Chaotic Random Number Generator Research Articles

New chaos function of composition function Gauss map and dyadic transformation map for digital image encryption

Encryption algorithms mostly use key-streams generated from random number generators. Several recent studies have shown that the random number generator used is a chaos function. In this paper, a new chaos function will be developed which can be used as a chaotic random number generator. The development is carried out by forming a new chaos function using the function composition method. The function that is composed is the Gauss Map function against the Dyadic Transformation Map. The results of the new chaos function are chaotic, this is based on the results of the analysis obtained from the results of the bifurcation diagram, the Lyapunov Exponent and the National Institute of Standard Technologies Test (NIST) standard randomness test. The results of the bifurcation diagram show that the density is for the value of α ∈ [−30,0] and has periodic properties to choose the values of β ∈ [−1.02, −0.75], β ∈ [−0.60, −0.30], β ∈ [0.10, 0.25] and β ∈ [0.55, 0.75]. A positive value of Lyapunov Exponential diagram will be employed alpha equal to negative value (α < 0). The results of the NIST standard randomness test with values x0 = 0.9, α = −15 and β = 0.7 resulted in 100 % passing the test (16 tests).

A novel image encryption algorithm based on least squares generative adversarial network random number generator

In cryptosystems, the generation of random keys is crucial. The random number generator is required to have a sufficiently fast generation speed to ensure the size of the keyspace. At the same time, the randomness of the key is an important indicator to ensure the security of the encryption system. The chaotic random number generator has been widely used in cryptosystems due to the uncertainty, non-repeatability, and unpredictability of chaotic systems. However, chaotic systems, especially high-dimensional chaotic systems, have slow calculation speed and long iteration time. This caused a conflict between the number of random keys and the speed of generation. In this paper, we introduce the Least Squares Generative Adversarial Networks(LSGAN)into random number generation. Using LSGAN’s powerful learning ability, a novel learning random number generator is constructed. Six chaotic systems with different structures and different dimensions are used as training sets to realize the rapid and efficient generation of random numbers. Experimental results prove that the encryption key generated by this scheme can pass all randomness tests of the National Institute of Standards and Technology (NIST). Hence, our result shows that LSGAN has the potential to improve the quality of the random number generators. Finally, the results are successfully applied to the image encryption scheme based on selective scrambling and overlay diffusion, and good results are achieved.

Low power and high-speed FPGA implementation for 4D memristor chaotic system for image encryption

In this paper, we proposed a novel low power and high-speed FPGA implementation of the 4D memristor chaotic system with cubic nonlinearity based on Xilinx System Generator (XSG) model. Firstly, a pseudo-random number generator based on the proposed XSG FPGA implementation of the proposed 4D memristor chaotic system which implemented into Xilinx Spartan-6 X6SLX45 board with 32 fixed-point format. The aim of the FPGA implementation is increasing the frequency of the memristor chaotic random number generators. The FPGA implementation of the memristor chaotic system results show that the new design approach achieves a maximum frequency of 393 MHz and dissipates 117 m watt. The standard fifteen randomization tests are used to measure the quality of the proposed pseudo-random number generator based on the 4D memristor chaotic system and it gives an excellent randomization analysis. Also, the gray image encryption scheme based on the 4D memristor chaotic system has been introduced. The proposed cryptosystem has a large keyspace, very low correlation values, high entropy which is much closer to the ideal entropy value, a high number of pixels change rate and high unified average changing intensity values. The results and security analysis of the proposed encryption scheme demonstrate that the investigated encryption approach can protect high speed and high security against various attack.

