Pseudorandom Number Generator Research Articles

A non-degenerate n-dimensional integer domain chaotic map model with application to PRNG

To address the limitations of existing chaotic maps, we proposed a non-degenerate n-dimensional (n ≥ 2) integer domain chaotic map (nD-IDCM) model that can construct any non-degenerate n-dimensional integer domain chaotic maps. Moreover, we analyzed its chaotic behavior through Lyapunov exponent, and found that the nD-IDCM generates chaotic sequences in the integer domain, which effectively resolves the issue of finite precision effect when implementing existing chaotic maps on computers or digital devices. To verify the effectiveness of nD-IDCM, we presented two instances to demonstrate how the positive Lyapunov exponents can be regulated by manipulating the parameter matrix. Subsequently, we have scrutinized their dynamical behavior using Kolmogorov entropy, sample entropy, correlation dimension and randomness testing via TestU01. Finally, to assess the feasibility of nD-IDCM, we devised a keyed pseudo random number generator (PRNG) based on a 3D-IDCM that can ensure superior randomness and unpredictability. Experimental results indicated that integer domain chaotic maps constructed using nD-IDCM have desirable Lyapunov exponents and exhibit ergodicity within a sufficient larger chaotic range.

Enhancing Smart Communication Security: A Novel Cost Function for Efficient S-Box Generation in Symmetric Key Cryptography

In the realm of smart communication systems, where the ubiquity of 5G/6G networks and IoT applications demands robust data confidentiality, the cryptographic integrity of block and stream cipher mechanisms plays a pivotal role. This paper focuses on the enhancement of cryptographic strength in these systems through an innovative approach to generating substitution boxes (S-boxes), which are integral in achieving confusion and diffusion properties in substitution–permutation networks. These properties are critical in thwarting statistical, differential, linear, and other forms of cryptanalysis, and are equally vital in pseudorandom number generation and cryptographic hashing algorithms. The paper addresses the challenge of rapidly producing random S-boxes with desired cryptographic attributes, a task notably arduous given the complexity of existing generation algorithms. We delve into the hill climbing algorithm, exploring various cost functions and their impact on computational complexity for generating S-boxes with a target nonlinearity of 104. Our contribution lies in proposing a new cost function that markedly reduces the generation complexity, bringing down the iteration count to under 50,000 for achieving the desired S-box. This advancement is particularly significant in the context of smart communication environments, where the balance between security and performance is paramount.

Artificial cerebellum on FPGA: realistic real-time cerebellar spiking neural network model capable of real-world adaptive motor control.

The cerebellum plays a central role in motor control and learning. Its neuronal network architecture, firing characteristics of component neurons, and learning rules at their synapses have been well understood in terms of anatomy and physiology. A realistic artificial cerebellum with mimetic network architecture and synaptic plasticity mechanisms may allow us to analyze cerebellar information processing in the real world by applying it to adaptive control of actual machines. Several artificial cerebellums have previously been constructed, but they require high-performance hardware to run in real-time for real-world machine control. Presently, we implemented an artificial cerebellum with the size of 104 spiking neuron models on a field-programmable gate array (FPGA) which is compact, lightweight, portable, and low-power-consumption. In the implementation three novel techniques are employed: (1) 16-bit fixed-point operation and randomized rounding, (2) fully connected spike information transmission, and (3) alternative memory that uses pseudo-random number generators. We demonstrate that the FPGA artificial cerebellum runs in real-time, and its component neuron models behave as those in the corresponding artificial cerebellum configured on a personal computer in Python. We applied the FPGA artificial cerebellum to the adaptive control of a machine in the real world and demonstrated that the artificial cerebellum is capable of adaptively reducing control error after sudden load changes. This is the first implementation and demonstration of a spiking artificial cerebellum on an FPGA applicable to real-world adaptive control. The FPGA artificial cerebellum may provide neuroscientific insights into cerebellar information processing in adaptive motor control and may be applied to various neuro-devices to augment and extend human motor control capabilities.

МЕТОДИ ОЦІНКИ ВІДПОВІДНОСТІ ПСЕВДОВИПАДКОВОЇ ПОСЛІДОВНОСТІ ДО ВИПАДКОВОГО РОЗПОДІЛУ В ЗАДАЧАХ АВТОМАТИЗАЦІЇ, КІБЕРБЕЗПЕЦІ, КОМП’ЮТЕРНО-ІНТЕГРОВАНИХ ТЕХНОЛОГІЯХ ТА НЕРУЙНІВНОМУ КОНТРОЛІ

Creation of methods for determining the degree of closeness of a given pseudorandom sequence to a random distribution is a very relevant task in many fields where pseudorandom numbers are used. For example, in cryptography it is important that pseudorandom sequences are unpredictable and have the properties of random numbers. Methods for determining proximity to a random distribution help in assessing the quality of such sequences and identifying flaws in them. In scientific research and engineering projects, pseudorandom numbers are used to model complex systems and simulate random phenomena. It is important to have a means of determining how well such numbers reproduce a random process. In statistics, it is important that pseudorandom sequences meet the requirements of various statistical properties. Methods of determining proximity to a random distribution help in evaluating the properties of these sequences. In software engineering and other fields, it is important to test the quality of pseudorandom number generators to avoid vulnerabilities and flaws in programs. Thus, the development and improvement of methods for determining the degree of closeness of pseudorandom sequences to a random distribution is an urgent task with important practical applications.

