic Generator." Applied Sciences 11, no. 2 (2021): 625. http://dx.doi.org/10.3390/app11020625.

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In this study, with an FPGA-board using VHDL, we designed a secure chaos-based stream cipher (SCbSC), and we evaluated its hardware implementation performance in terms of computational complexity and its security. The fundamental element of the system is the proposed secure pseudo-chaotic number generator (SPCNG). The architecture of the proposed SPCNG includes three first-order recursive filters, each containing a discrete chaotic map and a mixing technique using an internal pseudo-random number (PRN). The three discrete chaotic maps, namely, the 3D Chebyshev map (3D Ch), the 1D logistic map

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10

Kumari, Abinaya, B. Akshaya, B. Umamaheswari, K. Thenmozhi, Rengarajan Amirtharajan, and Padmapriya Praveenkumar. "3D Lorenz Map Governs DNA Rule in Encrypting DICOM Images." Biomedical and Pharmacology Journal 11, no. 2 (2018): 897–906. http://dx.doi.org/10.13005/bpj/1446.

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This paper introduces a framework for the secure encryption of healthcare images. The objective of this paper is to encrypt medical images based on Deoxyribo Nucleic Acid (DNA), 3D Lorenz chaotic map, BITXOR operations. The different keys are employed to provide confusion, permutation, encoding and diffusion operations in the encryption procedure to provide uncorrelated image pixels. The proposed algorithm uses 3D Lorenz attractor as chaotic system for encrypting colour Digital Imaging and Communication in Medicine (DICOM) images. Further the encrypted image will be validated using encryption

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11

Zhang, Bowen, and Lingfeng Liu. "A novel delayed exponent coupled chaotic map with countering dynamical degradation." AIMS Mathematics 9, no. 1 (2024): 99–121. http://dx.doi.org/10.3934/math.2024007.

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<abstract> <p>While chaotic systems have found extensive applications across diverse scientific domains due to their inherent advantages, they often degrade into cyclic patterns when simulated on hardware with limited computational precision. This results in a pronounced decline in properties related to chaotic dynamics. To address this issue, we introduce the delayed exponent coupled chaotic map (DECCM). This model is designed to enhance the chaotic dynamics of the original map, especially at lower computational precisions. Additionally, DECCM can transform any proficient 1-dimens

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12

Adnan, Ibrahem Salih, Alabaichi Ashwaq, and Yaseen Tuama Ammar. "Enhancing advance encryption standard security based on dual dynamic XOR table and mixcolumns transformation." Indonesian Journal of Electrical Engineering and Computer Science 19, no. 3 (2020): 1574–81. https://doi.org/10.11591/ijeecs.v19.i3.pp1574 -1581.

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An efficient approach to secure information is critically needed at present. Cryptography remains the best approach to achieve security. On this basis, the National Institute of Standards and Technology (NIST) selected Rijndael, which is a symmetric block cipher, as the advanced encryption standard (AES). The MixColumns transformation of this cipher is the most important function within the linear unit and the major source of diffusion. Dynamic MixColumns transformation can be used to enhance the AES security. In this study, a method to enhance the AES security is developed on the basis of two

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13

Jafari, Sajad, Viet-Thanh Pham, and Tomasz Kapitaniak. "Multiscroll Chaotic Sea Obtained from a Simple 3D System Without Equilibrium." International Journal of Bifurcation and Chaos 26, no. 02 (2016): 1650031. http://dx.doi.org/10.1142/s0218127416500310.

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Recently, many rare chaotic systems have been found including chaotic systems with no equilibria. However, it is surprising that such a system can exhibit multiscroll chaotic sea. In this paper, a novel no-equilibrium system with multiscroll hidden chaotic sea is introduced. Besides having multiscroll chaotic sea, this system has two more interesting properties. Firstly, it is conservative (which is a rare feature in three-dimensional chaotic flows) but not Hamiltonian. Secondly, it has a coexisting set of nested tori. There is a hidden torus which coexists with the chaotic sea. This new syste

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14

Liu, Hongjun, Abdurahman Kadir, and Chengbo Xu. "Color Image Encryption with Cipher Feedback and Coupling Chaotic Map." International Journal of Bifurcation and Chaos 30, no. 12 (2020): 2050173. http://dx.doi.org/10.1142/s0218127420501734.

