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Image Encryption and Privacy Protection Based on Chaotic Systems—Second Edition
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Image Encryption and Privacy Protection Based on Chaotic Systems—Second Edition

A special issue of Entropy (ISSN 1099-4300). This special issue belongs to the section "Multidisciplinary Applications".

Deadline for manuscript submissions: closed (15 January 2025) | Viewed by 8458

Special Issue Editor

Prof. Dr. Congxu Zhu

E-Mail Website
Guest Editor
School of Computer Science and Engineering, Central South University, Changsha 410083, China
Interests: chaos; chaotic system; image encryption; cryptography; complex system; image process; computer science; software engineering; electronic and communication engineering; complexity analysis; nonlinear dynamics
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

This is the second edition of the Special Issue titled “Image Encryption and Privacy Protection Based on Chaotic Systems".

The first Special Issue of this topic collected high-quality papers, both theoretical and experiment-related ones, written by experts in this area, and it attracted a lot of interest (including numerous downloads). That is why we have decided to proceed with creating a second edition focused on this research field.

Chaos is a universal physical phenomenon in nature and the engineering world, and it is also one of the core research contents of nonlinear science. The application fields of chaotic systems are everywhere, especially in the applications of secure communication, multimedia information encryption, and the privacy protection of sensitive information. Chaotic systems have unique application advantages. They can help to carry out chaotic system modeling and can be used in dynamic complexity analysis methods to verify the chaotic behavior of nonlinear systems. Additionally, using Shannon information theory, the complexity of such systems can be studied to explain and predict their dynamic characteristics. As such, the applications of new complex chaotic systems to design high-performance image encryption algorithms and privacy protection schemes have attracted extensive attention.

Research on chaotic system modeling, complexity analysis, and security application is growing steadily; nevertheless, this field requires further exploration and innovation. New statistical techniques based on Shannon information theory, the complexity of known techniques, and a better understanding of the meaning of entropy in complex systems are needed. It is necessary to combine new computer technology and artificial intelligence methods to explore new methods for the security application of chaotic systems. Papers which focus on solving these problems are welcome to contribute to this Special Issue.

This Special Issue aims to become a forum to introduce new and improved technologies of chaotic system modeling and complexity analysis. In particular, with the help of chaotic system models, combined with new computer technology and artificial intelligence methods, proposing new image encryption algorithms and privacy protection schemes falls within the scope of this Special Issue.

Prof. Dr. Congxu Zhu
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Entropy is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • chaos
  • chaotic system
  • complexity analysis
  • information theory
  • entropy analysis and calculation
  • image encryption algorithms
  • privacy protection schemes
  • complex network and artificial intelligence technology

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Related Special Issue

Published Papers (5 papers)

