1D Chaotic Maps Research Articles

Hardware Implementation of a 2D Chaotic Map-Based Audio Encryption System Using S-Box

This paper presents a hardware-based audio encryption system using a 2D chaotic map and dynamic S-box design implemented on an Artix-7 FPGA platform. Three distinct chaotic maps—logistic–fraction (2D-LF), logistic–sine (2D-LS), and fraction–sine (2D-FS)—were investigated and implemented on an FPGA. The 2D-LF map was employed in the encryption system for its throughput and power efficiency performance. The proposed encryption system benefits from the randomness of chaotic sequences for block permutation and S-box substitution to enhance the diffusion and confusion properties of the encrypted speech signal. The system’s encryption strength is validated through performance evaluations, using the mean squared error (MSE), signal-to-noise ratio (SNR), correlation coefficients, and NIST randomness tests, which confirm the unpredictability of the encrypted speech signal. The hardware implementation results show a throughput of 2880 Mbps and power consumption of 0.13 W.

OFDM Transmission in Rayleigh Fading Channel for S-Box and 3D Chaotic Maps Based Encrypted Image

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 this study, various encryption techniques, including cipher algorithms and substitution box, are combined with the OFDM system to establish a secure image transmission over a Rayleigh fading channel. QPSK modulation is used to ensure the simplicity of the proposed system. Six gray images are used, Lena, the cameraman, Barbara, Baboon, pepper and Elaine for testing and comparing with previous works. Security analysis is performed to evaluate the quality and security of the encryption process, the entropy value reach 7.99, correlation coefficient is around zero and the histogram is uniform. In addition, the key size is 2630. For image transmission evaluation, the PSNR and BER are utilized and it reached 10-5 for BER. According to the statistical results, the proposed image encryption scheme is secure and efficient.

Integration of a novel 3D chaotic map with ELSS and novel cross-border pixel exchange strategy for secure image communication

This paper proposes a robust image encryption algorithm that utilizes a Novel three-dimensional (3D) Chaotic map and an Enhanced Logistic Sine System (ELSS). We leverage the unpredictability of 3D chaotic dynamics alongside the complexity of ELSS and DNA Sequence to forge a formidable image encryption scheme. Firstly, the image pixels are converted from decimal to hexadecimal notation and sorted in a 1D pixel array carrying a unique sequence of three channels of the RGB image. Secondly, the secret key is appended to XOR, the values with that 1-D pixels array. Thirdly, values are sorted by performing the binary right shift operation and encoded into DNA. Fourthly, a novel chaotic map is used to perform scrambling operations. Lastly, a novel enormous keyspace ELSS is used to perform efficient Border and Cross-Border (B &CB) pixel exchange, further enhancing the encryption quality of the proposed algorithm. Comprehensive security analysis proved that the proposed algorithm exhibits remarkable resilience against powerful known and chosen plaintext attacks and other prevalent cryptanalysis attacks, including differential attacks and exhaustive key search attacks. Henceforth, the proposed algorithm’s superior security and low computational cost make it an ideal choice for real-time secure image communication across various platforms, including satellite, multimedia, and military communications.

Hybrid Block Chaotic Compressive Sensing and Chaotic Scrambling Algorithms for Color Image Encryption System

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 image is first decomposed into three sub-images based on the tricolor theory; then, a discrete wavelet transform is used to sparsely process the three decomposed images. A 2D Henon map is used to scramble the compressed image after compression. This process further enhances the security of the system by increasing the complexity of the encryption process. The results showed that the proposed system provides better security and has a lower computational complexity than other methods. Furthermore, the proposed system is resistant to known attacks such as brute force and statistical attacks.

A secure image steganography based on LSB technique and 2D chaotic maps

This paper introduces a pioneering, effective data-hiding algorithm using different sizes of cover images and different types of secret data (image, txt, and audio). The proposed algorithm is based on a hybrid 1D chaotic map combined with a 2D composite chaotic map paired with optimization and Least Significant Bits (LSB) techniques. We employ chaotic maps to create the initial embedding position vector, and LSB to hide the secret message in the cover image. The optimization technique utilizes the chaotic maps to optimize the random embedding sites, looking for value matches between the cover image pixels and the secret data bits. This partial improvement leads to a high-quality stego-image, a large embedding capacity, imperceptibility to the human eye, undetectability, and enhanced security. The outcomes of the extensive experiments show that when the payload is 4.2 bits per pixel, the peak signal-to-noise ratio value (PSNR), which expresses the visual quality, is above 30 dB. Furthermore, the experimental results illustrate that the system exhibits robustness against various types of attacks. As a final point of strength, the large key space (2^206) prevents the secret data from being resolved if stego-images are accessed by intruders or third parties. Even minor changes in key bits can significantly alter the extracted secret data, resulting in entirely different secret data.

