Mathematics

Research

26 pages, 9163 KiB

Open AccessArticle

A Novel Multi-Channel Image Encryption Algorithm Leveraging Pixel Reorganization and Hyperchaotic Maps

by Wei Feng, Jiaxin Yang, Xiangyu Zhao, Zhentao Qin, Jing Zhang, Zhengguo Zhu, Heping Wen and Kun Qian

Mathematics 2024, 12(24), 3917; https://doi.org/10.3390/math12243917 - 12 Dec 2024

Cited by 29 | Viewed by 1497

Abstract

Chaos-based encryption is promising for safeguarding digital images. Nonetheless, existing chaos-based encryption algorithms still exhibit certain shortcomings. Given this, we propose a novel multi-channel image encryption algorithm that leverages pixel reorganization and hyperchaotic maps (MIEA-PRHM). Our MIEA-PRHM algorithm employs two hyperchaotic maps to [...] Read more.

Chaos-based encryption is promising for safeguarding digital images. Nonetheless, existing chaos-based encryption algorithms still exhibit certain shortcomings. Given this, we propose a novel multi-channel image encryption algorithm that leverages pixel reorganization and hyperchaotic maps (MIEA-PRHM). Our MIEA-PRHM algorithm employs two hyperchaotic maps to jointly generate chaotic sequences, ensuring a larger key space and better randomness. During the encryption process, we first convert input images into two fused matrices through pixel reorganization. Then, we apply two rounds of scrambling and diffusion operations, coupled with one round of substitution operations, to the high 4-bit matrix. For the low 4-bit matrix, we conduct one round of substitution and diffusion operations. Extensive experiments and comparisons demonstrate that MIEA-PRHM outperforms many recent encryption algorithms in various aspects, especially in encryption efficiency. Full article

(This article belongs to the Special Issue Chaos-Based Secure Communication and Cryptography, 2nd Edition)

► Show Figures

Figure 1

27 pages, 5786 KiB

Open AccessArticle

Drone-Captured Wildlife Data Encryption: A Hybrid 1D–2D Memory Cellular Automata Scheme with Chaotic Mapping and SHA-256

by Akram Belazi and Héctor Migallón

Mathematics 2024, 12(22), 3602; https://doi.org/10.3390/math12223602 - 18 Nov 2024

Viewed by 954

Abstract

In contemporary wildlife conservation, drones have become essential for the non-invasive monitoring of animal populations and habitats. However, the sensitive data captured by drones, including images and videos, require robust encryption to prevent unauthorized access and exploitation. This paper presents a novel encryption [...] Read more.

In contemporary wildlife conservation, drones have become essential for the non-invasive monitoring of animal populations and habitats. However, the sensitive data captured by drones, including images and videos, require robust encryption to prevent unauthorized access and exploitation. This paper presents a novel encryption algorithm designed specifically for safeguarding wildlife data. The proposed approach integrates one-dimensional and two-dimensional memory cellular automata (1D MCA and 2D MCA) with a bitwise XOR operation as an intermediate confusion layer. The 2D MCA, guided by chaotic rules from the sine-exponential (SE) map, utilizes varying neighbor configurations to enhance both diffusion and confusion, making the encryption more resilient to attacks. A final layer of 1D MCA, controlled by pseudo-random number generators, ensures comprehensive diffusion and confusion across the image. The SHA-256 hash of the input image is used to derive encryption parameters, providing resistance against plaintext attacks. Extensive performance evaluations demonstrate the effectiveness of the proposed scheme, which balances security and complexity while outperforming existing algorithms. Full article

(This article belongs to the Special Issue Chaos-Based Secure Communication and Cryptography, 2nd Edition)

► Show Figures

Figure 1

18 pages, 2730 KiB

Open AccessArticle

Fast Color Image Encryption Algorithm Based on DNA Coding and Multi-Chaotic Systems

by Shaofang Wang, Jingguo Pan, Yanrong Cui, Zhongju Chen and Wei Zhan

Mathematics 2024, 12(20), 3297; https://doi.org/10.3390/math12203297 - 21 Oct 2024

Cited by 4 | Viewed by 1250

Abstract

At present, there is a growing emphasis on safeguarding image data, yet conventional encryption methods are full of numerous limitations. In order to tackle the limitations of conventional color image encryption methodologies, such as inefficiency and insufficient security, this paper designs an expedited [...] Read more.