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Based on the classic quadratic map (CQM) with abundant bifurcations and periodic windows, a new 3D improved coupling quadratic map (3D-ICQM) is constructed, and its phase diagram, Lyapunov exponent (LE) and randomness testing by TestU01 demonstrated that it has better ergodicity, more complex nonlinear behavior, larger chaotic range and better randomness. To investigate its application in cryptography, a 3D-ICQM based color image encryption algorithm with round key expansion is designed. To further enhance the randomness of key stream, the hash value of intermediate cipher of the previous roun

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15

Curiac, Daniel-Ioan, and Constantin Volosencu. "Path Planning Algorithm based on Arnold Cat Map for Surveillance UAVs." Defence Science Journal 65, no. 6 (2015): 483. http://dx.doi.org/10.14429/dsj.65.8483.

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During their task accomplishment, autonomous unmanned aerial vehicles are facing more and more threats coming from both ground and air. In such adversarial environments, with no a priori information about the threats, a flying robot in charge with surveilling a specified 3D sector must perform its tasks by evolving on misleading and unpredictable trajectories to cope with enemy entities. In our view, the chaotic dynamics can be the cornerstone in designing unpredictable paths for such missions, even though this solution was not exploited until now by researchers in the 3D context. This paper a

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16

Thapliyal, Pragati, and Madhu Sharma. "Image Encryption and Authentication Scheme using 3D Chaotic Map." International Journal of Computer Applications 117, no. 17 (2015): 15–18. http://dx.doi.org/10.5120/20646-3397.

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17

Ashwaq, T. Hashim, and D. Jalil Bahaa. "Color image encryption based on chaotic shit keying with lossless compression." International Journal of Electrical and Computer Engineering (IJECE) 10, no. 6 (2020): 5736–48. https://doi.org/10.11591/ijece.v10i6.pp5736-5748.

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In order to protect valuable data from undesirable readers or against illegal reproduction and modifications, there have been various data encryption techniques. Many methods are developed to perform image encryption. The use of chaotic map for image encryption is very effective, since it increases the security, due to its random behavior. The most attractive feature of deterministic chaotic systems is the extremely unexpected and random-look nature of chaotic signals that may lead to novel applications. A novel algorithm for image encryption based on compression and hyper chaotic map techniqu

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18

Wang, Ling, Qiwen Ran, and Junrong Ding. "Image Encryption Using Quantum 3D Mobius Scrambling and 3D Hyper-Chaotic Henon Map." Entropy 25, no. 12 (2023): 1629. http://dx.doi.org/10.3390/e25121629.

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In encryption technology, image scrambling is a common processing operation. This paper proposes a quantum version of the 3D Mobius scrambling transform based on the QRCI model, which changes not only the position of pixels but also the gray values. The corresponding quantum circuits are devised. Furthermore, an encryption scheme combining the quantum 3D Mobius transform with the 3D hyper-chaotic Henon map is suggested to protect the security of image information. To facilitate subsequent processing, the RGB color image is first represented with QRCI. Then, to achieve the pixel-level permutati

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19

Almatroud, Othman Abdullah, Amina-Aicha Khennaoui, Adel Ouannas, Saleh Alshammari, and Sahar Albosaily. "A New Fractional Discrete Memristive Map with Variable Order and Hidden Dynamics." Fractal and Fractional 8, no. 6 (2024): 322. http://dx.doi.org/10.3390/fractalfract8060322.

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This paper introduces and explores the dynamics of a novel three-dimensional (3D) fractional map with hidden dynamics. The map is constructed through the integration of a discrete sinusoidal memristive into a discrete Duffing map. Moreover, a mathematical operator, namely, a fractional variable-order Caputo-like difference operator, is employed to establish the fractional form of the map with short memory. The numerical simulation results highlight its excellent dynamical behavior, revealing that the addition of the piecewise fractional order makes the memristive-based Duffing map even more ch

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20

Alsalam Ali, Nashwan, Abdul Monem S. Rahma, and Shaimaa H. Shaker. "Survey on 3D Content Encryption." International Journal of Interactive Mobile Technologies (iJIM) 15, no. 15 (2021): 115. http://dx.doi.org/10.3991/ijim.v15i15.24179.

