Robust Chaotic Map Research Articles

Enhanced Chaotic Pseudorandom Number Generation Using Multiple Bernoulli Maps with Field Programmable Gate Array Optimizations

Certain methods for implementing chaotic maps can lead to dynamic degradation of the generated number sequences. To solve such a problem, we develop a method for generating pseudorandom number sequences based on multiple one-dimensional chaotic maps. In particular, we introduce a Bernoulli chaotic map that utilizes function transformations and constraints on its control parameter, covering complementary regions of the phase space. This approach allows the generation of chaotic number sequences with a wide coverage of phase space, thereby increasing the uncertainty in the number sequence generation process. Moreover, by incorporating a scaling factor and a sine function, we develop a robust chaotic map, called the Sine-Multiple Modified Bernoulli Chaotic Map (SM-MBCM), which ensures a high degree of randomness, validated through statistical mechanics analysis tools. Using the SM-MBCM, we propose a chaotic PRNG (CPRNG) and evaluate its quality through correlation coefficient analysis, key sensitivity tests, statistical and entropy analysis, key space evaluation, linear complexity analysis, and performance tests. Furthermore, we present an FPGA-based implementation scheme that leverages equivalent MBCM variants to optimize the electronic implementation process. Finally, we compare the proposed system with existing designs in terms of throughput and key space.

A family of robust chaotic S-unimodal maps based on the Gaussian function

This research paper introduces a family of one-dimensional S-unimodal maps based on the Gaussian function, designed to exhibit robust chaos across a wide range of parameters. These maps are developed to display robust chaos by avoiding multiple fixed points that are primarily responsible for the coexisting attractors in 1D maps. The parameter space analysis reveals that chaotic behaviour is sustained across the entire parameter space, except for a very narrow region. The study employs a comprehensive computational approach, including quantitative measures such as sample entropy, Lyapunov exponent, and invariant measures. The uniformly higher values of sample entropy, uniform positive values of the Lyapunov exponent, and the existence of invariant measures in a region of parameter space confirm the presence of robust chaos in these maps. Such a promising class of robust chaotic maps may be potentially used in diverse fields such as chaos-based cryptography, pseudo-random number generation, communication systems, and more.

A Robust Chaotic Map and Its Application to Speech Encryption in Dual Frequency Domain

When chaotic systems are used for speech encryption, their chaotic performance largely determines the security of speech encryption. However, traditional chaotic systems have problems such as parameter discontinuity, easy occurrence of chaos degradation, low complexity, and the existence of periodic windows in chaotic intervals. In real applications, chaotic mappings may fall into periodic windows, which is extremely unfavorable for security. In this paper, a new chaotic mapping 2D-LMSM is proposed by improving the chaotic logistic and sine mappings, and applied to speech encryption. Performance evaluation shows that this map can effectively generate robust chaotic signals in a wide parameter range. The 2D-LMSM achieves better robustness and desired chaotic properties than several existing two-dimensional chaotic maps. We propose a novel speech encryption algorithm using this map. First, it performs Fast Fourier Transform (FFT) on the input speech signal to obtain real and imaginary values, which are encrypted by one-time scrambling encryption and XOR diffusion encryption with pseudorandom numbers generated by chaos; then, it performs secondary scrambling encryption by Discrete Wavelet Transform (DWT) and 2D-LMSM; finally, it obtains encrypted speech data by Discrete Wavelet Inverse Transform (IDWT) and Fast Fourier Inverse Transform (IFFT). Experimental results show that this algorithm has good encryption and decryption performances and ensures system security.

Secure image encryption scheme based on a new robust chaotic map and strong S-box

Because the characteristics of chaotic systems are very consistent with the requirements of cryptosystem, chaotic systems are widely used in the encryption of big data, especially the chaos based image encryption is particularly feasible. In this paper, a one-dimensional (1D) piece-wise quadratic polynomial chaotic map (PWQPCM) is proposed to obtain a new system model with better chaotic characteristics. Compared with some existing 1D chaotic systems, the proposed PWQPCM system has better dynamic performance. In particular, it exhibits robust chaotic behavior over a larger continuous parameter range, which is more suitable for cryptographic applications. In addition, a strong S-box construction method and a secure image encryption algorithm based on PWQPCM model are proposed. In this encryption algorithm, a new method of pixel segmentation encryption, S-box substitution and diffusion encryption is combined. The cryptosystem proposed in this paper has the advantages of good performance against data loss, low time cost and flexible adjustment of security strength. Simulation experiments and security analysis verified the above good performance of the encryption system, showing its good application potential in real-time image security communication.

