2D Logistic Map Research Articles

A Multilayer Nonlinear Permutation Framework and Its Demonstration in Lightweight Image Encryption

As information systems become more widespread, data security becomes increasingly important. While traditional encryption methods provide effective protection against unauthorized access, they often struggle with multimedia data like images and videos. This necessitates specialized image encryption approaches. With the rise of mobile and Internet of Things (IoT) devices, lightweight image encryption algorithms are crucial for resource-constrained environments. These algorithms have applications in various domains, including medical imaging and surveillance systems. However, the biggest challenge of lightweight algorithms is balancing strong security with limited hardware resources. This work introduces a novel nonlinear matrix permutation approach applicable to both confusion and diffusion phases in lightweight image encryption. The proposed method utilizes three different chaotic maps in harmony, namely a 2D Zaslavsky map, 1D Chebyshev map, and 1D logistic map, to generate number sequences for permutation and diffusion. Evaluation using various metrics confirms the method’s efficiency and its potential as a robust encryption framework. The proposed scheme was tested with 14 color images in the SIPI dataset. This approach achieves high performance by processing each image in just one iteration. The developed scheme offers a significant advantage over its alternatives, with an average NPCR of 99.6122, UACI of 33.4690, and information entropy of 7.9993 for 14 test images, with an average correlation value as low as 0.0006 and a vast key space of 2800. The evaluation results demonstrated that the proposed approach is a viable and effective alternative for lightweight image encryption.

Unprecedented Security Analysis Results for a Novel Key Expansion Algorithm Based on Protein Sequences, Dynamic Mealy Machine, and 3D Logistic Map

Unprecedented Security Analysis Results for a Novel Key Expansion Algorithm Based on Protein Sequences, Dynamic Mealy Machine, and 3D Logistic Map

Design A Novel Image Encryption Algorithm Based on A PRNG with High Performance

This paper proposes a novel two-dimensional logistic map (2D-LM). Relative to the classical 2D logistic modulation map (2D-LMM), it has larger chaotic range and better chaos performance. In comparison with some 2D chaos maps, the proposed new 2D-LM also has unique advantages in the complexity of sequence. To further study its application, the novel image encryption algorithm is designed based on the proposed 2D-LM. The security tests show the higher anti-decryption ability of the design algorithm. Finally, we develop a FPGA test platform to realize the Pseudo-Random Number Generator (PRNG) based on the proposed 2D-LM. The experiment results show the feasibility of its industrial applications.

Image encryption algorithm based on 2D logistic map system in IoHT using 5G network

Image encryption algorithm based on 2D logistic map system in IoHT using 5G network

Correction to: Color image encryption based on novel kolam scrambling and modified 2D logistic cascade map (2D LCM)

Correction to: Color image encryption based on novel kolam scrambling and modified 2D logistic cascade map (2D LCM)

An Image Encryption Scheme Combining 2D Cascaded Logistic Map and Permutation-Substitution Operations

Confusion, diffusion, and encryption keys affect the quality of image encryption. This research proposes combining bit- and pixel-level permutation and substitution methods based on three advanced chaotic logistic map methods. The three chaotic methods are the 2D Logistic-adjusted-Sine map (2D-LASM), the 2D Logistic-sine-coupling map (2D-LSCM), and the 2D Logistic ICMIC cascade map (2D-LICM). The encryption method’s design consists of six stages of encryption, involving permutation operations based on chaotic order, substitution based on modulus and bitXOR, and hash functions. Hash functions are employed to enhance key space and key sensitivity quality. Several testing tools are utilized to assess encryption performance, including histogram and chi-square analysis, information entropy, correlation of adjacent pixels, differential analysis, key sensitivity and key space analysis, data loss and noise attacks, NIST randomness tests, and TestU01. Compared to using a single 2D logistic map, the amalgamation of bit-level and pixel-level encryption and the utilization of three 2D cascade logistic maps has improved encryption security performance. This method successfully passes the NIST, TestU01, and chi-square tests. Furthermore, it outperforms the previous method regarding correlation, information entropy, NPCR, and UACI tests.