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<p class="0abstract">The rapidly growing 3D content exchange over the internet makes securing 3D content became a very important issue. The solution for this issue is to encrypting data of 3D content, which included two main parts texture map and 3D models. The standard encryption methods such as AES and DES are not a suitable solution for 3D applications due to the structure of 3D content, which must maintain dimensionality and spatial stability. So, these problems are overcome by using chaotic maps in cryptography, which provide confusion and diffusion by providing uncorrelated numbers

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21

Al-Taani, Hussein, Ma’mon Abu Hammad, Mohammad Abudayah, Louiza Diabi, and Adel Ouannas. "Asymmetry and Symmetry in New Three-Dimensional Chaotic Map with Commensurate and Incommensurate Fractional Orders." Symmetry 16, no. 11 (2024): 1447. http://dx.doi.org/10.3390/sym16111447.

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According to recent research, discrete-time fractional-order models have greater potential to investigate behaviors, and chaotic maps with fractional derivative values exhibit rich dynamics. This manuscript studies the dynamics of a new fractional chaotic map-based three functions. We analyze the behaviors in commensurate and incommensurate orders, revealing their impact on dynamics. Through the maximum Lyapunov exponent (LEmax), phase portraits, and bifurcation charts. In addition, we assess the complexity and confirm the chaotic features in the map using the approximation entropy ApEn and C0

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22

Pan, Tian Gong, and Da Yong Li. "Image Encryption Algorithm Based on 3D Arnold Cat and Logistic Map." Advanced Materials Research 317-319 (August 2011): 1537–40. http://dx.doi.org/10.4028/www.scientific.net/amr.317-319.1537.

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Arnold cat map is a classical transformation of image encryption, but it has some shortcomings such as short key quantities, small period and so on. On the basis of Arnold cat map, it presented an algorithm of image encryption based on 3D Arnold cat and chaotic map. Simulation experiments show that the encryption algorithm has characters of strong keys, better effect and fast.

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23

Khennaoui, Amina-Aicha, Adel Ouannas, Zaid Odibat, Viet-Thanh Pham, and Giuseppe Grassi. "On the Three-Dimensional Fractional-Order Hénon Map with Lorenz-Like Attractors." International Journal of Bifurcation and Chaos 30, no. 11 (2020): 2050217. http://dx.doi.org/10.1142/s021812742050217x.

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A three-dimensional (3D) Hénon map of fractional order is proposed in this paper. The dynamics of the suggested map are numerically illustrated for different fractional orders using phase plots and bifurcation diagrams. Lorenz-like attractors for the considered map are realized. Then, using the linear fractional-order systems stability criterion, a controller is proposed to globally stabilize the fractional-order Hénon map. Furthermore, synchronization control scheme has been designed to exhibit a synchronization behavior between a given 2D fractional-order chaotic map and the 3D fractional-or

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Walaa Hadi Abdulnabi, Sadiq A. Mehdi, and Sawsen Abdulhadi Mahmood. "Development and Evaluation of an Innovative Three-Dimensional Hyperchaotic map." Mustansiriyah Journal of Pure and Applied Sciences 3, no. 2 (2025): 113–25. https://doi.org/10.47831/mjpas.v3i2.223.

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we are designing the new system which is 3D hyper-chaotic and subsequently examined the most critical characteristics of this proposed system with a dynamic behavior by using Mathematica software that performs numerical simulations of these dynamic behaviors. The findings indicated that the suggested system has three-dimensional with generates hyper-chaotic attractors, as it has two positive exponents of Lyapunov in (LE1= 1.14247, LE2= 0.01498), which makes it hyper-chaotic, and that it is unstable and possesses the butterfly effect, as its wave form is non-periodic and therefore has non-perio

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25

Demirtas, Mehmet. "A BIT-LEVEL AUDIO ENCRYPTION ALGORITHM USING A NEW HYBRID CHAOTIC MAP." Kahramanmaraş Sütçü İmam Üniversitesi Mühendislik Bilimleri Dergisi 27, no. 2 (2024): 601–14. http://dx.doi.org/10.17780/ksujes.1412850.