Image encryption algorithm based on digital filters controlled by 2D robust chaotic map

This paper introduces a new cryptosystem algorithm based on digital filters; as an encryption operation, second-order and third-order IIR digital filters are used, and as a decryption operation, second-order and third-order FIR digital filters are used: Chaos in digital filters is caused by the overflow non-linearity function. Both IIR and FIR digital filters are controlled by the first random sequence of zeros and ones produced by the 2D robust chaotic map, while the filters coefficients are generated by the second sequence, so that each pixel is encrypted and decrypted with different coefficients. Fisher-Yates shuffle has been used to obtain a random permutation of the position of the pixels of the original image, so that, the rows are shuffled first, then the columns, based on random numbers obtained by a hyperchaotic map 2D-LICM and 2D-SLIM respectively. Another algorithm based only on a single digital IIR/FIR filter is also presented in this work to allow us to demonstrate the development and high security of the proposed approach. Simulation and experimental results with performance analysis are carried out to demonstrate that our algorithm has high security and can resist various attacks such as differential attacks and statistical attacks.

A novel family of 1-D robust chaotic maps

Abstract Chaotic dynamics of various continuous and discrete-time mathematical models are used frequently in many practical applications. Many of these applications demand the chaotic behavior of the model to be robust. Therefore, it has been always a challenge to find mathematical models which exhibit robust chaotic dynamics. In the existing literature there exist a very few studies of robust chaos generators based on simple 1-D mathematical models. In this paper, we have proposed an infinite family consisting of simple one-dimensional piecewise smooth maps which can be effectively used to generate robust chaotic signals over a wide range of the parameter values.

A novel image encryption/decryption scheme based on integrating multiple chaotic maps

In this paper, a novel framework is presented for chaotic image encryption. The proposed method is based on integrating multiple chaotic maps (e.g., logistic, tent, quadratic, cubic, and Bernoulli) to generate more robust chaotic maps in order to increase the security and privacy needed by applying variable keys. The latter are generated by computing the sine square logistic map and are then applied to generate the chaotic maps employed in our framework. For this, we have performed many experiments to achieve the best period for each chaotic map in which it performed the best encryption. Here, we combine multiple chaotic maps to get a new map that works well when X ∈ [0, 1]. For using a chaotic map in the encryption process, it was necessary to find a way to choose the best of those chaotic maps for encryption. This selection was done with the lowest value for the correlation factor because the smaller value of correlation has an impression of good encryption. We have also noted a clear difference in the influence of one of these maps on some pictures from the others. We chose one of those maps according to the correlation value for each encoding process and compared them. Then, we used a chaotic map of the best of these values for encryption and decryption. Numerical results on various gray images showed the robustness of the proposed method to encrypt and decrypt the images based on the evaluation using different performance analyses. We compared our methods against other well-known approaches, e.g., circular mapping, S-boxes, and S-box with Arnold transform. Our pipeline outperforms those methods. Moreover, our results documented that the proposed scheme has an excellent security level with very low correlation coefficients and good information entropy.

A Parallel Programming for Robust Chaotic Map Generation Based on Two Dimensional Equation System

A Parallel Programming for Robust Chaotic Map Generation Based on Two Dimensional Equation System

A morphologically robust chaotic map based approach to embed patient's confidential data securely in non-QRS regions of ECG signal.

In e-healthcare paradigm, the physiological signals along with patient's personal information need to be transmitted to remote healthcare centres. Before sharing this sensitive information over the unsecured channel, it is prerequisite to protect it from unauthorised access. The proposed method explores ECG signal as the cover signal to hide patient's personal information without disturbing its diagnostic features. Chaotic maps are used to randomly select the embedding locations in the non-QRS region while excluding the sensitive QRS region of ECG train. Optimum Location Selection algorithm has been designed to select the embedding locations in non-QRS embedding region. The proposed algorithm is thoroughly examined and the distortion is measured in terms of statistical parameters and clinical measures such as PRD, PRDN, PRD1024, PSNR, SNR, MSE, MAE, KL-Divergence, WWPRD and WEDD. The robustness of the algorithm is verified using the parameters such as key space and key sensitivity. The implementation has been extensively tested on all the 48 records of the standard MIT-BIH Arrhythmia database, abnormal databases [CU-VT, BIDMC-CHF and PTB (leads I, II and III)] and self-recorded data of 20 subjects. The algorithm yields average PRD, MSE, KL-Divergence, PSNR, WWPRD and WEDD of 4.7 × 10-3, 1.13 × 10-5, 1.29 × 10-5, 50.28, 0.15 and 0.04at an average maximum EC of 0.45(96876 bits) on MIT-BIH Arrhythmia database and 0.016, 3.38 × 10-5, 1.8 × 10-4, 46.03, 0.13 and 0.03 respectively at an average maximum EC of 0.47 (102571 bits) on self-recorded data which clearly reveals the competency of the proposed algorithm in comparison with the other state of the art ECG steganography approaches.

