1D Chaotic Maps Research Articles

Semi-Poisson nearest-neighbor distance statistics for a 2D dissipative map

Typical pseudotrajectories of 2D ergodic maps are known to possess Wignerian nearest-neighbor distance distributions (NNDDs). In the case of 2D chaotic dissipative maps, bounded aperiodic pseudotrajectories typically evolve on planar strange attractors. In this microarticle, the hypothesis that such pseudotrajectories should possess NNDDs that are intermediate between the Poisson and Wigner distributions is put forward and a rare example for which the intermediate distribution can be clearly identified is presented. In particular, it is demonstrated numerically that typical pseudotrajectories evolving in the strange attractor of the standard 2D Ikeda map possess semi-Poissionian NNDDs.

A novel approach of image encryption using pixel shuffling and 3D chaotic map

– In recent years, with rapid development in information and communication technologies, sharing digital images in social media have facilitated. However, since images privacy matters in our society, keeping images protected became a big challenge we have to deal with. In this paper, we propose a new image encryption method using Image Pixel Shuffling and 3D Chaotic map. First, the plain image is encoded using pixel shuffling, then the result is XORed with a key, and finally, the 3D chaotic map is performed on it. The security will be increased by using three steps to encrypt the image. Our results show that the proposed approach has a good performance and it is better than those of some notable image encryption algorithms. We got entropy value 7.9901 of cipher image, NPCR of 99.6628%, and UACI of 33.6781%. MATLAB was used to implement the proposed image encryption approach.

A new colour image encryption approach using a combination of two 1D chaotic map

In this paper, we propose an improved chaotic map by coupling two existing methods. Numerical tests prove that the proposed technique presents closely complex behaviour and wider chaotic range than their seed maps. In this paper a new colour image encryption approach using the enhanced chaotic map has been suggested. The proposed scheme is based on the conventional confusion-diffusion structure that contains a new permutation process, it has designed to randomly scramble neighbouring pixels. The performance and the quality measurement of the proposed scheme are analysed by comparing it with some existing research.

Two-Dimensional Modular Chaotification System for Improving Chaos Complexity

Chaotic systems are widely studied in various research areas such as signal processing and secure communication. Existing chaotic systems may have drawbacks such as discontinuous chaotic ranges and incomplete output distributions. These drawbacks may lead to the defects of some chaos-based applications. To accommodate these challenges, this paper proposes a two-dimensional (2D) modular chaotification system (2D-MCS) to improve the chaos complexity of any 2D chaotic map. Because the modular operation is a bounded transform, the improved chaotic maps by 2D-MCS can generate chaotic behaviors in wide parameter ranges while existing chaotic maps cannot. Three improved chaotic maps are presented as typical examples to verify the effectiveness of 2D-MCS. The chaos properties of one example of 2D-MCS are mathematically analyzed using the definition of Lyapunov exponent. Performance evaluations demonstrate that these improved chaotic maps have continuous and large chaotic ranges, and their outputs are distributed more uniformly than the outputs of existing 2D chaotic maps. To show the application of 2D-MCS, we apply the improved chaotic maps of 2D-MCS to secure communication. The simulation results show that these improved chaotic maps exhibit better performance than several existing and newly developed chaotic maps in terms of resisting different channel noise.

An efficient image system-based grey wolf optimiser method for multimedia image security using reduced entropy-based 3D chaotic map

Chaotic maps play an important role in information sharing. In this paper a grey wolf optimiser used with reduced entropy-based 3D chaotic map. The selection and high coefficients are selected based on the reduced entropy value to identify the optimised parameters to get unpredictable random values. Time complexity, autocorrelation of V, H and D elements, histogram of original and cipher images, peak signal to noise ratio and NPCR and UACI values are computed from the cipher image. The empirical results show the proposed method provides good, better imperceptibility and defends various attacks. To prove this accomplishment of the method, several experiments were conducted and compared the results with existing systems.