Pseudo Random Number Generator Based on Cellular Automata with Self Organized Criticality

Pseudo Random Number Generator Based on Cellular Automata with Self Organized Criticality

Entropy Sources from Tunnelling in Standard CMOS Structures

Pseudo-random number generators are predominantly utilised as entropy sources in encryption and seeding processes, however, they are deterministic by nature. This paper presents the analysis and design methodology of an on-chip quantum noise source that may suitably be used as an entropy source in true random number generators. Quantum tunnelling is achieved through the strong biasing of a MOS structure to generate gate-referred shot noise. Structures are fabricated in a commercial 40 nm process and the sampled noise is tested against the NIST SP800-90B and SP800-22 test suites, showing a maximal entropy of 0.985 at a bias current of 1500 µA with a consistent pass rate across all NIST tests.

Dynamic Analysis and Circuit Design of a New 3D Highly Chaotic System and its Application to Pseudo Random Number Generator (PRNG) and Image Encryption

Dynamic Analysis and Circuit Design of a New 3D Highly Chaotic System and its Application to Pseudo Random Number Generator (PRNG) and Image Encryption

On the Efficiency of Generic, Quantum Cryptographic Constructions

One of the central questions in cryptology is how efficient generic constructions of cryptographic primitives can be. Gennaro, Gertner, Katz, and Trevisan [SIAM J. of Compt., 2005] studied the lower bounds of the number of invocations of a (trapdoor) one-way permutation in order to construct cryptographic schemes, e.g., pseudorandom number generators, digital signatures, and public-key and symmetric-key encryption. Recently, quantum machines have been explored to _construct_ cryptographic primitives other than quantum key distribution. This paper studies the efficiency of _quantum_ black-box constructions of cryptographic primitives when the communications are _classical_. Following Gennaro et al., we give the lower bounds of the number of invocations of an underlying quantumly-computable quantum-one-way permutation when the _quantum_ construction of pseudorandom number generator and symmetric-key encryption is weakly black-box. Our results show that the quantum black-box constructions of pseudorandom number generator and symmetric-key encryption do not improve the number of invocations of an underlying quantumly-computable quantum-one-way permutation.

Complexity enhancement and grid basin of attraction in a locally active memristor-based multi-cavity map

The complexity of memristive chaotic systems determines whether it is suitable for applications in different subjects. To enhance complexity both in performance and diversity, this article first proposes a discrete model of locally active memristor (LAM) and conceives a three-dimensional memristive multi-cavity map by coupling LAM with the existing sine and cosine modulation (SCM) map. This map is named LAM-SCM map and has numerous independent fixed points with different stabilities. Numerical simulations reveal the memristive parameters-relied lossless displacement and self-shift of multi-cavity attractors, indicating the dynamical effects of LAM on the existing SCM map. The initial-relied dynamics distributions are disclosed by grid basins of attraction, showing the emergence of initial-boosting coexistence. Besides, the performance comparisons verify the superiority of LAM-SCM map over the existing SCM map. Finally, a hardware platform has been developed on FPGA to implement the LAM-SCM map and the captured attractors validate the numerical results. On this basis, we devise a 32-bit pseudorandom number generator (PRNG) based on chaos and implement it on the FPGA-based hardware platform to obtain high-speed and reconfigurable pseudorandom numbers. The results show that the proposed map has enhanced chaos complexity and rich dynamics diversity, which ensures the availability of hardware PRNG.

Enhancing copyright protection with Hadamard transform-based blind digital watermarking using the cycling chaos system

The network's ease of use has brought a copyright dilemma for some multimedia works. It is consequently necessary to develop a safe digital watermarking technology to guarantee the protection of digital work's copyright. The proposed method addresses the pressing need for robust blind digital watermarking technology to safeguard the copyrights of multimedia works in the face of the accessibility provided by modern networks. Two approaches are presented in our research paper. First, a blind Hadamard transform-based method is proposed, leveraging the energy concentration concept inherent in the transform. This technique embeds watermarks into the highest energy coefficients of color host images in the transform domain. Notably, watermark extraction is achieved without accessing the original data. Extensive simulation tests validate the efficacy of this method. Second, we have explored the burgeoning field of chaotic systems in watermarking. An LSB-based strategy, termed the cycling chaos algorithm, is introduced. This approach seamlessly integrates data, into color images using the least significant bits. It employs a cycling chaos function to generate a key for a pseudorandom number generator, which, in turn, determines the intensity and pixel positions for storing privileged data in the original image. Through simulation trials, the significant impact of this method on various performance metrics is demonstrated. These contributions aim to not only address immediate copyright protection challenges but also inspire further exploration and advancement in digital watermarking.