Cryptanalysis of a random number generator based on continuous‐time chaos

This study presents the algebraic cryptanalysis of a continuous-time chaotic random number generator (RNG) based on a Zhongtang chaotic system. The chaos-based RNG provides key values for logic encryption, round key formation and the substitution box (S-box) generation steps in AES (advanced encryption standard). In this study, an attack method is proposed to exploit the weaknesses of the chaos-based RNG used in this cryptographic system. By observing a chaotic state variable and knowing the structure of the target RNG, output bit sequence of the target RNG is reproduced by a clone RNG used in master–slave synchronisation scheme. The feasibility of the attack system is confirmed through simulation and numerical results. Through this attack method, the same S-box parameters and key values can be obtained which can be used for decryption of the proposed encryption algorithm. This study targets a specific continuous-time chaos-based RNG and the associated cryptographic system as a case study. However, the cryptanalysis method described in this study is applicable to any continuous-time or discrete-time chaos-based RNGs. Therefore, this study highlights the security vulnerabilities of chaos-based RNGs and emphasises that deterministic chaos phenomena itself should not be considered as the actual source of randomness.

A novel data hiding method by using a chaotic system without equilibrium points

In this paper, we investigate how special is the choice of parameter values in the three-dimensional nonlinear system, proposed by Akgul and Pehlivan (2016), in producing a system, which exhibits chaos but has no real equilibrium states. Also, a data hiding method with a three-dimensional chaotic system without equilibrium point, developed by Akgul and Pehlivan, is realized. Numerous encryption studies have recently been made based on chaos. Encryption processes that are used with chaos bring about some security deficiencies in some cases. Steganography, unlike encryption studies, helps communicate the secret data by hiding it in an innocent-looking cover in order to avoid detection by third parties at first glance. In this work, a novel chaos-based data hiding method that hides an image with a different color into color images is proposed. Via the proposed method, data are hidden in bit spaces with the help of the chaotic random number generator (RNG). The generated random numbers are found with a chaotic system without equilibrium point, which is new in the literature. Shilnikov method cannot be applied to find whether the system is chaotic or not because they cannot have homoclinic or heteroclinic orbits. Thus, it can be useful in several engineering applications, especially in chaos-based cryptology and coding information. In the study, bits are hidden in pixels indicated by numbers generated by RNG. As the order of the hiding process is made randomly on a chaotic level, it has made data hiding algorithm stronger. The proposed method hides the data in cover image in such a way that it cannot be easily detected. Furthermore, the proposed method has been evaluated with steganalysis methods and image distortion measurement method PSNR. The chaos-based steganography method realized here has produced more best results in image distortion measurement method PSNR than other studies in the literature.

Improving the Security of Wireless Communications on High-Speed Trains by Efficient Authentication in SCN-R

Recently, we have witnessed the remarkable development in high-speed railways around the world. To provide a robust and fast wireless network for the onboard passengers, we have earlier proposed smart collaborative networking for railways (SCN-R). In the realization of SCN-R, its security is challenged by potential exploitation of authentication vulnerabilities since traditional authentication mechanisms are unsuitable for scenarios with fast moving objects due to their complex and relatively timely operations. In this paper, we address this issue by proposing a new efficient authentication mechanism, which is based on a new design of chaotic random number generator (RNG). Comparing with the recent proposal relying on the precise boundaries of chaotic map state spaces, our RNG uses two logistic maps to avoid the time-consuming boundary location process. The proposed authentication mechanism uses the RNG to generate and validate the one-time password (OTP). To support different authentication applications, different lengths of OTPs can be used to differentiate and identify the applications. We have implemented our proposed authentication mechanism under real-world conditions, with results showing the feasibility and effectiveness of our authentication mechanism.