Voice Scrambling Algorithm based on 3D Chaotic Map System (VSA3DCS) to Encrypt Audio Files

Here, a proposed voice scrambling algorithm established on one of two 3D chaotic maps systems (VSA3DCS) will be presented, discussed, and applied on audio signals file. The two 3D chaotic map systems in which any one of them is used to build VSA3DCS are Chen's chaotic map system and Lorenz chaotic map system. Also Arnold cat map-based scrambling algorithm will be applied on the same sample of audio signals. These Scrambling algorithms are used to encrypt the audio files by shuffling the positions of signals at different conditions with the audio file as one block or two blocks. Amplitude values of audio signals with signals' time are registered and plotted for original file versus encrypted files which are produced from applying VSA3DCS using Chen's, VSA3DCS using Lorenz, and Arnold-based algorithm. The spectrogram frequencies of audio signals with signals' time are plotted for original file versus encrypted files for all algorithms. Also, the histogram of the original file and encrypted audio signals are registered and plotted. The comparative analysis is presented by using some measuring factors for both of encryption and decryption processes, such as; the time of encryption and decryption, Correlation Coefficient of original and encrypted signals between the samples, the Spectral Distortion (SD) measure, Log-Likelihood Ratio (LLR) measure, and key sensitivity measuring factor. The results of several experimental and comparative analyses will show that the VSA3DCS algorithm using Chen's or Lorenz is a good algorithm to provide an effective and safe solution to voice signal encryption, and also VSA3DCS algorithm better than Arnold-based algorithm in all results with all cases.

An efficient image system-based grey wolf optimiser method for multimedia image security using reduced entropy-based 3D chaotic map

An efficient image system-based grey wolf optimiser method for multimedia image security using reduced entropy-based 3D chaotic map

Digital Color Image Encryption Using Cellular Automata and Chaotic Map

Today, with the expansion of multimedia communications, computer networks, and the distribution of information on the Internet, maintaining the security of information exchanged through insecure channels has become an important and essential issue in data communication. One way to protect the information in passive defense is to encrypt data so that people can communicate securely on a secure channel while maintaining their privacy and data authenticity. Because color image data has certain features compared to traditional data such as text and binary data, special algorithms are needed to encrypt digital images to maintain the efficiency, security, and speed of encryption. The present study provides a way to encrypt digital images using reversible cell automation and chaotic mapping. The basis for encrypting the proposed method is the use of the concepts of Shannon's confusion and diffusion technique, which takes place in two main stages. In the first step, the plain image is received as input, then it is permuted using the 3D chaotic map by using suitable key. In the second step, the cipher image from the previous step are extracted to 24 one-bit plates image and XOR by suitable 2D reversible cell automata. The proposed method will be compared with several cryptographic methods and has good outperform results.

A DNA Based Image Data Hiding Using 3D Logistic Chaotic Map

A DNA Based Image Data Hiding Using 3D Logistic Chaotic Map

Chaotic-precoder based PAPR reduction in MIMO SFBC-OFDM

ABSTRACT This letter demonstrates the chaotic precoding approach in multiple-input multiple-output space frequency block coded orthogonal frequency division multiplexing (MIMO SFBC-OFDM) communication systems as an appropriate solution for peak-to-average power ratio (PAPR) reduction. Firstly, we have proposed four cascades chaotic generators (CCGs) by using at each time two conventional one dimension (1D) chaotic maps in series. We further proposed a hybrid chaotic system (HCS) based on combination of three 1D maps. Simulation results show that HCS-based precoded MIMO SFBC-OFDM system can achieve better PAPR reduction performance and lower bit error rate (BER) compared to conventional MIMO SFBC-OFDM systems, with less computational complexity and without side information requirement.

A Tweak-Cube Color Image Encryption Scheme Jointly Manipulated by Chaos and Hyper-Chaos

This paper proposes a novel tweak-cube color image encryption scheme jointly manipulated by chaos and hyper-chaos. One-dimensional (1D) chaotic maps are effortless to operate, but the key space is relatively small. The hyperchaotic system has complex dynamics properties, which are capable of compensating for the defects of 1D chaotic maps. Thus, we first raise an improved 1D chaotic map with an increased key space. Then, we associate it with a four-dimensional (4D) hyperchaotic system to generate the key streams and further rotate and shift the rows and columns of each component of Red (R), Green (G), and Blue (B) for the color image. The permuting mode is to disturb the original position of the pixels by mimicking the way of twisting the Rubik’s cube. Moreover, the key stream updated by the plain images is also utilized for diffusion and scramble at the bit level. As a consequence, our cryptosystem enhances the security without at the expense of increasing time cost.