At present, there is a growing emphasis on safeguarding image data, yet conventional encryption methods are full of numerous limitations. In order to tackle the limitations of conventional color image encryption methodologies, such as inefficiency and insufficient security, this paper designs an expedited encryption method for color images that uses DNA coding in conjunction with multiple chaotic systems. The encryption algorithm proposed in this paper is based on three-dimensional permutation, global scrambling, one-dimensional diffusion and DNA coding. First of all, the encryption algorithm uses three-dimensional permutation algorithms to scramble the image, which disrupts the high correlation among the image pixels. Second, the RSA algorithm and the SHA-256 hashing algorithm are utilized to derive the starting value necessary for the chaotic system to produce the key. Third, the image is encrypted by using global scrambling and one-dimensional diffusion. Finally, DNA coding rules are used to perform DNA computing. The experimental results indicate that the encryption scheme exhibits a relatively weak inter-pixel correlation, uniform histogram distribution, and an information entropy value approaching eight. This shows that the proposed algorithm is able to protect the image safely and efficiently. Full article

(This article belongs to the Special Issue Chaos-Based Secure Communication and Cryptography, 2nd Edition)

► Show Figures

Figure 1

17 pages, 9539 KiB

Open AccessArticle

A Chaos-Based Encryption Algorithm to Protect the Security of Digital Artwork Images

by Li Shi, Xiangjun Li, Bingxue Jin and Yingjie Li

Mathematics 2024, 12(20), 3162; https://doi.org/10.3390/math12203162 - 10 Oct 2024

Cited by 3 | Viewed by 897

Abstract

Due to the security weaknesses of chaos-based pseudorandom number generators, in this paper, a new pseudorandom number generator (PRNG) based on mixing three-dimensional variables of a cat chaotic map is proposed. A uniformly distributed chaotic sequence by a logistic map is used in [...] Read more.

Due to the security weaknesses of chaos-based pseudorandom number generators, in this paper, a new pseudorandom number generator (PRNG) based on mixing three-dimensional variables of a cat chaotic map is proposed. A uniformly distributed chaotic sequence by a logistic map is used in the mixing step. Both statistical tests and a security analysis indicate that our PRNG has good randomness and is more complex than any one-dimensional variable of a cat map. Furthermore, a new image encryption algorithm based on the chaotic PRNG is provided to protect the content of artwork images. The core of the algorithm is to use the sequence generated by the pseudorandom number generator to achieve the process of disruption and diffusion of the image pixels, so as to achieve the effect of obfuscation and encryption of the image content. Several security tests demonstrate that this image encryption algorithm has a high security level. Full article

(This article belongs to the Special Issue Chaos-Based Secure Communication and Cryptography, 2nd Edition)

► Show Figures

Figure 1

23 pages, 5476 KiB

Open AccessArticle

Modeling a Single-Channel Synergetic Observer for Chaos-Based Secure Communication System Applications

by Alexey Mushenko, Ekaterina Pakulova, Elena Basan, Alexey Nekrasov, Mária Gamcová and Pavol Kurdel

Mathematics 2024, 12(17), 2764; https://doi.org/10.3390/math12172764 - 6 Sep 2024

Viewed by 881

Abstract

This paper explores secure communication systems with a chaotic carrier. The use of chaotic oscillations instead of regular van der Pol oscillators as a signal carrier is a promising and active research area, providing not only communication systems with new protection principles and [...] Read more.

This paper explores secure communication systems with a chaotic carrier. The use of chaotic oscillations instead of regular van der Pol oscillators as a signal carrier is a promising and active research area, providing not only communication systems with new protection principles and organization but also high steganographic efficiency when transmitting short messages. The problem is to select methods and techniques for mixing a useful signal into a chaotic one and its recovery on the receiver side, featuring a set of properties acceptable for implementation and real-world application. We demonstrate application of synergetic control theory (SCT), which provides advanced observer-basing methods for nonlinear dynamic systems as well as explore example of data transmission system consisting of a Genesio–Tesi chaotic oscillator, data signal transmission with a method of nonlinear modulation, and recovering with a single-channel synergetic observer at the receiver side. The paper presents a nonlinear state observer modeling procedure followed by building a MATLAB/Simulink simulation model of the data transmission system for the PC-platform along with software implementation for the Raspberry Pi platform, with simulation and experimental run results showing data transmission rates seem to be acceptable for the considered practical applications. Practical applications and limitations issues are discussed. Future research will be universal modeling procedures for different classes of chaotic generators and whole system experimental hardware implementation. The obtained results can be primarily used in short messages and/or encryption keys secure transmission systems, cyber-physical system component command communications, as well as chaotic carrier system R&D competitive studies and other applications. Full article