A Security Algorithm for Images Based on 2D Logistic Map Using Bit-level and Pixel-level Image Encryption Approaches

A Security Algorithm for Images Based on 2D Logistic Map Using Bit-level and Pixel-level Image Encryption Approaches

Color image encryption based on novel kolam scrambling and modified 2D logistic cascade map (2D LCM)

Color image encryption based on novel kolam scrambling and modified 2D logistic cascade map (2D LCM)

Image encryption based on 2DNA encoding and chaotic 2D logistic map

DNA has recently been investigated as a possible medium concerning ultra-compact information storage and ultra-scale computation. The development of secure image encryption systems has recently received a certain effective and new direction from chaos-based cryptographic algorithms. This paper proposes a novel image encryption algorithm, 2DNALM, based on double-dynamic DNA sequence encryption and a chaotic 2D logistic map. The three phases regarding the suggested approach are as follows: the first phase involves permuting the positions of the pixels using a position key-based scrambling operation. The second phase involves double DNA encoding on scrambled images using various rules by DNA cryptography concept to produce an encoded image, and in the final step, an image which has been encoded is encrypted using XOR operation and chaotic keys created through a chaotic 2D logistic map. The entropy analysis and experimental findings show that the suggested scheme exhibits great encryption and withstands several common attacks.

A 3D discrete memristor hyperchaotic map with application in dual-channel random signal generator

Chaotic systems are widely used in many applications for their pseudo-random sequences of fixed mathematical models. Several academics and engineers prefer using discrete maps for their simplicity in mathematical models and quick implementation. Nevertheless, the easily disrupted chaotic behavior of most discrete maps, such as the Logistic Map, is a significant barrier to their generalization. This paper proposes a 3D parallel memristive logistic map (3D-PMLM) to address this issue. The 3D-PMLM can enhance the complexity of a 1D Logistic map by introducing multidimensional controllable parameters. Performance evaluations demonstrate that the 3D-PMLM has more robust hyperchaotic behavior across a broader range of chaos than existing discrete maps. An experimental platform, based on FPGA and DAC, is put forth to implement the chaotic behavior of 3D-PMLM in hardware. Moreover, the application of 3D-PMLM is further demonstrated through the design and implementation of a dual-channel random signal generator featuring an update period of 1us. The experimental results indicate that the output analog signal is random in three dimensions.

Region based medical image encryption using advanced zigzag transform and 2D logistic sine map (2DLSM)

A large number of medical images are generated for diagnostic purposes, disease monitoring, research and education, quality control in health services, and so on. The secure transmission and storage of them demand a significant effort. Most of the available encryption schemes are designed for non-medical images, whereas medical images need a higher level of security and robust authentication. Additionally, in certain cases, only a specific part of the image, which may be separated into the region of interest and the region of background, medical images can be divided into these two regions. A region-based medical image encryption using a 2D logistic sine map (2DLSM) and an advanced zig zag transform is used to secure medical images. First, the Region of Interest (ROI) is extracted from the original medical image using basic morphological techniques, including edge detection, dilation, and erosion. Secondly, the ROI is encrypted using a complex zigzag transform and a 2D logistic sine map (2DLSM). Advanced zigzag transform that crosses in both directions while beginning at random points to jumble the image. This new zigzag transform method is more complex than existing zigzag transform techniques because the number of sequence types is equal to the number of pixels in the plaintext image. The confused image is diffused using a random sequence created using the 2D logistic sine map approach after numerous iterations of an advanced zigzag transformation. In order to save time and computational resources, the background region pixels are eliminated during encryption. Experiments and security analyses show that the suggested approach is strong in defending against diverse assaults and can effectively secure ROI of different types and sizes of medical photos.

3D Content Encryption Using Multi-Level Chaotic Maps

Nowadays, 3D content is becoming an essential part of multimedia applications, when the 3D content is not protected, hackers may attack and steal it. This paper introduces a proposed scheme that provides high protection for 3D content by implementing multiple levels of security with preserving the original size using weight factor (w). First level of security is implemented by encrypting the texture map based on a 2D Logistic chaotic map. Second level is implemented by shuffling vertices (confusion) based on a 1D Tent chaotic map. Third level is implemented by modifying the vertices values (diffusion) based on a 3D Lorenz chaotic map. Results illustrate that the proposed scheme is completely deform the entire 3D content according to Hausdorff Distance (HD) approximately around 100 after the encryption process. It provides a high security against brute force attack because it has large key space equal to 10165 and secret key sensitivity using NPCR near 99:6% and UACI near 33:4%. The histogram and HD indicate the decrypted 3D content is identical to the origin where HD values approximate zero.