A novel color image LSB steganography using improved 1D chaotic map

Conventional one-dimensional (1D) chaotic map have a simple structure, which is easy to implement and has a low computational cost, but has a drawback that the range of chaotic behaviors is narrow and the distribution of key sequence is uniform. In order to overcome the drawback, we proposed an improved 1D chaotic system model and evaluate the proposed model through experiments with the logistic map and a sine map. Simulation and performance evaluation shows that the 1D chaotic map improved by the proposed model can overcome the existing defects sufficiently. We also proposed a color image LSB steganography algorithm using the improved 1D chaotic map. Through experiments, we confirmed the accuracy of the proposed color image LSB steganography algorithm. Experimental results proved that the algorithm has a better performance than the previous methods, showing an excellent performance against statistical analysis attacks. We also analyzed the effect of secret data type on the quality of stego image.

ChaosNet: A chaos based artificial neural network architecture for classification.

Inspired by chaotic firing of neurons in the brain, we propose ChaosNet-a novel chaos based artificial neural network architecture for classification tasks. ChaosNet is built using layers of neurons, each of which is a 1D chaotic map known as the Generalized Luröth Series (GLS) that has been shown in earlier works to possess very useful properties for compression, cryptography, and for computing XOR and other logical operations. In this work, we design a novel learning algorithm on ChaosNet that exploits the topological transitivity property of the chaotic GLS neurons. The proposed learning algorithm gives consistently good performance accuracy in a number of classification tasks on well known publicly available datasets with very limited training samples. Even with as low as seven (or fewer) training samples/class (which accounts for less than 0.05% of the total available data), ChaosNet yields performance accuracies in the range of 73.89%-98.33%. We demonstrate the robustness of ChaosNet to additive parameter noise and also provide an example implementation of a two layer ChaosNet for enhancing classification accuracy. We envisage the development of several other novel learning algorithms on ChaosNet in the near future.

Deterministic chaotic finite-state automata

Chaotic dynamics have been widely applied in various domains such as cryptography, watermarking and optimization algorithms. Enhancing chaotic complexity of simple one-dimensional (1D) chaotic maps has been a popular topic of research in recent years. However, most of the proposed methods have low complexity and are not suitable for practical applications. To overcome these issues, this paper introduces a novel approach known as deterministic chaotic finite-state automata (DCFSA). Existing 1D chaotic maps are associated with deterministic finite automata states. Then, a transition rule dynamically selects which 1D chaotic map to compute. DCFSA allows the creation of a large number of possible chaotic configurations with enhanced nonlinearity while retaining the computational complexity comparable to a 1D map. Theoretical and performance analyses show that DCFSA provides a larger chaotic parameter range, higher nonlinearity and chaotic complexity, as well as longer cycle length as compared to its underlying 1D chaotic maps. Moreover, performance comparison against other existing chaotification methods demonstrates DCFSA’s superiority.

An improved image encryption algorithm with finite computing precision

When a digital chaotic system is realized on hardware of finite computing precision, it will lead to short period orbits. Although many existing image encryption algorithms declared that the average cycle lengths of their digital chaotic systems are larger than the required cycle lengths in image encryption, there are still many period orbits whose lengths are far smaller than the average cycle length. To further improve security with finite precision, an improved cryptosystem is proposed based on a new two-dimensional chaotic map derived from the Sine map, the Chebyshev map and a linear function (2D-SCL). Performance estimation demonstrates that the 2D-SCL has good ergodicity, hyperchaotic behavior, large cycle lengths under low computing precisions, and its complexity is larger and more stable than that of several newly developed 2D chaotic maps. Thus we design an improved cryptosystem based on the 2D-SCL map. In the scheme, we combine the confusion and diffusion processes in one stage to improve the running speed. Based on the SHA-1 hash values of plain image and the chaotic sequence, a pseudorandom sequence is designed and then an anti-degradation method is introduced to improve the dynamic degradation of the 2D-SCL map under finite computing precision. Meanwhile, this algorithm also updates the initial values of the 2D-SCL map in real-time, thus enhancing the ability to resist known-plaintext and chosen-plaintext attacks. The largest precision is set at 2−16, and simulation results show that this algorithm has high security, low time complexity, and the ability to withstand common attacks.

