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In recent decades, image encryption, as one of the significant information security fields, has attracted many researchers and scientists. However, several studies have been performed with different methods, and novel and useful algorithms have been suggested to improve secure image encryption schemes. Nowadays, chaotic methods have been found in diverse fields, such as the design of cryptosystems and image encryption. Chaotic methods-based digital image encryptions are a novel image encryption method. This technique uses random chaos sequences for encrypting images, and it is a highly-secured and fast method for image encryption. Limited accuracy is one of the disadvantages of this technique. This paper researches the chaos sequence and wavelet transform value to find gaps. Thus, a novel technique was proposed for digital image encryption and improved previous algorithms. The technique is run in MATLAB, and a comparison is made in terms of various performance metrics such as the Number of Pixels Change Rate (NPCR), Peak Signal to Noise Ratio (PSNR), Correlation coefficient, and Unified Average Changing Intensity (UACI). The simulation and theoretical analysis indicate the proposed scheme’s effectiveness and show that this technique is a suitable choice for actual image encryption.

Random and pseudo-random number and bit sequence generators with a uniform distribution law are the most widespread and in demand in the market of pseudo-random generators. Depending on the specific field of application, the requirements for their implementation and the quality of the generator’s output sequence change. In this article, we have optimized the structures of the classical additive Fibonacci generator and the modified additive Fibonacci generator when they work together. The ranges of initial settings of structural elements (seed) of these generators have been determined, which guarantee acceptable statistical characteristics of the output pseudo-random sequence, significantly expanding the scope of their possible application, including cybersecurity. When studying the statistical characteristics of the modified additive Fibonacci generator, it was found that they significantly depend on the signal from the output of the logic circuit entering the structure. It is proved that acceptable statistical characteristics of the modified additive Fibonacci generator, and the combined generator realized on its basis, are provided at odd values of the module of the recurrent equation describing the work of such generator. The output signal of the combined generator has acceptable characteristics for a wide range of values of the initial settings for the modified additive Fibonacci generator and the classic additive Fibonacci generator. Regarding the use of information security, it is worth noting the fact that for modern encryption and security programs, generators of random numbers and bit sequences and approaches to their construction are crucial and critical.

In the present work, we introduce and study the notion of statistical probability convergence for sequences of random variables as well as the idea of statistical convergence for sequences of real numbers, which are defined over a Banach space via the product of deferred Cesàro and deferred weighted summability means. We first establish a theorem presenting aconnection between them. Based upon our proposed methods, we then prove a Korovkin-type approximation theorem with algebraic test functions for a sequence of random variables on a Banach space, and demonstrate that our theorem effectively extends and improves most (if not all) of the previously existing results (in classical as well as in statistical versions). Furthermore, an illustrative example is presented here by means of the generalized Meyer–König and Zeller operators of a sequence of random variables in order to demonstrate that our established theorem is stronger than its traditional and statistical versions. Finally, we estimate the rate of the product of deferred Cesàro and deferred weighted statistical probability convergence, and accordingly establish a new result.

Realization of modern telecommunication systems is inconceivable without use of different binary sequences. In this paper, an overview of random binary sequences used in different telecommunication systems is given. Basic principles of pseudorandom, chaotic, and true random sequence generation are presented, as well as their application in telecommunications in respect to advantages and drawbacks of the same. Moreover, particular scheme for true random binary sequence generation is given, as well as results of randomness assessment obtained by NIST statistical test suite. Finally, short insight into importance of random binary sequence in secure communications is given.

In this paper, we investigate the use of low-discrepancy sequences to generate an initial population for population-based optimization algorithms. Previous studies have found that low-discrepancy sequences generally improve the performance of a population-based optimization algorithm. However, these studies generally have some major drawbacks like using a small set of biased problems and ignoring the use of non-parametric statistical tests. To address these shortcomings, we have used 19 functions (5 of them quasi-real-world problems), two popular low-discrepancy sequences and two well-known population-based optimization methods. According to our results, there is no evidence that using low-discrepancy sequences improves the performance of population-based search methods.