An improved reversible watermarking scheme using embedding optimization and quaternion moments

Digital watermarking of images is an essential method for copyright protection and image security. This paper presents an innovative, robust watermarking system for color images based on moment and wavelet transformations, algebraic decompositions, and chaotic systems. First, we extended classical Charlier moments to quaternary Charlier moments (QCM) using quaternion algebra. This approach eliminates the need to decompose color images before applying the discrete wavelet transform (DWT), reducing the computational load. Next, we decompose the resulting DWT matrix using QR and singular value decomposition (SVD). To enhance the system's security and robustness, we introduce a modified version of Henon's 2D chaotic map. Finally, we integrate the arithmetic optimization algorithm to ensure dynamic and adaptive watermark insertion. Our experimental results demonstrate that our approach outperforms current color image watermarking methods in security, storage capacity, and resistance to various attacks, while maintaining a high level of invisibility.

A secure fractal compression scheme based on irregular Latin square, Julia and 2D-FCICM

With the proliferation of digital image data, ensuring its secure and efficient storage and transmission has become important. One-dimensional (1D) chaotic maps come with their set of limitations, such as chaotic interval discontinuity and simple chaotic behavior. To increase the complexity of chaotic systems, this paper proposed a novel 2D fractal coupled model (2D-FCM) to generate chaotic systems and extend it to n-dimensional chaotic systems. Meanwhile, the newly generated 2D-FCICM is employed in secure fractal compression. Compared to existing chaotic systems, the pseudo-random sequences generated by the 2D-FCICM exhibit better randomness and complexity. To enhance the plaintext sensitivity of the algorithm, a localized magnified fractal image is produced using plaintext information. Control parameters for the chaotic system are then derived from both the fractal and the original images. Given the compressed data's I × 5 size, this study proposed a technique for generating irregular Latin squares and integrated it into the scrambling phase. The experimental findings indicate that this scheme boasts high security levels, strong plaintext sensitivity and key sensitivity, and is resilient against various statistical attacks.

Cryptanalysis and construction of keyed strong S-Box based on random affine transformation matrix and 2D hyper chaotic map

As the only nonlinear module, S-Box (substitution box) is widely used in stream cipher, hash function, and so on. However, there exist some weaknesses in existing S-Boxes, such as fixed point, reverse fixed point and short iteration period rings. Furthermore, the S-Boxes in AES and SM4.0 were fixed, which makes them vulnerable to attack. To address these weaknesses, first, a non-degenerate 2D chaotic map (2D-NDCM) with ergodicity in phase space was constructed. Second, based on 2D-NDCM, the seed S-Boxes with high nonlinearity were constructed in batches by affine transformation and Boolean function, and then three possible weaknesses were eliminated to obtain strong keyed S-Boxes. Statistical analysis demonstrated the effectiveness and practicability of the proposed S-Box batch generating algorithm.

An improved robust algorithm for optimisation-based colour medical image watermarking

Recently, significant attention has been focused on copyright protection of medical images, causing watermarking to become a prevalent research topic. In this paper, we propose an optimisation-based robust watermarking algorithm for the copyright protection of colour medical images. Initially, we decompose a host medical image by lifting wavelet transform (LWT), followed by discrete cosine transform (DCT) into transformed coefficients, and then embed multiple watermarks into the transformed host image by using hybrid optimisation algorithms. To further improve security and reduce the channel noise distortion, we then apply hashing and Hamming code to image and text mark, respectively, before the embedding process. Finally, we utilise 2D chaotic map to encrypt the marked media, aiming to achieve enhanced security and confidentiality. The experimental outcome shows satisfactory invisibility, watermark payload and robustness against image-processing attacks. Furthermore, through numerous comparative experiments with nine state-of-the-art algorithms on two standard datasets, the effectiveness of the proposed algorithm is demonstrated.