Image encryption based on a new 2D logistic adjusted logistic map

This paper proposes an encryption scheme based on a new 2-dimensional chaotic map. The new 2D chaotic map is derived from the idea of giving the two outputs of a 2D logistic map to two separate 1-dimensional logistic maps. The resulting 2D chaos based pseudo-random number generator is demonstrated to have significantly better randomness and unpredictability characteristics in terms of Lyapunov exponents as well as trajectory plots, in comparison to some recently proposed schemes based on other 2D chaotic maps. This new 2D chaotic map is then used to implement encryption of images. The proposed encryption scheme is demonstrated to be significantly better in terms of the required computational effort. For the proposed scheme, the commonly used measures of security, unpredictability and sensitivity to initial states are successfully established with the help of a set of standard simulation results.

Application Based Construction and Optimization of Substitution Boxes Over 2D Mixed Chaotic Maps

Chaotic maps play a vital role in the development of cryptographic techniques being used in today’s world. Efficient and highly secure algorithms can be constructed based on chaotic maps. Chaotic maps have the intrinsic property of being highly sensitive to initial conditions. In this paper, we have presented a novel scheme for construction and optimization of substitution boxes (S-boxes) based on mixed two dimensional (2D) chaotic maps in which cryptographic properties of S-boxes are optimized based on initial conditions of their parent 2D chaotic map. The proposed scheme and the resulting substitution boxes are analyzed with existing cryptanalysis techniques and their results have been compared with some other algorithms available in literature. The proposed scheme has been found to be more efficacious than other algorithms. The outcomes of security analysis indicate that our proposed technique and resulting optimized non-linear component in the current era of information technology.

Cryptanalysis and Improvement of a Color Image Encryption Scheme Based on DNA Sequences and Multiple 1D Chaotic Maps

This paper presents cryptanalysis of a color image encryption scheme. DNA encoding and multiple 1D chaotic maps are used in the encryption process which increases its computational speed. The key streams generated in this scheme are dependent on secret keys, updated using the sum of pixel intensities of plain image of size [Formula: see text]. This paper analyzes the security of encryption scheme against the chosen plaintext attack and finds that only [Formula: see text] different key matrices for diffusion are possible, an equivalent version of which can be revealed with [Formula: see text] chosen plain images. Experimental results are presented to prove that equivalent diffusion keys and block permutation sequence can be effectively revealed through the attack. In addition, low sensitivity of keys towards changes in plaintext along with insecure diffusion process involved in encryption process is also reported. Finally, to remedy the shortcomings of the original encryption scheme, an enhanced encryption scheme is generated that can resist chosen/known plaintext attack while maintaining the merits of the original encryption scheme.

Two-Dimensional Sine Chaotification System With Hardware Implementation

Chaotic systems are widely employed in many practical applications for their significant properties. Existing chaotic systems may suffer from the drawbacks of discontinuous chaotic ranges and frail chaotic behaviors. To solve this issue, this paper proposes a two-dimensional (2D) sine chaotification system (2D-SCS). 2D-SCS can not only significantly enhance the complexity of 2D chaotic maps, but also greatly extend their chaotic ranges. As examples, this paper applies 2D-SCS to two existing 2D chaotic maps to obtain two enhanced chaotic maps. Performance evaluations show that these two enhanced chaotic maps have robust chaotic behaviors in much larger chaotic ranges than existing 2D chaotic maps. A microcontroller-based experiment platform is also designed to implement these enhanced chaotic maps in hardware devices. Furthermore, to investigate the application of 2D-SCS, these two enhanced chaotic maps are applied to design a pseudorandom number generator. Experiment results show that these enhanced chaotic maps can produce better random sequences than the existing 2D and several state-of-the-art one-dimensional (1D) chaotic maps.

Image encryption based on the pseudo-orbits from 1D chaotic map.

Chaotic systems have been extensively applied in image encryption as a source of randomness. However, dynamical degradation has been pointed out as an important limitation of this procedure. To overcome this limitation, this paper presents a novel image encryption scheme based on the pseudo-orbits of 1D chaotic maps. We use the difference of two pseudo-orbits to generate a random sequence. The generated sequence has been successful in all NIST tests, which implies it has adequate randomness to be employed in encryption process. Confusion and diffusion requirements are also effectively implemented. The usual low key space of 1D maps has been improved by a novelty procedure based on multiple perturbations in the transient time. A factor using the plain image is one of the perturbation conditions, which ensures a new and distinct secret key for each image to be encrypted. The proposed encryption scheme has been efficaciously verified using the Lena, Baboon, and Barbara test images.