Electrochemical impedance spectroscopy (EIS) is a measurement method widely used for non-destructive analysis and diagnostics in various electrochemical fields. From the measured dependence of the battery impedance on the frequency, it is possible to determine the parameters of various equivalent electrical circuit models of the battery. The conventional method of battery measurement using single-sine EIS is currently one of the most widely used methods for the analysis of lithium-ion batteries. However, its most significant disadvantage is the relatively long measurement time. For this reason, there is a growing demand for faster methods using fast-Fourier transform or pseudo-random sequences. A description of various EIS methods applications is provided in this paper. Graphical abstract

A pseudo-random signal generator based on 0.5μm CMOS technology is presented, and it is applied for an auto-zero operational amplifier. The generator circuit includes a linear feedback shift register for generating pseudo-random sequences, and a multi-level counter module for counting the system clock pulses. A group of pseudo-random codes generated by the linear feedback shift register are as the initial value of the counter. When the counter reaches the maximum value, the output of the counter will control the output signal to flip. At the same time, a new group of the pseudo-random code will reset the counter again, and finally generate a square wave signal whose frequency varies randomly. The generator circuit is simulated and verified. The simulation results show that the frequency of the output signal can vary from 2 kHz to 4 kHz with random characteristic. The generated pseudo-random signal can be used for the switching clock control of the auto-zero operational amplifier offset calibration circuit, so that the switching glitch of the auto-zero op-amp is random, which can significantly reduce the harmonics in the output signal of the op-amp.

The understanding of eco-evolutionary dynamics, and in particular the mechanism of coexistence of species, is still fragmentary and in need of test bench model systems. To this aim we developed a variant of SELEX in vitro selection to study the evolution of a population of ∼10 15 single-strand DNA oligonucleotide ‘individuals’. We begin with a seed of random sequences which we select via affinity capture from ∼10 12 DNA oligomers of fixed sequence (‘resources’) over which they compete. At each cycle (‘generation’), the ecosystem is replenished via PCR amplification of survivors. Massive parallel sequencing indicates that across generations the variety of sequences (‘species’) drastically decreases, while some of them become populous and dominate the ecosystem. The simplicity of our approach, in which survival is granted by hybridization, enables a quantitative investigation of fitness through a statistical analysis of binding energies. We find that the strength of individual resource binding dominates the selection in the first generations, while inter- and intra-individual interactions become important in later stages, in parallel with the emergence of prototypical forms of mutualism and parasitism.

This paper introduces a novel pseudo-random sequence generator, applicable across all uses of pseudo noise (PN)-sequence. The proposed generator, coined as the circular pseudo-random signal generator, embodies a unique fusion of graphical representation and mathematical modeling. The cornerstone of this method is its capability to offer variable configurations in pseudo-random sequence generation, enabling the adaptive operation of the pseudo-random sequence between the transmitter and the receiver. Uniquely, the circular pseudo-random sequence generator can generate pseudo-random sequences of varying lengths, with practical implementation feasible through multiple methodologies, including microcontrollers or field-programmable gate array (FPGA) technology. Consequently, the paper endeavors to elucidate the mathematical model of generation, supplemented with illustrative examples, and demonstrate the real-world implementation using FPGA technology. With broad applicability, this sequence generator is well-suited to all applications requiring such a generator, notably in security applications and pilot generations.

The recent advancement in multimedia technology has undoubtedly made the transmission of objects of information efficiently. Interestingly, images are the prominent and frequent representations communicated across the defence, social, private and aerospace networks. Image ciphering or image encryption is adopted as a secure medium of the confidential image. The utility of soft computing for encryption looks to offer an uncompromising impact in enhancing the metrics. Aligning with neural networks, a Hopfield attractor-based encryption scheme has proposed in this work. The parameter sensitivity, random similarity and learning ability have been instrumental in choosing this attractor for performing confusion and diffusion. The uniqueness of this scheme is the achievement of average entropy of 7.997, average correlation of 0.0047, average NPCR of 99.62 and UACI of 33.43 without using any other chaotic maps, thus proposing attack-resistant image encryption against attackable chaotic maps.