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Research

24 pages, 14297 KiB  
Article
Image Encryption Method Based on Three-Dimensional Chaotic Systems and V-Shaped Scrambling
by Lei Wang, Wenjun Song, Jiali Di, Xuncai Zhang and Chengye Zou
Entropy 2025, 27(1), 84; https://doi.org/10.3390/e27010084 - 17 Jan 2025
Viewed by 788
Abstract
With the increasing importance of securing images during network transmission, this paper introduces a novel image encryption algorithm that integrates a 3D chaotic system with V-shaped scrambling techniques. The proposed method begins by constructing a unique 3D chaotic system to generate chaotic sequences [...] Read more.
With the increasing importance of securing images during network transmission, this paper introduces a novel image encryption algorithm that integrates a 3D chaotic system with V-shaped scrambling techniques. The proposed method begins by constructing a unique 3D chaotic system to generate chaotic sequences for encryption. These sequences determine a random starting point for V-shaped scrambling, which facilitates the transformation of image pixels into quaternary numbers. Subsequently, four innovative bit-level scrambling strategies are employed to enhance encryption strength. To further improve randomness, DNA encoding is applied to both the image and chaotic sequences, with chaotic sequences directing crossover and DNA operations. Ciphertext feedback is then utilized to propagate changes across the image, ensuring increased complexity and security. Extensive simulation experiments validate the algorithm’s robust encryption performance for grayscale images, yielding uniformly distributed histograms, near-zero correlation values, and an information entropy value of 7.9975, approaching the ideal threshold. The algorithm also features a large key space, providing robust protection against brute force attacks while effectively resisting statistical, differential, noise, and cropping attacks. These results affirm the algorithm’s reliability and security for image communication and transmission. Full article
(This article belongs to the Special Issue Image Encryption and Privacy Protection Based on Chaotic Systems—Second Edition)
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20 pages, 2860 KiB  
Article
A Secure Image Encryption Scheme Based on a New Hyperchaotic System and 2D Compressed Sensing
by Muou Liu, Chongyang Ning and Congxu Zhu
Entropy 2024, 26(7), 603; https://doi.org/10.3390/e26070603 - 16 Jul 2024
Cited by 2 | Viewed by 1839
Abstract
In insecure communication environments where the communication bandwidth is limited, important image data must be compressed and encrypted for transmission. However, existing image compression and encryption algorithms suffer from poor image reconstruction quality and insufficient image encryption security. To address these problems, this [...] Read more.
In insecure communication environments where the communication bandwidth is limited, important image data must be compressed and encrypted for transmission. However, existing image compression and encryption algorithms suffer from poor image reconstruction quality and insufficient image encryption security. To address these problems, this paper proposes an image-compression and encryption scheme based on a newly designed hyperchaotic system and two-dimensional compressed sensing (2DCS) technique. In this paper, the chaotic performance of this hyperchaotic system is verified by bifurcation diagrams, Lyapunov diagrams, approximate entropy, and permutation entropy, which have certain advantages over the traditional 2D chaotic system. The new 2D chaotic system as a pseudo-random number generator can completely pass all the test items of NIST. Meanwhile, this paper improves on the existing 2D projected gradient (2DPG) algorithm, which improves the quality of image compression and reconstruction, and can effectively reduce the transmission pressure of image data confidential communication. In addition, a new image encryption algorithm is designed for the new 2D chaotic system, and the security of the algorithm is verified by experiments such as key space size analysis and encrypted image information entropy. Full article
(This article belongs to the Special Issue Image Encryption and Privacy Protection Based on Chaotic Systems—Second Edition)
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31 pages, 28677 KiB  
Article
Color Image Encryption Based on an Evolutionary Codebook and Chaotic Systems
by Yuan Cao and Yinglei Song
Entropy 2024, 26(7), 597; https://doi.org/10.3390/e26070597 - 12 Jul 2024
Viewed by 1131
Abstract
Encryption of images is an important method that can effectively improve the security and privacy of crucial image data. Existing methods generally encrypt an image with a combination of scrambling and encoding operations. Currently, many applications require highly secure results for image encryption. [...] Read more.