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Audio data is increasingly transmitted worldwide, necessitating robust encryption techniques to safeguard it from malicious actors. To secure transmitted audio files, a novel, and effective audio encryption method is introduced using a newly designed 1D chaotic map and bit-level operations in this work. The Sine-Chebyshev Hybrid Map (SCHM) is a new chaotic map with high randomness, created using two classical maps, such as the Sine map and the Chebyshev map. Two-dimensional (2D) and three-dimensional (3D) phase trajectories, bifurcation diagrams, initial condition sensitivity, Lyapunov exponen

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Hashim, Ashwaq T., and Bahaa D. Jalil. "Color image encryption based on chaotic shit keying with lossless compression." International Journal of Electrical and Computer Engineering (IJECE) 10, no. 6 (2020): 5736. http://dx.doi.org/10.11591/ijece.v10i6.pp5736-5748.

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In order to protect valuable data from undesirable readers or against illegal reproduction and modifications, there have been various data encryption techniques. Many methods are developed to perform image encryption. The use of chaotic map for image encryption is very effective, since it increase the security, due to its random behavior. The most attractive feature of deterministic chaotic systems is he extremely unexpected and random-look nature of chaotic signals that may lead to novel applications. A novel image encryption algorithm based on compression and hyper chaotic map techniques is

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27

BELOZYOROV, VASILIY YE, and SERGEY V. CHERNYSHENKO. "GENERATING CHAOS IN 3D SYSTEMS OF QUADRATIC DIFFERENTIAL EQUATIONS WITH 1D EXPONENTIAL MAPS." International Journal of Bifurcation and Chaos 23, no. 06 (2013): 1350105. http://dx.doi.org/10.1142/s0218127413501058.

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New existence conditions of homoclinic orbits for some systems of ordinary quadratic differential equations with singular linear part are found. A realization of these conditions guarantees the existence of chaotic attractors at 3D autonomous quadratic systems. In addition, a chaotic behavior of solutions of these systems is determined by the 1D discrete map [Formula: see text] at some values of parameters r > 0, p ∈ ℝ, and γ ∈ (-d, ∞), where d > 0; n = 0, 1, 2, …. Examples of chaotic attractors are given.

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28

Abualhomos, Mayada, Abderrahmane Abbes, Gharib Mousa Gharib, et al. "Bifurcation, Hidden Chaos, Entropy and Control in Hénon-Based Fractional Memristor Map with Commensurate and Incommensurate Orders." Mathematics 11, no. 19 (2023): 4166. http://dx.doi.org/10.3390/math11194166.

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In this paper, we present an innovative 3D fractional Hénon-based memristor map and conduct an extensive exploration and analysis of its dynamic behaviors under commensurate and incommensurate orders. The study employs diverse numerical techniques, such as visualizing phase portraits, analyzing Lyapunov exponents, plotting bifurcation diagrams, and applying the sample entropy test to assess the complexity and validate the chaotic characteristics. However, since the proposed fractional map has no fixed points, the outcomes reveal that the map can exhibit a wide range of hidden dynamical behavio

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29

Namuq, Jenan. "S-Box Design Utilizing 3D Chaotic Maps for Cryptographic Application." Basrah journal for engineering science 24, no. 2 (2024): 68–73. http://dx.doi.org/10.33971/bjes.24.2.9.

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In the realm of cryptography, the Substitution-box (S-box) is a critical component for enhancing the security of encryption algorithms. The inherent characteristics of Chaos, such as sensitivity to beginning conditions and unpredictability, make it a highly suitable choice for encryption applications. In this paper, proposed a method for generating S-Boxes using 3D chaotic maps algorithms including (Cat map, Henon map, Sine map, and Cosine map). The primary focus is on enhancing the security and efficiency of cryptographic systems by leveraging the inherent complexity and unpredictability of c

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Broumandnia, Ali. "Scale invariant digital image encryption using 3D modular chaotic map." Multimedia Tools and Applications 79, no. 17-18 (2020): 11327–55. http://dx.doi.org/10.1007/s11042-019-08337-y.