RESEARCH OF ALGORITHMS FOR SEARCHING PRIMITIVE ELEMENTS OF A FINITE FIELD OF HIGH ORDER

One of the most important unsolved and notoriously difficult problems in computational finite field theory is the development of a fast algorithm for constructing primitive roots in a finite field. It is known that for many applications, instead of a primitive root, just an element of high multiplicative order is sufficient. Such applications include, but are not limited to, cryptography, coding theory, pseudorandom number generation, and combinatorial schemes. Explicit constructions of high-order elements usually rely on combinatory methods that can provide a provable lower bound on the order, but this does not compute the exact order. Its execution usually implies knowledge of the factorization of the order. Ideally, we should be able to get a primitive element for any finite field in a reasonable amount of time. However, if the simple factorization of the group order is unknown, it is difficult to achieve the goal. Thus, we set the task of constructing an element, probably of a high order. This article discusses various algorithms that find a high-order element for general or special finite fields. This work also represents another contribution to the theory of Gauss periods over finite fields and their generalizations and analogues, which have already proven their usefulness for a number of different applications.

Enhancing Data Protection through Advanced Encryption or Improving Data Security with Advanced Encryption

The protection of information content is becoming a key concern with the recent exponential growth of digital data interchange over computer networks. Numerous security vulnerabilities can readily jeopardize the information sent over a network. An enhanced modification for the Advanced Encryption Standard (AES) algorithm is proposed and implemented using an additional key that generated using a linear feedback shift register (LFSR), which provides an efficient technique to pseudo random number generation and also reduces the number of rounds. Cryptography plays a crucial role in ensuring the security of digital data transmission over these unsafe networks. When compared to the original AES algorithm result, the suggested technique produces the expected results for several data types, including text, images, It is more important than ever to strengthen data protection procedures in an era of rising cyber dangers and growing reliance on digital data. A thorough framework for "Enhancing Data Protection through Advanced Encryption" (EDPAE) is introduced in this study. The project's goal is to protect sensitive data by utilizing state-of-the-art encryption techniques in response to the ever-changing cyber security scenario. In addition, the project places a strong emphasis on how to seamlessly incorporate advanced encryption into current data storage and communication systems in order to minimize interference with user operations and greatly improve overall security posture. In order to guarantee the secure creation, distribution, and storage of encryption keys and to reduce potential risks related to key compromise, key management features are addressed.

Efficient spectral tests for multiple recursive generators

. Large-order maximum-period Multiple Recursive Generators (MRGs) have become popular in the area of computer simulation. They have the nice properties of high-dimensional equi-distribution, generating efficiency, long period, and portability. The spectral test is a commonly used criterion for ranking pseudo-random number generators. Procedures for computing the spectral test values of MRGs are available in the literature but may not be efficient when the order of the MRG is large. In this article, we propose a novel method for the spectral test computation of MRGs that is simple, intuitive, and particularly efficient for MRGs with few non zero terms. With the proposed method, we are able to provide a list of ready-to-use “better” generators with respect to the spectral test performance among the DX generators of order k for various values of k.

A simple 4D no-equilibrium chaotic system with only one quadratic term and its application in pseudo-random number generator

Simple-form chaotic systems with complex behaviors have always attracted the attention of researchers. This article introduces a novel 4D chaotic system that has only a quadratic nonlinear term as compared with the existing no-equilibrium continuous chaotic ones with two quadratic or higher nonlinearity. Despite the simplicity of its model, this new system exhibits complicated chaotic behaviors. Many interesting phenomena including the coexistence of different hidden attractors, offset boosting and antimonotonicity have been discovered by various numerical analysis such as bifurcation diagrams, Lyapunov exponent spectra, and phase portraits. The further circuit simulation of this new system verifies its feasibility and practicality. Moreover, the new system is applied to construct Pseudo-Random Number Generators (PRNG), following a thorough assessment of its complexity and randomness by sample entropy. The generated numbers are subsequently assessed using 15 statistical tests. The results confirm that the new system can produce unpredictable numbers with high randomness, making it ideal for information encryption.

