Enhancing logistic chaotic map for improved cryptographic security in random number generation

This paper experimentally investigates the effect of nine chaotic maps on the performance of two Particle Swarm Optimization (PSO) variants, namely, Random Inertia Weight PSO (RIW‐PSO) and Linear Decreasing Inertia Weight PSO (LDIW‐PSO) algorithms. The applications of logistic chaotic map by researchers to these variants have led to Chaotic Random Inertia Weight PSO (CRIW‐PSO) and Chaotic Linear Decreasing Inertia Weight PSO (CDIW‐PSO) with improved optimizing capability due to better global search mobility. However, there are many other chaotic maps in literature which could perhaps enhance the performances of RIW‐PSO and LDIW‐PSO more than logistic map. Some benchmark mathematical problems well‐studied in literature were used to verify the performances of RIW‐PSO and LDIW‐PSO variants using the nine chaotic maps in comparison with logistic chaotic map. Results show that the performances of these two variants were improved more by many of the chaotic maps than by logistic map in many of the test problems. The best performance, in terms of function evaluations, was obtained by the two variants using Intermittency chaotic map. Results in this paper provide a platform for informative decision making when selecting chaotic maps to be used in the inertia weight formula of LDIW‐PSO and RIW‐PSO.

Communication is essential to every society, and securely exchanging data are critical in the age of digital data. The image has been the center of interest for security; chaotic maps image encryption become widely used in recent years. In our study, authors assessed the pixel rearrangement (permutation) and pixel dissemination (diffusion) stage used in cipher image established on designed scheme Pseudo-random number Generators (PRNGs) and Logistic chaotic map. Logistic maps used to generate seed value for PRNG and two-permutation stage and PRNGs used in diffusion operation. The proposed design through experimental tests demonstrate decent Statistical output, and high security for our image encryption schema, Our PRNGs passed NIST SP 800-22, and TestU01 practical randomness test suggests PRNGs have suitable statistical property.

In this paper, a novel one dimensional chaotic map $ K(x) = \frac{\mu x(1\, -x)}{1+ x} $, $ x\in [0, 1], \mu > 0 $ is proposed. Some dynamical properties including fixed points, attracting points, repelling points, stability and chaotic behavior of this map are analyzed. To prove the main result, various dynamical techniques like cobweb representation, bifurcation diagrams, maximal Lyapunov exponent, and time series analysis are adopted. Further, the entropy and probability distribution of this newly introduced map are computed which are compared with traditional one-dimensional chaotic logistic map. Moreover, with the help of bifurcation diagrams, we prove that the range of stability and chaos of this map is larger than that of existing one dimensional logistic map. Therefore, this map might be used to achieve better results in all the fields where logistic map has been used so far.

Pseudo random number generators (PRNG) play a key role in various security and cryptographic applications where the performance of these applications is directly related to the quality of generated random numbers. The design of such random number generators is a challenging task. In this paper, we propose an application of Hopfield Neural Networks (HNN) as pseudo random number generator. This is done based on a unique property of HNN, i.e., its unpredictable behavior under certain conditions. We compare the main features of ideal random number generators with those of PRNG based on Hopfield Neural Networks. We use a battery of statistical tests developed by National Institute of Standards and Technology (NIST) to measure the performance, and to evaluate the quality of the proposed Hopfield random number generator.

Very well know discrete time chaotic random number generator used in cryptographic applications is Logistic Map. In this paper, we present the implementation of hybrid random number generator based on Logistic Map on Field Programmable Gate Arrays (FPGA). The numbers generated by the hybrid system have been obtained at 32 bit floating point notation. For the usage of cryptographic applications of obtained numbers, these values have been normalized to 0 and 1. Total 20000 numbers have been generated by hybrid system, and they have been tested according to NIST(National Institute of Standarts and Technology) test suite. According to the test result of the numbers obtained from hybrid system, it has been shown that can be used in cryptography applications.

The current information age demands enormous opportunities, where, the sensitive data and information is being exchanged, analyzed and made use of. It has led to several concerns and challenges, mainly in the areas of information privacy, authentication and integrity. This concern, attracted cryptographers to device more effective methodologies and algorithms to ensure better protection to sensitive information. In this context, the application of chaotic based systems is considered to design a pseudorandom sequence generator, which is used as a key stream generator in the additive Stream Cipher system. Chaotic map is a mathematic function that generates highly nonlinear and random real sequence which is very sensitive to initial conditions. In this view, this work focusses on the study of Logistic map, considered from a bunch of various Chaotic functions available [1], [2]. Chaotic real sequence is binarized using a new binarization algorithm using Linear Feedback Shift Register (LFSR), which is designed in such a way that the randomness of Chaotic real sequence is not affected as far as possible. Using Logistic map, about 50 sequences are generated each of length ≥ 106. To ensure the randomness of binary sequences, NIST(National Institute of Standards and Technology) test is used. It is observed that, all the sequences have strictly passed most of the NIST tests with an average passing proportion ≥ 0.87. These sequences are used as key sequences in image encryption and decryption. It is interesting to observe that, encrypted image does not contain any residual information. This result is cross verified by plotting the Histogram, computing the Correlation coefficient and Entropy of the output images. It is observed that, Histograms are almost flat indicating the equiprobable distribution of pixels. Also, Entropy of the encrypted image is close to 8 and Correlation coefficient value is very negligible indicating that neighboring pixels are heavily uncorrelated. As the key sequence based on Chaotic functions is sensitive to initial conditions, the sequence generated will be highly nonlinear and random which encourages one to use in cryptographic applications.