A probabilistic image authentication method based on chaos

Fragile watermarking methods have been used as active image authentication methods. These methods must have capabilities like high capacity, high visual quality, high image authentication ability and image recovery capability. Many of the fragile watermarking methods suggested in the literature do not provide all of these capabilities. In this article, a new probabilistic image authentication method with high capacity, high visual quality, high image authenticity ability and image recovery capability is proposed. Chaotic pseudo random number generators, a new watermark generation network which similar to neural network, modulo based watermark embedding functions, modulo based watermark extraction functions, tamper detection algorithm and perceptual hash based image recovery algorithm are utilized for creating a new probabilistic image authentication method in this article. The proposed method is a block based authentication method and 3 × 3 size of overlapping neighborhood blocks are used in this method. The proposed watermark generation network uses symmetric pixels as inputs and weights to generate predicted pixel. In this step, modulo operator and random numbers are used for calculating embeddable value. Owing to chaotic random number generator, the proposed method gains probabilistic and nonlinear structure. To generate random number, logistic map is used as random number generator in the proposed image watermarking method. Then, a modulo based watermark embedding function is used for embedding embeddable value (generated watermark). In the watermark extraction step, modulo operator is used. If the predicted value differs from the extracted value, tamper detection is performed. Otherwise, image authentication is success. A new image recovery algorithm is proposed in this method. This algorithm provides image recovery for tampered areas with high visual quality. The proposed image watermarking method can authenticate grayscale and color images. The experimental results demonstrated that, the proposed method has high payload capacity, high visual quality and high image authentication ability.

A simple chaotic circuit with a hyperbolic sine function and its use in a sound encryption scheme

In this work, one of the most simple chaotic autonomous circuits, which has been reported in the literature, is presented. The proposed circuit, that belongs to jerk systems family, is described mathematically by a 3-D dynamical system with only five terms, and it has only one nonlinear term, which is the hyperbolic sine term implemented with two antiparallel diodes. This new jerk system presents interesting chaotic phenomena, such as coexisting attractors and antimonotonicity. Also, as an application of the proposed system a sound encryption scheme that is based on a random number generator, which is implemented with the jerk system, is presented. The practical usefulness of the proposed simple chaotic jerk circuit is confirmed from the results of NIST-800-22 tests of the chaotic random number generator, as well as from the successful sound encryption and decryption process.

DESIGN OF CHAOTIC MOBILE COMMUNICATION SYSTEM USING ARDUINO

Security and secrecy are some of the significant concerns in the communications world. In the last years, several encryption techniques had been proposed to improve the secrecy of the information transition. Chaos-based encryption techniques are being exceedingly studied as part of the because of the random-look nature and very unpredictable of the chaotic signals. In this study, a digital-based mobile communication system was proposed that uses chaotic encryption code, Arduino platforms was utilized for this work because it possess an open-source prototyping platform, software and hardware very accessible and extremely flexible to be customized and extended. The ASCII code of input message signal was encrypted using a Chaotic Random Number Generator it will send to the receiver side through mobile GSM system. In the receiver side, the ASCII coded message was decrypted using the same Chaotic Random Number Generator code for decryption. The target of this system is to make a more security based on the mobile communication system, the obtained results of this study confirm a secure system for sending and receiving SMS-based on the mobile communication system.

A New Approach to Analysis and Design of Chaos-Based Random Number Generators Using Algorithmic Converter

This paper presents a new approach to analysis and design of ADC-based random number generators. To this end, different full-bit and half-bit redundant stages of algorithmic converter are used to design chaotic maps. It is shown that, in the redundant and nonredundant structures, output probability density function of the converter stages and their related chaotic functions always converge to uniformity. It is demonstrated that residues become independent and uniformly distributed. This fact leads to the randomness and uniformity of distribution of the random number generator output bits. Moreover, it is shown that some common chaotic maps that are employed in chaotic random number generators can be implemented using nonredundant and half-bit redundant stages of algorithmic converter. In this way, the capability of ADC-based generators in designing chaotic maps and producing random number sequences is illustrated. The validity of the proposed chaos-based random number generator is confirmed using NIST statistical tests even in the presence of nonidealities in algorithmic converter. Since the ADCs are mixed-signal integrated circuits and can be used in high-speed applications, the ADC-based random number generator has high throughput and is easily embeddable in all analog and digital circuits.