Encryption of images is an important method that can effectively improve the security and privacy of crucial image data. Existing methods generally encrypt an image with a combination of scrambling and encoding operations. Currently, many applications require highly secure results for image encryption. New methods that can achieve improved randomness for both the scrambling and encoding processes in encryption are thus needed to further enhance the security of a cipher image. This paper proposes a new method that can securely encrypt color images. As the first step of the proposed method, a complete bit-level operation is utilized to scramble the binary bits in a color image to a full extent. For the second step, the bits in the scrambled image are processed with a sweeping operation to improve the encryption security. In the final step of encryption, a codebook that varies with evolutionary operations based on several chaotic systems is utilized to encrypt the partially encrypted image obtained in the second step. Experimental results on benchmark color images suggest that this new approach can securely encrypt color images and generate cipher images that remain secure under different types of attacks. The proposed approach is compared with several other state-of-the-art encryption approaches and the results show that it can achieve improved encryption security for cipher images. Experimental results thus suggest that this new approach can possibly be utilized practically in applications where color images need to be encrypted for content protection. Full article
(This article belongs to the Special Issue Image Encryption and Privacy Protection Based on Chaotic Systems—Second Edition)
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23 pages, 36196 KiB  
Article
An n-Dimensional Chaotic Map with Application in Reversible Data Hiding for Medical Images
by Yuli Yang, Ruiyun Chang, Xiufang Feng, Peizhen Li, Yongle Chen and Hao Zhang
Entropy 2024, 26(3), 254; https://doi.org/10.3390/e26030254 - 13 Mar 2024
Cited by 3 | Viewed by 1788
Abstract
The drawbacks of a one-dimensional chaotic map are its straightforward structure, abrupt intervals, and ease of signal prediction. Richer performance and a more complicated structure are required for multidimensional chaotic mapping. To address the shortcomings of current chaotic systems, an n-dimensional cosine-transform-based [...] Read more.
The drawbacks of a one-dimensional chaotic map are its straightforward structure, abrupt intervals, and ease of signal prediction. Richer performance and a more complicated structure are required for multidimensional chaotic mapping. To address the shortcomings of current chaotic systems, an n-dimensional cosine-transform-based chaotic system (nD-CTBCS) with a chaotic coupling model is suggested in this study. To create chaotic maps of any desired dimension, nD-CTBCS can take advantage of already-existing 1D chaotic maps as seed chaotic maps. Three two-dimensional chaotic maps are provided as examples to illustrate the impact. The findings of the evaluation and experiments demonstrate that the newly created chaotic maps function better, have broader chaotic intervals, and display hyperchaotic behavior. To further demonstrate the practicability of nD-CTBCS, a reversible data hiding scheme is proposed for the secure communication of medical images. The experimental results show that the proposed method has higher security than the existing methods. Full article
(This article belongs to the Special Issue Image Encryption and Privacy Protection Based on Chaotic Systems—Second Edition)
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24 pages, 7314 KiB  
Article
A Hybrid Cryptosystem Incorporating a New Algorithm for Improved Entropy
by Víctor Manuel Silva-García, Rolando Flores-Carapia and Manuel Alejandro Cardona-López
Entropy 2024, 26(2), 154; https://doi.org/10.3390/e26020154 - 10 Feb 2024
Viewed by 1979
Abstract
Today, safeguarding sensitive content through encryption is crucial. This work presents a hybrid cryptosystem for images that employs both asymmetric and symmetric encryption. The asymmetric component involves applying the Diffie–Hellman protocol and the ElGamal cryptosystem to securely transmit two constants. These constants are [...] Read more.
Today, safeguarding sensitive content through encryption is crucial. This work presents a hybrid cryptosystem for images that employs both asymmetric and symmetric encryption. The asymmetric component involves applying the Diffie–Hellman protocol and the ElGamal cryptosystem to securely transmit two constants. These constants are necessary for the symmetrical aspect to generate dynamic permutations, substitution boxes, and round keys. Following an encryption process with fourteen rounds, the encrypted images are processed by an algorithm proposed to enhance entropy, a critical metric for assessing encryption quality. It increases the frequencies of the basic colors to achieve a histogram closely resembling a uniform distribution, but it increases the image size by approximately 8%. This improves the entropy values achieved by the hybrid cryptosystem, bringing them remarkably close to the ideal value of 8.0. In specific instances, the entropy values were elevated from 7.99926 to 8.0. The proposed method exhibits resilience against various attacks, including differential, linear, brute force, and algebraic attacks, as evaluated through the entropy, correlation, goodness of fit, Discrete Fourier Transform (DFT), Number of Pixels Change Rate (NPCR), Unified Average Changing Intensity (UACI), Avalanche Criteria (AC), contrast, energy, and homogeneity. Further, encrypted images are subjected to noise attacks ranging from 20% to 50% noise, including additive, multiplicative, occlusion noise, as well as the newly introduced χ2 noise. The noise damage is quantified using the proposed Similarity Parameter (SP), and a 3 × 3 median filter is employed to enhance the visual quality. Full article
(This article belongs to the Special Issue Image Encryption and Privacy Protection Based on Chaotic Systems—Second Edition)
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