Pseudo random number generators (PRNGs) are one of the most important components in security and cryptography applications. We propose an application of Hopfield Neural Networks (HNN) as pseudo random number generator. This research is done based on a unique property of HNN, i.e., its unpredictable behavior under certain conditions. Also, we propose an application of Fuzzy Hopfield Neural Networks (FHNN) as pseudo random number generator. We compare the main features of ideal random number generators with our proposed PRNGs. We use a battery of statistical tests developed by National Institute of Standards and Technology (NIST) to measure the performance of proposed HNN and FHNN. We also measure the performance of other standard PRNGs and compare the results with HNN and FHNN PRNG. We have shown that our proposed HNN and FHNN have good performance comparing to other PRNGs accordingly.

The use of random numbers in day-to-day digital life is increasing drastically to make the digital data more secure in various disciplines, particularly in cryptography, cloud data storage, and big data applications. Generally, all the random numbers or sequences are not truly random enough to be used in various applications of randomness, predominantly in cryptographic applications. Therefore, the sequences generated by pseudorandom number generator (PRNGs) are not cryptographically secure. Hence, this study proposes a concept that the diffusion sequences which are used during cryptographic operations need to be validated for randomness, though the random number generator produces the random sequences. This study discusses the NIST, Diehard and ENT test suite results of random diffusion sequences generated by two improved random number generators namely, Enhanced Chaotic Economic Map (ECEM), and Improved Linear Congruential Generator (ILCG).

In this paper, after a short survey describing several known constructions recommended for generating sequences of pseudo-random numbers based on elliptic curves over finite fields of prime order, we propose a method of generating such sequences of points with algorithms driven by a chaotic map. Our construction improves randomness of the sequence generated since it combines good statistical properties of an ECPRNG (Elliptic Curve Pseudo-Random Number Generator) and a CPRNG (Chaotic Pseudo-Random Number Generator). Theoretical analysis shows that periods of the proposed constructions are longer than in the case of the ECPRNG without modulation by a chaotic map. In the second part of the paper we present numerical analysis of the proposed construction to obtain optimal parameters of the generator. We also use some tests from the NIST’s SP 800-22 Statistical Test Suite for Random and Pseudorandom Number Generators for Cryptographic Applications to analyze statistical properties of the proposed constructions for different values of parameters.

Image steganography conceals secret information in a cover image .It is used for secure data transfer. Various LSB (least significant bits) approaches have been used over the years in steganography. This paper proposes a novel technique to improve the conventional LSB technique for image steganography by using pseudo random number generation using Henon chaotic map. The random numbers are used to encrypt the hide image which is embedded in the cover picture. This encryption using pseudo random generator provides sufficient security to the payload as the same set of random numbers cannot be regenerated without knowing the exact random generator function and thus the secret data cannot be retrieved easily. The proposed technique has been tested successfully on various .jpg files and corresponding PSNR values have been calculated.

Advancement of medical imaging in health care sector emerges new challenge of secure image transmission. Security of medical imaging is a prominent issue to keep patients information safe. In this paper an efficient and secure biomedical image encryption algorithm is proposed with two phases of encryption. In the first phase the image has to undergone a random substitution of 20 Amino Acid based Codon with one or more than alternate Codon in the form of triplets using the base DNA code (A, T, C and G) using Linear Congruential Generator. Upshot of the first phase encrypted image is divided into blocks and a logistic map is used to generate a series of unique initial condition and control parameter. Using a random ASCII character as a seed the unique initial conditions for each block is generating some Pseudo Random Number Generator. The seed is encrypted using RSA. Each block is circularly shifted using unique PRNG. These unique initial conditions and control parameters are utilized by a series of Tent Maps to perform block by block confusion in the second phase encryption using XOR operation. Keys used in both the phases are encrypted using AES technique. Proposed method is used to encrypt any biomedical and other images also. All type of security measure such as Differential attack, key space analysis to resist Brute force attack, Correlation analysis, key sensitivity test, resistance to Noise attack and plain text attack along with time analysis has been taken into consideration to test the vulnerability of the proposed algorithm. From the comparative study the proposed method outperform in many aspects than the existing methods.