(This article belongs to the Special Issue Chaos-Based Secure Communication and Cryptography, 2nd Edition)

► Show Figures

Figure 1

25 pages, 8543 KiB

Open AccessArticle

Block Cipher Nonlinear Component Generation via Hybrid Pseudo-Random Binary Sequence for Image Encryption

by Dania Saleem Malik, Tariq Shah, Sara Tehsin, Inzamam Mashood Nasir, Norma Latif Fitriyani and Muhammad Syafrudin

Mathematics 2024, 12(15), 2302; https://doi.org/10.3390/math12152302 - 23 Jul 2024

Cited by 8 | Viewed by 1052

Abstract

To analyze the security of encryption, an effectual encryption scheme based on colored images utilizing the hybrid pseudo-random binary sequence (HPRBS) and substitution boxes, known as S-boxes, is proposed. The presented work aims to design S-boxes using pseudo-random binary numbers acquired by Linear [...] Read more.

To analyze the security of encryption, an effectual encryption scheme based on colored images utilizing the hybrid pseudo-random binary sequence (HPRBS) and substitution boxes, known as S-boxes, is proposed. The presented work aims to design S-boxes using pseudo-random binary numbers acquired by Linear Feedback Shift Registers (LFSRs) in combination with a modified quadratic chaotic map. Firstly, cryptographically robust S-boxes are constructed by using binary pseudo-random number sequences, and then the cryptographic properties of the presented S-boxes are tested. The suggested S-boxes showed good results. Secondly, an RGB image encryption algorithm utilizing sequences generated by modified quadratic chaotic maps and S-boxes is offered. The new color image encryption techniques comprise two steps, including a permutation and a substitution step. The key association with the content of the image is also addressed. This strategy can result in a “one-time pad” effect and make the algorithm resistant to chosen-plaintext attack (CPA). The proposed scheme has been confirmed to be more valuable than most of the existing schemes. S-boxes are analyzed by the nonlinearity test, bit independence criterion (BIC), linear and differential approximation probabilities (LPs; DPs), and Strict-Avalanche Criterion (SAC) tests. A comparison with different S-boxes presented in the literature is also carried out. The comparison shows encouraging results about the quality of the proposed box. From security and experimental outcomes, the effectiveness of the presented color image encryption technique is verified. The proposed scheme has evident efficiency benefits, which implies that the proposed colored encryption of the image scheme has better potential for application in encryption schemes in real-time. Full article

(This article belongs to the Special Issue Chaos-Based Secure Communication and Cryptography, 2nd Edition)

► Show Figures

Figure 1

8 pages, 1811 KiB

Open AccessArticle

Physical Layer Encryption for CO-OFDM Systems Enabled by Camera Projection Scrambler

by Yujin Li, Dongfei Wang, Haiyang Ding, Zhenzhen Li and Xiangqing Wang

Mathematics 2024, 12(12), 1807; https://doi.org/10.3390/math12121807 - 11 Jun 2024

Viewed by 1169

Abstract

In this paper, we propose a camera projection approach to enhance the physical layer security of coherent optical orthogonal frequency division multiplexing (CO-OFDM) systems. The data are converted to the new location by the camera projection module in the encryption system, where the [...] Read more.