Medical image encryption system based on a simultaneous permutation and diffusion framework utilizing a new chaotic map

In telemedicine, diverse medical images transmitted between doctors and patients contain sensitive personal information. Thus, there is an urgent need for reliable and efficient medical image encryption to protect these medical images during transmission. In this paper, a simultaneous permutation and diffusion framework (SPDF) is introduced for medical image encryption based on a new chaotic map. Firstly, combining the Chebyshev map and the iterative chaotic map with infinite collapse (ICMIC), we propose a one-dimensional chaotic system (1D-CICMIC) which exhibits higher ergodicity and unpredictability compared to other 1D chaotic maps through comprehensive analyses. Secondly, in order to enhance permutation effect, we modify traditional Josephus traversing with a dynamic scrambling method where the scrambling scheme of the current pixel depends on the value of the previous diffused pixel. Thirdly, we develop a simultaneous permutation and diffusion framework, wherein the diffusion is embedded into the modified Josephus traversing to prevent attackers from targeting the scrambling and diffusion phases separately. Finally, based on 1D-CICMIC and SPDF, an encryption system is proposed. It adopts plaintext correlation in the diffusion operation, which strikes a balance between ciphertext sensitivity and plaintext sensitivity, offering resistance against chosen-plaintext attack (CPA), noise attack and data loss. Simulation results show that the proposed algorithm has high encryption efficiency and can withstand various common attacks.

Constructing a non-degeneracy nD chaotic map model and counteracting dynamic degradation through adaptive impulsive perturbation

The characteristics of state point trajectory in phase space of a chaotic map, such as ergodicity, aperiodicity, broadband and noise-like, have been proved to be suitable for cryptography. However, some weaknesses, such as small key space, multiple bifurcations and dense windows that exist in some classic 1D and 2D chaotic maps, effect their practical application. To solve these problems, we constructed a non-degeneracy nD chaotic model, and instantiated it to obtain a 3D chaotic map (3D-NDCM), the dynamics analysis results demonstrated that the 3D-NDCM has a sufficiently large chaotic range, its state point trajectories has ergodicity in phase space. To counteract dynamic degradation and extend the aperiodic length of state time sequences, we further constructed a 6D-NDCM based on the model. Experimental analysis results demonstrated that, a state time sequence with longer aperiodicity can be obtained, through both dimension expansion and adaptive impulsive perturbation.

An n-Dimensional Chaotic Map with Application in Reversible Data Hiding for Medical Images.

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.

Super-resolution deep neural network (SRDNN) based multi-image steganography for highly secured lossless image transmission

Information exchange and communication through the Internet are one of the most crucial aspects of today’s information technology world. The security of information transmitted online has grown to be a critical concern, particularly in the transfer of medical data. To overcome this, the data must be delivered securely without being altered or lost. This can be possibly done by combining the principles of cryptography and steganography. In the recent past, steganography is used with simpler methods like the least significant bit manipulation technique, in order to encode a lower-resolution image into a higher-resolution image. Here, we attempt to use deep neural networks to combine many two-dimensional colour images of the same resolution into a single cover image with the same resolution. In this technique, many secret images are concealed inside a single cover image using deep neural networks. The embedded cover image is then encrypted using a 3D chaotic map for diffusion and elliptic curve cryptography (ECC) for confusion to increase security.Supporting the fact that neural networks experience losses, the proposed system recovers up to 93% of the hidden image concealed in the original image. As the secret image features are identified and combined along with the cover image, the time complexity involved in the security process is minimized by 78% compared to securing the original data.

Image encryption based on s-box and 3D-chaotic maps and secure image transmission through ofdm in rayleigh fading channel

Image encryption based on s-box and 3D-chaotic maps and secure image transmission through ofdm in rayleigh fading channel

An optimized chaotic S-box for real-time image encryption scheme based on 4-dimensional memristive hyperchaotic map

As digital products communicate over public networks, digital image security becomes essential. Despite advancements in encryption technology, protecting data from secure images remains a complex computational issue that necessitates using an encrypted environment to protect data transmitted from devices over networks. Encryption is critical for protecting sensitive information, especially images, from unauthorized access or failure. Image encryption is distinct from text encryption. Images contain extensive data with high redundancy and a high correlation between nearby pixels, making them difficult to process with traditional technology. In recent decades, chaos maps have become popular in the crypto community. This work proposes a new encryption technology based on chaotic map substitution boxes (S-box) and cellular automata (CA) to address the frequent challenges in chaotic encryption methods. To address the inadequate randomness provided by the 1D chaotic map, this work presented a 4D memristive hyperchaos with a more excellent chaotic range, increased uncertainty, and ergodicity as an alternative to the software-based approach, which is vulnerable and offers low throughput. The suggested encryption technique was implemented on an Intel Cyclone IV EP4CE115F29C7 FPGA. It is less prone to tampering and has a better throughput. This suggested encryption scheme employs 1384 LEs. In comparison to traditional algorithms, the suggested Number of Pixels Change Rate (NPCR) (99.9706%), unified averaged changed intensity (UACI) (33.3956%), and information entropy (IE) (7.984) accomplish more effective. Statistical studies such as IE, histogram, correlation, peak signal-to-noise ratio (PSNR), differential analysis such as NPCR and UACI, and noise attack analyses are employed to validate the suggested encryption design. Regarding security, the suggested hybrid method outperforms conventional algorithms while protecting image quality.