Dynamics and Optimization Control of a Robust Chaotic Map

Robust chaos in the discrete system is suggested to have practical as well as theoretical importance since it can obtain reliable operation in the chaotic mode. However, it receives only moderate attention and only focuses on a finite chaotic parameter space and small Lyapunov exponents. This paper introduces a two-dimensional smooth map and studies its robustness of chaos in the infinite parameter space. Then, a compound operation-based optimization control method is introduced to increase the map complexity in the measure of Lyapunov exponent. The introduced method is simple and provides a new pathway for exploring the robustness and complexity of discrete chaotic system. Finally, we design a chaos-based pseudo-random number generator (CPNG) based on the optimized robust chaotic map, and the careful analysis shows that the proposed CPNG has high quality of randomness and has passed the rigorous National Institute of Standards and Technology (NIST) test.

Multiple-image encryption by using robust chaotic map in wavelet transform domain

With the superiority of capacity space in storage and transmission, multiple-image encryption has become the new focus of information security technology. In this paper, we introduce a multiple-image encryption scheme by using robust chaotic map in wavelet domain, based on the architecture of unified permutation and separate diffusion. Firstly, the original images are decomposed using discrete wavelet transform (DWT) and the low-frequency components are reassembled as the plain image (approximate image). Then, the plain image is entirely scrambled by using Arnold cat map. Thirdly, the scrambled image is further decomposed and the resulted block images are separately employed to combine with the amplitude parameter of robust chaotic map (RCM) to generate key stream in each diffusion process. Since the keys in every diffusion process depend on the plain image and each encrypted block image contains aliased information of multiple images, it is difficult for the intruder to decipher the intercepted encrypted information. Numerical simulations are made to further demonstrate the reliability of the encryption scheme.

On the Enlargement of Robust Region of Chaotic Tent Map for the Use in Key Based Substitution-Box (S-Box)

Robust chaotic maps with wide robust region are favored in cryptography as it extends the key length. Chaotic tent map has robust chaos for control parameter μ = 2. Perturbation of control parameter values beyond control parameter 2, results in orbit diverging towards infinity and trajectories vanish. Thus, to avoid trajectories diverging to infinity and to keep trajectories chaotic beyond parameter value 2, a new technique is proposed that makes use of modulo and scaling operators. The parameter space of non-smooth maps is never considered for enlargement. Herein, modified tent map results in larger parameter space that in turn can be used to design key based S-box. The recently published chaotic key based S-box with chaotic map's parameter space does not achieve large key space. For modified tent map, the modulo operation keeps trajectories in domain (0, 1) while scaling allows for uniform distribution of points in domain (0, 1). These operations keep chaotic orbits globally stable and robust. In results, the robustness of chaotic tent map and modified chaotic tent map is compared using bifurcation diagram. The improved robust region of tent map justifies the effectiveness of proposed method that results to design key based S-box.

Wavelet-Based Color Pathological Image Watermark through Dynamically Adjusting the Embedding Intensity

This paper proposes a new dynamic and robust blind watermarking scheme for color pathological image based on discrete wavelet transform (DWT). The binary watermark image is preprocessed before embedding; firstly it is scrambled by Arnold cat map and then encrypted by pseudorandom sequence generated by robust chaotic map. The host image is divided into n × n blocks, and the encrypted watermark is embedded into the higher frequency domain of blue component. The mean and variance of the subbands are calculated, to dynamically modify the wavelet coefficient of a block according to the embedded 0 or 1, so as to generate the detection threshold. We research the relationship between embedding intensity and threshold and give the effective range of the threshold to extract the watermark. Experimental results show that the scheme can resist against common distortions, especially getting advantage over JPEG compression, additive noise, brightening, rotation, and cropping.

Color image encryption based on one-time keys and robust chaotic maps

We designed a stream-cipher algorithm based on one-time keys and robust chaotic maps, in order to get high security and improve the dynamical degradation. We utilized the piecewise linear chaotic map as the generator of a pseudo-random key stream sequence. The initial conditions were generated by the true random number generators, the MD5 of the mouse positions. We applied the algorithm to encrypt the color image, and got the satisfactory level security by two measures: NPCR and UACI. When the collision of MD5 had been found, we combined the algorithm with the traditional cycle encryption to ensure higher security. The ciphered image is robust against noise, and makes known attack unfeasible. It is suitable for application in color image encryption.