In this paper, we propose a camera projection approach to enhance the physical layer security of coherent optical orthogonal frequency division multiplexing (CO-OFDM) systems. The data are converted to the new location by the camera projection module in the encryption system, where the 5D hyperchaotic system provides the keys for the camera projection module. The simulated 16QAM CO-OFDM security system over 80 km SSMF is shown to provide a key space of about 9 × 10⁹⁰ through the five-dimensional (5D) hyperchaotic system, making it impossible for eavesdroppers to obtain valid information, and the peak-to-average power ratio (PAPR) is reduced by about 0.8 dB. Full article

(This article belongs to the Special Issue Chaos-Based Secure Communication and Cryptography, 2nd Edition)

► Show Figures

Figure 1

15 pages, 269 KiB

Open AccessFeature PaperEditor’s ChoiceArticle

Secure Key Exchange in Tropical Cryptography: Leveraging Efficiency with Advanced Block Matrix Protocols

by Mariana Durcheva and Kiril Danilchenko

Mathematics 2024, 12(10), 1429; https://doi.org/10.3390/math12101429 - 7 May 2024

Cited by 1 | Viewed by 1409

Abstract

In the quest for robust and efficient digital communication, this paper introduces cutting-edge key exchange protocols leveraging the computational prowess of tropical semirings and the structural resilience of block matrices. Moving away from the conventional use of finite fields, these protocols deliver markedly [...] Read more.

In the quest for robust and efficient digital communication, this paper introduces cutting-edge key exchange protocols leveraging the computational prowess of tropical semirings and the structural resilience of block matrices. Moving away from the conventional use of finite fields, these protocols deliver markedly faster processing speeds and heightened security. We present two implementations of our concept, each utilizing a different platform for the set of commuting matrices: one employing tropical polynomials of matrices and the other employing Linde–de la Puente matrices. The inherent simplicity of tropical semirings leads to a decrease in operational complexity, while using block matrices enhances our protocols’ security profile. The security of these protocols relies on the Matrix Decomposition Problem. In addition, we provide a comparative analysis of our protocols against existing matrix block-based protocols in finite fields. This research marks a significant shift in cryptographic protocol design, is specifically tailored for demanding engineering applications, and sets a new standard in secure and efficient digital communication. Full article

(This article belongs to the Special Issue Chaos-Based Secure Communication and Cryptography, 2nd Edition)

► Show Figures

Figure 1

21 pages, 23005 KiB

Open AccessArticle

Coherent Chaotic Communication Using Generalized Runge–Kutta Method

by Ivan Babkin, Vyacheslav Rybin, Valery Andreev, Timur Karimov and Denis Butusov

Mathematics 2024, 12(7), 994; https://doi.org/10.3390/math12070994 - 27 Mar 2024

Cited by 2 | Viewed by 1335

Abstract

Computer simulation of continuous chaotic systems is usually performed using numerical methods. The discretization may introduce new properties into finite-difference models compared to their continuous prototypes and can therefore lead to new types of dynamical behavior exhibited by discrete chaotic systems. It is [...] Read more.

Computer simulation of continuous chaotic systems is usually performed using numerical methods. The discretization may introduce new properties into finite-difference models compared to their continuous prototypes and can therefore lead to new types of dynamical behavior exhibited by discrete chaotic systems. It is known that one can control the dynamics of a discrete system using a special class of integration methods. One of the applications of such a phenomenon is chaos-based communication systems, which have recently attracted attention due to their high covertness and broadband transmission capability. Proper modulation of chaotic carrier signals is one of the key problems in chaos-based communication system design. It is challenging to modulate and demodulate a chaotic signal in the same way as a conventional signal due to its noise-like shape and broadband characteristics. Therefore, the development of new modulation–demodulation techniques is of great interest in the field. One possible approach here is to use adaptive numerical integration, which allows control of the properties of the finite-difference chaotic model. In this study, we describe a novel modulation technique for chaos-based communication systems based on generalized explicit second-order Runge–Kutta methods. We use a specially designed test bench to evaluate the efficiency of the proposed modulation method and compare it with state-of-the-art solutions. Experimental results show that the proposed modulation technique outperforms the conventional parametric modulation method in both coverage and noise immunity. The obtained results can be efficiently applied to the design of advanced chaos-based communication systems as well as being used to improve existing architectures. Full article

(This article belongs to the Special Issue Chaos-Based Secure Communication and Cryptography, 2nd Edition)

► Show Figures

Figure 1

Journal Menu

Journal Browser

Chaos-Based Secure Communication and Cryptography, 2nd Edition

Share This Special Issue

Special Issue Editor

Special Issue Information

Keywords

Benefits of Publishing in a Special Issue

Related Special Issue

Published Papers (9 papers)

Research

Further Information

Guidelines

MDPI Initiatives

Follow MDPI