Lightweight image encryption based on composite pseudo-random number generator

Lightweight image encryption based on composite pseudo-random number generator

Chaotic Path-Planning Algorithm Based on Courbage–Nekorkin Artificial Neuron Model

Developing efficient path-planning algorithms is an essential topic in modern robotics and control theory. Autonomous rovers and wheeled and tracked robots require path generators that can efficiently cover the explorable space with minimal redundancy. In this paper, we present a new path-planning algorithm based on the chaotic behavior of the Courbage–Nekorkin neuron model with a coverage control parameter. Our study aims to reduce the number of iterations required to cover the chosen investigated area, which is a typical efficiency criterion for this class of algorithms. To achieve this goal, we implemented a pseudorandom bit generator (PRBG) based on a Courbage–Nekorkin chaotic map, which demonstrates chaotic behavior and successfully passes all statistical tests for randomness. The proposed PRBG generates a bit sequence that can be used to move the tracked robot in four or eight directions in an operation area of arbitrary size. Several statistical metrics were applied to evaluate the algorithm’s performance, including the percentage of coverage of the study area and the uniformity of coverage. The performance of several competing path-planning algorithms was analyzed using the chosen metrics when exploring two test areas of the sizes 50 × 50 cells and 100 × 100 cells, respectively, in four and eight directions. The experimental results indicate that the proposed algorithm is superior compared to known chaotic path-planning methods, providing more rapid and uniform coverage with the possibility of controlling the covered area using tunable parameters. In addition, this study revealed the high dependence of the coverage rate on the starting point. To investigate how the coverage rate depends on the choice of chaotic map, we implemented six different PRBGs using various chaotic maps. The obtained results can be efficiently used for solving path-planning tasks in both real-life and virtual (e.g., video games) applications.

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.

Estimation of quantiles with the exact bootstrap method

A problem with the estimation of quantiles occurs when the sample comes from an unknown distribution. The estimation uses the bootstrap method in the version that the literature refers to as exact. Three bootstrap estimators were used: two of them based on one order statistic, and the third on a linear combination of two order statistics (for an integer). The distribution of the exact bootstrap estimator based on a single order statistic is known. It has been shown that there is no general form of the distribution of the exact bootstrap estimator based on two order statistics. However, it is possible to calculate such a distribution – the article presents the algorithm that performs such a task. The bootstrap confidence intervals were constructed using the exact percentile method. It has been shown that if the estimator is based on a single order statistic, it is known in advance which elements of the primary sample are the limits of the confidence intervals, so there is no need to resample. The intervals determined by the exact percentile method were compared with those constructed using other methods. It has been shown that the information on the direction of the asymmetry of the distribution that the sample comes from is worth considering when selecting the rank of the order statistic used as an estimator. Attention is paid to the influence of the quality of the pseudorandom number generators on the results of the Monte Carlo simulation.

Generalized time-bin quantum random number generator with uncharacterized devices

Random number generators (RNG) based on quantum mechanics are captivating due to their security and unpredictability compared to conventional generators, such as pseudo-random number generators and hardware-random number generators. This work analyzes evolutions in the extractable amount of randomness with increasing the Hilbert space dimension, state preparation subspace, or measurement subspace in a class of semi-device-independent quantum-RNG, where bounding the states’ overlap is the core assumption, built on the prepare-and-measure scheme. We further discuss the effect of these factors on the complexity and draw a conclusion on the optimal scenario. We investigate the generic case of time-bin encoding scheme, define various input (state preparation) and outcome (measurement) subspaces, and discuss the optimal scenarios to obtain maximum entropy. Several input designs were experimentally tested and analyzed for their conceivable outcome arrangements. We evaluated their performance by considering the device’s imperfections, particularly the after-pulsing effect and dark counts of the detectors. Finally, we demonstrate that this approach can boost the system entropy, resulting in more extractable randomness.

A Quantum Adaptation for the Morra Game and Some of Its Variants

The Morra game is quite old. Back in time, traces of it can be found in ancient Egypt, ancient Rome, and even China. It involves two players who, for a limited number of turns, must try to suppose the sum of the number personally chosen with the number chosen by the opponent. The rules are simple, but it is rather difficult to play at a high level as there are multiple cognitive, motor, and perceptual processes involved. <p xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">The goal of this paper is to illustrate the process of implementing a quantum random player for the Morra game and some of its variants. This can be done by using a quantum number generator circuit to generate two numbers and a quantum adder to obtain the supposed sum. The advantage of this proposal is that, unlike the implementations of the Morra game on classical computers, which only allow the generation of pseudo-random numbers, true randomness can be obtained through quantum computing. <p xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">In addition to the description of the entire algorithms, the source code of the implementations is provided to give everyone the freedom to easily test both the quantum implementation of the Morra game and the variants discussed in the paper.