An efficient image cipher based on the 1D scrambled image and 2D logistic chaotic map

An efficient image cipher based on the 1D scrambled image and 2D logistic chaotic map

Analysis of logistic map based neurons in neurochaos learning architectures for data classification

Artificial neurons used in Artificial Neural Networks and Deep Learning architectures do not mimic the chaotic behavior of biological neurons found in the brain. Recently, a chaos based learning algorithm namely Neurochaos Learning (NL) for classification has been proposed that gives comparable performance with state-of-the-art Machine Learning methods and sometimes exceeding them, especially in the low training sample regime. NL uses 1D chaotic maps namely Generalized Lüroth Series (GLS) as neurons and the success of NL owes to the rich properties of these chaotic GLS maps. In this study, we propose for the first time, two extensions to NL: (a) 1D Logistic map neurons instead of GLS neurons, and (b) Heterogeneous Neurochaos Learning (HNL) architecture which incorporates both GLS and Logistic map neurons which is inspired by the presence of heterogeneous types of neurons in the human brain and central nervous system. We evaluate the performance of these proposed schemes on classification tasks on well known publicly available datasets such as Iris, Ionosphere, Wine, Bank Note Authentication, Haberman’s Survival, Breast Cancer Wisconsin, Statlog (Heart) and Seeds. We extract chaos-based features (ChaosFEX) from these NL architectures and feed them to SVM to further boost classification performance. Results indicate the superior performance of these proposed architecture over homogeneous NL (GLS neurons) architecture in most cases. We also investigate the relationship between the degree of chaos as measured by the Lyapunov exponent and the classification accuracies obtained by NL using logistic map (with different ‘r’ values) and heterogeneous neurons.

Secured Drone Communication Based on Esalsa20 Algorithm

The Unmanned Aerial Vehicle (UAV) (sometimes known as a ""drone"") is used in a variety of fields. Unfortunately, as they become more popular and in demand, they become more vulnerable to a variety of security threats. To combat such attacks and security threats, a proper design of a robust security and authentication system based on and stream cipher lightweight salsa20 algorithm with chaotic maps is required. By using a proposed key generation method which is based on a 1d Logistic chaotic map to produce a flight session key for a drone with a flight plan, and then records the flight session key and the drone’s flight plan in a central database that can be accessed. Finally, while the drone is flying, a GCS checks authentication of the current flight session based on the on flight session key and its flight plan as the message authentication code key to authenticate the drone by any flight session, and the drone after which uses salsa20 lightweight to cipher payload data to improve security Network Transfer of RTCM Messages over Internet Protocol Protocol (NTRIP) communication protocol and send it to GCS, and at last, a GCS verifies authentication of the current flight session based on the on flight session key and its flight plan as the message authentication code key to authenticate the drone. The proposed system is superior to other similar systems in terms of security and performance, according to the review.

Secured drone communication based on Esalsa20 algorithm and 1d logistic map

<span lang="EN-US">Over recent years, drones are increasingly being used not only for military tasks only, but also for civilian tasks too, such as environment and traffic monitoring, delivery services, and aerial surveys. Unfortunately, as they become more popular and in demand, they become more vulnerable to a variety of security threats. To combat such attacks and security threats, a proper design of a robust security and authentication system based on and stream cipher lightweight salsa20 algorithm with chaotic maps to cipher payload data to improve security network transfer of radio technical commission for maritime services (RTCM) messages over (NTRIP) communication protocol. By using a proposed key generation method which is based on a 1d logistic map to produce a flight session key for a drone with a flight plan, and then records the flight session key and the drone's flight plan in a central database that can be accessed. The proposed system is superior to other similar systems in terms of security and performance, according to the review.</span>

3DL-PS: an image encryption technique using 3D logistic map, hashing functions and pixel scrambling techniques

3DL-PS: an image encryption technique using 3D logistic map, hashing functions and pixel scrambling techniques

A new fractional fuzzy dispersion entropy and its application in muscle fatigue detection.