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Shokouh Saljoughi, Ahmad, and Hamid Mirvaziri. "A new method for image encryption by 3D chaotic map." Pattern Analysis and Applications 22, no. 1 (2018): 243–57. http://dx.doi.org/10.1007/s10044-018-0765-5.

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Broumandnia, Ali. "The 3D modular chaotic map to digital color image encryption." Future Generation Computer Systems 99 (October 2019): 489–99. http://dx.doi.org/10.1016/j.future.2019.04.005.

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33

Pati, Sangram, Minati Mishra, and Jayanti Rout. "Securing Audio with 3D-Chaotic Map Based Hybrid Encryption Technique." International Journal of Computing and Digital Systems 18, no. 1 (2025): 1–15. https://doi.org/10.12785/ijcds/1571111843.

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Moysis, Lazaros, Karthikeyan Rajagopal, Aleksandra V. Tutueva, Christos Volos, Beteley Teka, and Denis N. Butusov. "Chaotic Path Planning for 3D Area Coverage Using a Pseudo-Random Bit Generator from a 1D Chaotic Map." Mathematics 9, no. 15 (2021): 1821. http://dx.doi.org/10.3390/math9151821.

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This work proposes a one-dimensional chaotic map with a simple structure and three parameters. The phase portraits, bifurcation diagrams, and Lyapunov exponent diagrams are first plotted to study the dynamical behavior of the map. It is seen that the map exhibits areas of constant chaos with respect to all parameters. This map is then applied to the problem of pseudo-random bit generation using a simple technique to generate four bits per iteration. It is shown that the algorithm passes all statistical NIST and ENT tests, as well as shows low correlation and an acceptable key space. The genera

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Salih, Adnan Ibrahem, Ashwaq Mahmood Alabaichi, and Ammar Yaseen Tuama. "Enhancing advance encryption standard security based on dual dynamic XOR table and MixColumns transformation." Indonesian Journal of Electrical Engineering and Computer Science 19, no. 3 (2020): 1574. http://dx.doi.org/10.11591/ijeecs.v19.i3.pp1574-1581.

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An efficient approach to secure information is critically needed at present. Cryptography remains the best approach to achieve security. On this basis, the National Institute of Standards and Technology (NIST) selected Rijndael, which is a symmetric block cipher, as the advanced encryption standard (AES). The MixColumns transformation of this cipher is the most important function within the linear unit and the major source of diffusion. Dynamic MixColumns transformation can be used to enhance the AES security. In this study, a method to enhance the AES security is developed on the basis of two

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Feng, Wei, Quanwen Wang, Hui Liu, et al. "Exploiting Newly Designed Fractional-Order 3D Lorenz Chaotic System and 2D Discrete Polynomial Hyper-Chaotic Map for High-Performance Multi-Image Encryption." Fractal and Fractional 7, no. 12 (2023): 887. http://dx.doi.org/10.3390/fractalfract7120887.

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Chaos-based image encryption has become a prominent area of research in recent years. In comparison to ordinary chaotic systems, fractional-order chaotic systems tend to have a greater number of control parameters and more complex dynamical characteristics. Thus, an increasing number of researchers are introducing fractional-order chaotic systems to enhance the security of chaos-based image encryption. However, their suggested algorithms still suffer from some security, practicality, and efficiency problems. To address these problems, we first constructed a new fractional-order 3D Lorenz chaot

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Hampton, Amanda E., and James D. Meiss. "The three-dimensional generalized Hénon map: Bifurcations and attractors." Chaos: An Interdisciplinary Journal of Nonlinear Science 32, no. 11 (2022): 113127. http://dx.doi.org/10.1063/5.0103436.

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We study dynamics of a generic quadratic diffeomorphism, a 3D generalization of the planar Hénon map. Focusing on the dissipative, orientation preserving case, we give a comprehensive parameter study of codimension-one and two bifurcations. Periodic orbits, born at resonant, Neimark–Sacker bifurcations, give rise to Arnold tongues in parameter space. Aperiodic attractors include invariant circles and chaotic orbits; these are distinguished by rotation number and Lyapunov exponents. Chaotic orbits include Hénon-like and Lorenz-like attractors, which can arise from period-doubling cascades, and

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Xu, Lu, Yun Chen, Yanlin Qin, and Zhichao Yang. "A Mixed Chaotic Image Encryption Method Based on Parallel Rotation Scrambling in Rubik’s Cube Space." Entropy 27, no. 6 (2025): 574. https://doi.org/10.3390/e27060574.