A novel compression-based 2D-chaotic sine map for enhancing privacy and security of biometric identification systems

Human biometric images are utilized for cell phone authentication, airport security, and biometric passports. To improve the biometric identification process, this should be protected from cyber attackers because it is sensitive to any minor changes. Thus, security is a major concern in biometric images. Traditional encryption and compression methods are ineffective for encrypting biometric images due to their high execution time and algorithm complexity. In this paper, a novel 2D chaotic sine map is proposed for generating encryption keys and improving security for biometric identification systems. The proposed scheme uses the 2D chaotic map to generate the private key and diffusion process. Here, the Hénon-Sine Map (HSM-512), Secure Hash Algorithm (SHA-256), and DNA computing are also used in the key generation process. The pixel values of the original images in the proposed schemes are shuffled using Mersenne Twister (MT) to improve the security of biometric images. Moreover, the Differential Huffman Compression (DHC) method is used for lossless compression while performing the XOR-based encryption process. The proposed model has been tested on different RGB biometric images, namely the SOCOFing dataset and the COVID-19 chest X-ray dataset. The experiment results have been evaluated using many performance metrics, such as entropy, key space, histogram analysis, key sensitivity, robustness analysis, correlation, and similarity analysis. The outcomes demonstrate that the proposed scheme is more effective than the state-of-the-art schemes.

Secure Selective Image Encryption Based on Wavelet Domain, 3D-Chaotic Map, and Discrete Fractional Random Transform

Secure Selective Image Encryption Based on Wavelet Domain, 3D-Chaotic Map, and Discrete Fractional Random Transform

BCLM: a novel chaotic map for designing cryptography-based security mechanism for IEEE C37.118.2 PMU communication in smart grid

Abstract Today, creating a smart grid that is resistant to cyberattacks is a subject of utmost significance. One of the components of the smart grid that is most susceptible to a cyber-attack is the phasor measuring unit (PMU). The reason is that PMU employs IEEE C37.118.2 communication standards, which specify the structure and sequencing of data packets but offer no security measures. Users must implement the security techniques to ensure the protection of PMU data. Additionally, PMU communicates via a public wide-area network, raising the risk to security. In addition, PMU is a crucial component of the smart grid, enabling different crucial choices for the reliable functioning of the smart grid to be made using its data. This research suggests a chaos-based data encryption solution to close the knowledge gap and reduce the confidentiality assault on PMU data. For this, a brand-new boost converter logarithmic map (BCLM), a one-dimensional (1D) chaotic map, has been presented. The research demonstrates how the suggested chaotic map has better chaotic qualities than conventional chaotic maps. The pseudorandom generator is the chaotic BCLM system. The PMU data are encrypted using the random sequence produced by the BCLM chaotic system. The suggested chaotic map is not computationally demanding, making it simple to implement in a PMU device with limited resources.

Chaos based speech encryption using microcontroller

In this work a real-time chaos-based speech encryption scheme designed for low-cost microcontroller implementation is presented. The method involves a two-step encryption process: shuffling based on a hash algorithm and XOR operation with a pseudo-random bit sequence from a chaotic map. Key findings include the use of a 1D chaotic map for speed, a hash algorithm to simplify shuffling and enhance overall speed, and implementation on an inexpensive STM32 microcontroller for cost-effective high security. Various tests, including Log-likelihood ratio, entropy, correlation coefficient, and spectral distortion, validate the encryption scheme’s effectiveness. The result is a secure and agile system designed for sequential encryption and transmission.

Comparison of two new chaos-based pseudorandom number generators implemented in microcontroller

Chaos-based encryption algorithms uses a pseudorandom number generator (PRNG) to generate chaotic dynamics to carry out the processes to encrypt different types of information. One of the main problems is that some chaotic systems do not present high randomness and uniformity in time series affecting directly the security of the chaos-based cryptosystem. In this work, we proposed two new 2D hyperchaotic maps designed from 1D chaotic maps to use in the design of two new PRNGs for cryptographic applications. The proposed PRNGs were implemented in Renesas RA4M1 32-bit microcontroller for first time in the literature. The chaotic sequences with double-precision floating-point format are also validated with different randomness and security analyses such as the Lyapunov exponent, key space, histograms, autocorrelation, information entropy and the NIST SP800-22 test. In addition, a comparison of the results with similar schemes in the literature about design, security and performance is made. The results achieved in this work can help scholars and designers to improve the effectiveness in randomness of new chaos-based PRNGs for cryptographic applications.