A novel chaos‐based encryption algorithm over TCP data packet for secure communication

AbstractIn this article, a new algorithm that can encrypt data on TCP data segment by using a novel chaotic random number generator was developed. First of all, dynamic analyses of the chaotic system to be used were made and the original pseudo‐random number generator (PRNG) with a new approach was designed. Key series produced by PRNG was tested on NIST and passed all the tests. The chaos‐based encryption here was performed on TCP, one of the most fundamental protocols in data communication. Following this, TCP data segments were encrypted by the sender on bit base with key series produced by PRNG, and then they were decrypted by the receiver. Security level of the chaos‐based encryption carried out here was tested with histogram, its key length, key sensitivity and entropy method. Memory and time usages were measured in performance analysis. So as to reveal the performance of the encryption, memory usage, encryption and decryption times were analyzed by comparison on different security algorithms. According to tests and analyses results, this chaos‐based encryption has a high level of performance and security; and it is an original study that can be used in real‐time implementations with TCP protocol. Copyright © 2016 John Wiley & Sons, Ltd.

Analysis of chaotic behavior in pipelined analog to digital converters

This paper presents a new approach to analysis of chaotic behavior in pipelined analog to digital converters. To this end, the fundamental theorem for function of a random variable is exploited and the propagation of the output pdf of chaotic maps in successive stages of pipelined converter is shown. It is illustrated that 1-bit stage of this converter can be used to implement the Bernoulli map, and also the 2k-way Bernoulli shift map can be implemented using k×1-bit stages or one k-bit stage. It is revealed that in the half-bit redundant structure, after a sufficiently large number of cycles, residue density becomes concentrated in the center half of the stage full-scale range. In this way, the 1.5-bit stage characteristic will be fully equivalent to the common chaotic map that is employed to generate random number sequences. By applying the proposed approach to the joint density of residue stages, it is shown that residues become independent and uniformly distributed. This feature is used to design multi bit chaotic random number generator using full-bit and half-bit redundant pipelined ADC structure. The validity of the proposed random number generator is confirmed by passing all NIST statistical tests even in the presence of nonidealities.

Research on the quantifications of chaotic random number generators

It has been proved that Local-Period phenomena widely exist in any chaotic binary sequences. Among the reasons of Local-Period phenomena, the quantifications of chaotic binary random number generators are the key factors. This paper proposed that different quantifications could make the generated sequences from the same chaotic real value sequence appear different randomness. Moreover, the simulation results illustrated that for the same logistic real value sequence quantified by different quantifications, such as L-bits quantification, C-threshold quantification and Region quantification, Local-Period phenomena are located in different places by binary sequence period detection BSPD detecting method. Meanwhile, statistical data inferred that C-threshold quantification has less effect on the randomness of original chaotic real value sequence.

Exploring pseudo- and chaotic random Monte Carlo simulations

Computer simulations are an increasingly important area of geoscience research and development. At the core of stochastic or Monte Carlo simulations are the random number sequences that are assumed to be distributed with specific characteristics. Computer-generated random numbers, uniformly distributed on (0, 1), can be very different depending on the selection of pseudo-random number (PRN) or chaotic random number (CRN) generators. In the evaluation of some definite integrals, the resulting error variances can even be of different orders of magnitude. Furthermore, practical techniques for variance reduction such as importance sampling and stratified sampling can be applied in most Monte Carlo simulations and significantly improve the results. A comparative analysis of these strategies has been carried out for computational applications in planar and spatial contexts. Based on these experiments, and on some practical examples of geodetic direct and inverse problems, conclusions and recommendations concerning their performance and general applicability are included.

Chaotic Random Number Generator and It’s Evaluation by Genetic Algorithm

Chaotic Random Number Generator and It’s Evaluation by Genetic Algorithm

Design of image group code based on chaotic systems

Chaotic capability will decline after digitalizing chaotic system.Aiming at this question,a chaotic random number generator based on Logistic mapping was presented in this paper,Piecewise Linear Chaotic Mapping(PLCM) and shift mapping defined on(0,1).Through the iterations of different chaotic systems,the generating random sequence was confirmed by four trajectories.Therefore,it has better random characteristic and longer cycle under finite precision.A group image encryption algorithm based on this chaotic random number generator is also presented.This algorithm has stronger robustness.The restore effect is also well while the encryption image is partly damaged or deleted.This algorithm has more control parameters and a large space of keys.It is sensitive to key and it has excellent performance against attacks.