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Most image encryption methods based on Rubik’s cube scrambling adopt the idea of cyclic shift or map the image pixels to the cube surface, not fully considering the cube’s three-dimensional (3D) properties. In response to this defect, we propose a mixed chaotic color image encryption method based on parallel rotation scrambling in 3D Rubik’s cube space. First, a seven-dimensional hyperchaotic system is introduced to generate chaotic pseudo-random integer sequences. Then, a proven lemma is applied to preprocess the red (R), green (G), and blue (B) channels of the plain image to realize the firs

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Li, Shih-Yu, Lap-Mou Tam, Shih-Ping Wu, et al. "The Performance Investigation of Smart Diagnosis for Bearings Using Mixed Chaotic Features with Fractional Order." Sensors 23, no. 8 (2023): 3801. http://dx.doi.org/10.3390/s23083801.

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This article presents a performance investigation of a fault detection approach for bearings using different chaotic features with fractional order, where the five different chaotic features and three combinations are clearly described, and the detection achievement is organized. In the architecture of the method, a fractional order chaotic system is first applied to produce a chaotic map of the original vibration signal in the chaotic domain, where small changes in the signal with different bearing statuses might be present; then, a 3D feature map can be obtained. Second, five different featu

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MAO, YAOBIN, GUANRONG CHEN, and SHIGUO LIAN. "A NOVEL FAST IMAGE ENCRYPTION SCHEME BASED ON 3D CHAOTIC BAKER MAPS." International Journal of Bifurcation and Chaos 14, no. 10 (2004): 3613–24. http://dx.doi.org/10.1142/s021812740401151x.

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Symmetric block encryption schemes, designed on invertible two-dimensional chaotic maps on a torus or a square, prove feasible and secure for real-time image encryption according to the commonly used criteria given in the literature. In this paper, a typical map of this kind, namely, the baker map, is further extended to be three-dimensional and then used to speed up image encryption while retaining its high degree of security. The proposed algorithm is described in detail, along with its security analysis and implementation. Experimental results show that this three-dimensional baker map is 2

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Panwar, K., and R. K. Purwar. "Design and Analysis of a Permutation Strategy using 3D Chaotic Map." International Journal of Computer Sciences and Engineering 7, no. 6 (2019): 295–99. http://dx.doi.org/10.26438/ijcse/v7i6.295299.

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Sathiyamurthi, P., and S. Ramakrishnan. "Speech encryption algorithm using FFT and 3D-Lorenz–logistic chaotic map." Multimedia Tools and Applications 79, no. 25-26 (2020): 17817–35. http://dx.doi.org/10.1007/s11042-020-08729-5.

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Kanso, A., and M. Ghebleh. "A novel image encryption algorithm based on a 3D chaotic map." Communications in Nonlinear Science and Numerical Simulation 17, no. 7 (2012): 2943–59. http://dx.doi.org/10.1016/j.cnsns.2011.11.030.

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Awad, Zeinab, Magdy Zakria, and Rasha Hassan. "A DNA Based Image Data Hiding Using 3D Logistic Chaotic Map." Mansoura Journal for Computer and Information Sciences 15, no. 2 (2019): 35–44. http://dx.doi.org/10.21608/mjcis.2019.321066.

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Lester, Daniel R., Marco Dentz, and Tanguy Le Borgne. "Chaotic mixing in three-dimensional porous media." Journal of Fluid Mechanics 803 (August 17, 2016): 144–74. http://dx.doi.org/10.1017/jfm.2016.486.