Recently, fuzzy dispersion entropy (DispEn) has attracted much attention as a new nonlinear dynamics method that combines the advantages of both DispEn and fuzzy entropy. However, it suffers from limitation of insensitivity to dynamic changes. To solve this limitation, we proposed fractional fuzzy dispersion entropy (FFDispEn) based on DispEn, a novel fuzzy membership function and fractional calculus. The fuzzy membership function was defined based on the Euclidean distance between the embedding vector and dispersion pattern. Simulated signals generated by the one-dimensional (1D) logistic map were used to test the sensitivity of the proposed method to dynamic changes. Moreover, 29 subjects were recruited for an upper limb muscle fatigue experiment, during which surface electromyography (sEMG) signals of the biceps brachii muscle were recorded. Both simulated signals and sEMG signals were processed using a sliding window approach. Sample entropy (SampEn), DispEn and FFDispEn were separately used to calculate the complexity of each frame. The sensitivity of different algorithms to the muscle fatigue process was analyzed using fitting parameters through linear fitting of the complexity of each frame signal. The results showed that for simulated signals, the larger the fractional order q, the higher the sensitivity to dynamic changes. Moreover, DispEn performed poorly in the sensitivity to dynamic changes compared with FFDispEn. As for muscle fatigue detection, the FFDispEn value showed a clear declining tendency with a mean slope of -1.658 × 10-3 as muscle fatigue progresses; additionally, it was more sensitive to muscle fatigue compared with SampEn (slope: -0.4156 × 10-3) and DispEn (slope: -0.1675 × 10-3). The highest accuracy of 97.5% was achieved with the FFDispEn and support vector machine (SVM). This study provided a new useful nonlinear dynamic indicator for sEMG signal processing and muscle fatigue analysis. The proposed method may be useful for physiological and biomedical signal analysis.

Color Image Encryption Through Chaos and KAA Map

The unprecedented growth in production and exchange of multimedia over unsecured channels is overwhelming mathematicians, scientists and engineers to realize secure and efficient cryptographic algorithms. In this paper, a color image encryption algorithm combining the KAA map with multiple chaotic maps is proposed. The proposed algorithm makes full use of Shannon’s ideas of security, such that image encryption is carried out through bit confusion and diffusion. Confusion is carried out through employing 2 encryption keys. The first key is generated from the 2D Logistic Sine map and a Linear Congruential Generator, while the second key is generated from the Tent map and the Bernoulli map. Diffusion is attained through the use of the KAA map. An elaborate mathematical analysis is carried out to showcase the robustness and efficiency of the proposed algorithm, as well as its resistance to visual, statistical, differential and brute-force attacks. Moreover, the proposed image encryption algorithm is also shown to successfully pass all the tests of the NIST SP 800 suite.

Optimized Deep Learning-Enabled Hybrid Logistic Piece-Wise Chaotic Map for Secured Medical Data Storage System

Background: In recent times, medical technology has generated massive reports such as scanned medical images and electronic patient accounts. These reports are necessary to be stored in the highly secured platform for further reference. Traditional storage systems are infeasible for storing massive data. In addition, it suffers to provide secure storage and privacy protection at the time of medical services. It is necessary to provide secure storage and full utilization of personal medical records for the common people in practice. The healthcare system based on IoT enhances the support for the patients and doctors in diagnosing the sufferers at an accurate time using the monitored health data. Yet, doctors make an inappropriate decision regarding the sufferer’s sickness when the information regarding health data saved in the cloud gets lost or hacked owing to an external attack or also power failure. Hence, it is highly essential for verifying the truthfulness of the sufferer’s information regarding health data saved on the cloud.Hypothesis: The major intention of this task is to adopt a new chaotic-based healthcare medical data storage system for storing medical data (medical images) with high protection. Methodology: Initially, the input medical images are gathered from the benchmark datasets concerning different modalities. The collected medical images are enciphered by developing Hybrid Chaotic Map by adapting the 2D-Logistic Chaotic Map (2DLCM), and Piece-Wise Linear Chaotic Map (PWLCM) referred to as Hybrid Logistic Piece-Wise Chaotic Map (HLPWCM). An Optimized Recurrent Neural Network (O-RNN) is proposed for key generation using Best Fitness-based Coefficient vector improved Spotted Hyena Optimizer (BF-CSHO). The O-RNN-based key generation utilizes the extracted image features like first and second-order statistical features and the targets are acquired as a unique encrypted key, which is used for securing the medical data. The same BF-CSHO is used for improving the training algorithm (weight optimization) of RNN to minimize the Mean Absolute Error (MAE) between the cipher (encrypted) images and original images. Results: From the result analysis, the suggested BF-CSHO-RNN-HLPWCM, by considering the image size at [Formula: see text] shows 10.4%, 8.5%, 3.97%, 0.62%, 3.88%, 2.40%, and 7.82% provides better computational efficiency than LCM, PWLCM, LPWCM, PSO-RNN-HLPWCM, JA-RNN-HLPWCM, GWO-RNN-HLPWCM, and SHO-RNN-HLPWCM, respectively. Conclusion: Thus, the simulation findings show the effective efficiency of the offered method owing to the security of the stored medical data.