Recently, due to the initial sensitivity, ergodicity, boundedness, and unpredictability of chaos, it has been widely used in the fields of secure communication, signal processing, chaotic synchronization, etc. Moreover, due to the low complexity of hardware implementation, widespread attention to one-dimensional (1D) chaotic maps has been paid from researchers. However, some existing 1D maps have simple chaotic behaviors and discrete chaotic intervals, which have significantly affected the practical application. To address these shortcomings, this paper proposes a 1D chaotic model based on the absolute value function and the cosine function called the cosine-coupled chaotic model (CCCM). It can use existing 1D chaotic maps as seed maps to construct a series of 1D chaotic maps with continuous chaotic intervals and complex chaotic behaviors. To verify the effectiveness of the CCCM, we first generate three new chaotic maps using the CCCM, and then their chaotic properties are analyzed by using various measures including Lyapunov exponent (LE), sample entropy (SE), correlation dimension (CD), 0-1 test and sensitivity. The experimental results confirm that the new chaotic maps have wider chaotic intervals and more complex chaotic behaviors than the corresponding seed maps and some other advanced chaotic maps. Then we use a field programmable gate array (FPGA) as the hardware platform for simple hardware implementations of the new chaotic maps. And a new pseudo-random number generator (PRNG) is introduced to verify practical applications of the new maps. Finally, experimental results show that the new chaotic maps can be implemented on FPGA and the proposed PRNG has strong random properties.

The Internet advances in the past decade have been upping at a tremendous pace; especially in the fields like medicine, military, and technology, where lot of internet threats have also been raising, at least at the same rate, if not higher. The communication takes place in the form of text, image, voice, and video signals etc. And we deal with more image-based applications. There are many encryption techniques existing-DES, AES, RSA, etc. but they provide less security and are vulnerable to brute force attacks due to factors like small key space, to avoid which, chaos-based encryption was introduced. Chaotic systems are very sensitive to initial conditions and distort the image to beyond reversible state, except with a protection key with which it is encrypted, which is hard to find in such a large key space. In this paper we will discuss image encryption using combined chaos by combining various chaotic maps like logistics map, singer map, tent map, sine map, piecewise map etc. and attempt to compare the results for better combination for encryption.

Chaotic systems are widely used in various aspects such as information security, signal processing, and synchronous control. The structural complexity and the chaotic behavior of chaotic systems are two significant factors affecting their practical applications. In this paper, we propose a universal two-dimensional (2D) absolute-cosine chaotic model (ACCM). The 2D-ACCM is composed of a nonlinear bounded cosine function and an absolute value function. It can construct new chaotic maps with simple structures and complex chaotic behaviors on the basis of existing chaotic systems. To verify the effectiveness of the proposed system, we first choose two existing one-dimensional (1D) chaotic maps and one existing 2D chaotic map as the seed maps of the 2D-ACCM to generate two new maps, respectively. The results of chaotic behavior analysis show that these two new maps have more complex chaotic behavior and wider chaotic ranges than seed maps and some advanced chaotic maps. Then a hardware experiment platform based on a field-programmable gate array (FPGA) is used for the hardware implementation of the new maps. Finally, a simple chaos-based pseudo-random number generator (PRNG) is introduced to show the practical application. The experimental results show that the new maps can be easily implemented on the FPGA and the chaos-PRNGs can generate pseudo-random numbers with excellent randomness.

Classifying study objects into groups is facilitated by fuzzy classifiers based on a set of rules and membership functions. Typically, the characteristics of the study objects are used to establish the criteria for classification. This work arises from the need to design fuzzy classifiers in contexts where real data is scarce or highly random, proposing a design based on statistics and chaotic maps that simplifies the design process. This study introduces the development of a fuzzy classifier, assuming that three features of the population to be classified are random variables. A Mamdani fuzzy inference system and three pseudorandom number generators based on one-dimensional chaotic maps are utilized to achieve this. The logistic, Bernoulli, and tent chaotic maps are implemented to emulate the random features of the target population, and their statistical distribution functions serve as input to the fuzzy inference system. Four experimental tests were conducted to demonstrate the functionality of the proposed classifier. The results show that it is possible to achieve a symmetric and robust classification through simple adjustments to membership functions, without the need for supervised training, which represents a significant methodological contribution, especially because this indicates that designers with minimal experience can build effective classifiers in just a few steps. Real applications of the proposed design may focus on the classification of biomedical signals (sEMG), network traffic, and personalized medical assistance systems, where data exhibits high variability and randomness.