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Under steady flow conditions, the topological complexity inherent to all random three-dimensional (3D) porous media imparts complicated flow and transport dynamics. It has been established that this complexity generates persistent chaotic advection via a 3D fluid mechanical analogue of the baker’s map which rapidly accelerates scalar mixing in the presence of molecular diffusion. Hence, pore-scale fluid mixing is governed by the interplay between chaotic advection, molecular diffusion and the broad (power-law) distribution of fluid particle travel times which arise from the non-slip condition

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Ayad, Jenan, Fadhil Sahib Hasan, and Alaa H. Ali. "OFDM Transmission in Rayleigh Fading Channel for S-Box and 3D Chaotic Maps Based Encrypted Image." Iraqi Journal of Industrial Research 11, no. 2 (2024): 62–74. http://dx.doi.org/10.53523/ijoirvol11i2id410.

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Data encryption is an important part of the communication system. The Chaos essential properties, make it a crucial candidate for encryption applications. There is a compromise between complexity and security in previous studies. In this study, high security was achieved with low complexity. This paper proposed a 3D chaotic map and S-Box has been cascaded to get a high efficiency as complex algorithms or multi-iteration schemes. The first stage is ciphering using 3D cat-map, the second stage is S-box based on 3D henon map, while the third stage is another ciphering stage using 3D henon map. In

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H. Sahar, Asaad, Hussein A. Hussein Al-Delfi, and Ali F. Hassoon. "Hybrid Block Chaotic Compressive Sensing and Chaotic Scrambling Algorithms for Color Image Encryption System." Journal of Engineering and Sustainable Development 28, no. 5 (2024): 656–63. http://dx.doi.org/10.31272/jeasd.28.5.11.

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This paper suggests a new image encryption algorithm based on block compressive sensing (BCS) and chaotic scrambling techniques. With compressive sensing (CS), signals can be sampled much lower than the Nyquist-Shannon rate while preserving their information content. BCS can be used as a one-step process by using a 3D logistic chaotic map, the measurement matrix is used as a secret key for encryption. BCS algorithm used an individual image reconstruction algorithm that leverages l_1norm minimization to promote signal sparsity, and a smoothing operator to enhance image quality. An encrypted ima

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Ashwak, ALabaichi, Abid Ali K. Al-Dabbas Maisa'a, and Salih Adnan. "Image steganography using least significant bit and secret map techniques." International Journal of Electrical and Computer Engineering (IJECE) 10, no. 1 (2020): 935–46. https://doi.org/10.11591/ijece.v10i1.pp935-946.

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In steganography, secret data are invisible in cover media, such as text, audio, video and image. Hence, attackers have no knowledge of the original message contained in the media or which algorithm is used to embed or extract such message. Image steganography is a branch of steganography in which secret data are hidden in host images. In this study, image steganography using least significant bit and secret map techniques is performed by applying 3D chaotic maps, namely, 3D Chebyshev and 3D logistic maps, to obtain high security. This technique is based on the concept of performing random ins

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Alqadi, Ziad, and Rushdi Abu Zneit. "Multiple 3D Chaotic Keys to Protect Digital Images." International Journal of Computer Science and Mobile Computing 12, no. 4 (2023): 1–16. http://dx.doi.org/10.47760/ijcsmc.2023.v12i04.001.

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A simple, multipurpose, efficient, sensitive and highly qualities method of image cryptography will be introduced in this research paper. The method will be easily used to encrypt-decrypt any type of image with any size (gray and color images). The proposed method will secure the image by providing a high degree of image protection based on using a complex private key, which contains eight values, each of the has a double data type. The private key will provide the required key space to resist any hacking attack. The private key components will be used to calculate the size of the generated 3D

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Ye, Guodong, Kaixin Jiao, Chen Pan, and Xiaoling Huang. "An Effective Framework for Chaotic Image Encryption Based on 3D Logistic Map." Security and Communication Networks 2018 (October 21, 2018): 1–11. http://dx.doi.org/10.1155/2018/8402578.

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In this paper, an effective framework for chaotic encryption based on a three-dimensional logistic map is presented together with secure hash algorithm-3 (SHA-3) and electrocardiograph (ECG) signal. Following the analysis of the drawbacks, namely, fixed key and low sensitivity, of some current algorithms, this work tries to solve these two problems and includes two contributions: (1) removal of the phenomenon of summation invariance in a plain-image, for which SHA-3 is proposed to calculate the hash value for the plain-image, with the results being employed to influence the initial keys for ch

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