Pseudorandom Research Articles

Fast, high-quality pseudo random number generators for heterogeneous computing

Random number generation is key to many applications in a wide variety of disciplines. Depending on the application, the quality of the random numbers from a particular generator can directly impact both computational performance and critically the outcome of the calculation. High-energy physics applications use Monte Carlo simulations and machine learning widely, which both require high-quality random numbers. In recent years, to meet increasing performance requirements, many high-energy physics workloads leverage GPU acceleration. While on a CPU, there exist a wide variety of generators with different performance and quality characteristics, the same cannot be stated for GPU and FPGA accelerators. On GPUs, the most common implementation is provided by cuRAND - an NVIDIA library that is not open source or peer reviewed by the scientific community. The highest-quality generator implemented in cuRAND is a version of the Mersenne Twister. Given the availability of better and faster random number generators, high-energy physics moved away from Mersenne Twister several years ago and nowadays MIXMAX is the standard generator in Geant4 via CLHEP. The MIXMAX original design supports parallel streams with a seeding algorithm that makes it especially suited for GPU and FPGA where extreme parallelism is a key factor. In this study we implement the MIXMAX generator on both architectures and analyze its suitability and applicability for accelerator implementations. We evaluated the results against “Mersenne Twister for a Graphic Processor” (MTGP32) on GPUs which resulted in 5, 13 and 14 times higher throughput when a 240, 17 and 8 sized vector space was used respectively. The MIXMAX generator coded in VHDL and implemented on Xilinx Ultrascale+ FPGAs, requires 50% fewer total Look Up Tables (LUTs) compared to a 32-bit Mersenne Twister (MT-19337), or 75% fewer LUTs per output bit. In summary, the state-of-the art MIXMAX pseudo random number generator has been implemented on GPU and FPGA platforms and the performance benchmarked.

Securing air defense visual information with hyperchaotic Folded Towel Map-Based encryption

<p>In modern air defense systems, safeguarding sensitive information is crucial to prevent unauthorized access and cyber-attacks. Here, we present an innovative image encryption approach, leveraging chaotic logistic maps and hyperchaotic Folded Towel Map sequence generation. The proposed image encryption is a multi-layered procedure intended to secure image transmission. It initiates with permutation, where a chaotic logistic map generates pseudo-random sequences to scramble pixel positions. Next, key mixing creates complexity, randomness, and nonlinearity using an invertible key matrix. Finally, the diffusion phase employs hyperchaotic maps to produce a new sequence XORed with the pixels through a bitwise operation, further encrypting the image. This three-stage process efficiently protects images from unauthorized access, ensuring secure transmission. The proposed method enhances security by leveraging non-linearity, sensitivity, and robust mixing, properties making it highly resistant to cryptographic attacks. The experimental results showed robust encryption performance as established by metrics such as an entropy value of 7.9991, a UACI of 33.21%, and an NPCR of 99.61%. The proposed encryption approach outperformed existing methods in securing image transmission and storage, offering a reliable solution for protecting air defense communication strategic data.</p>

DRcipher: A pseudo-random dynamic round lightweight block cipher

The Internet of Things (IoT) has gained popularity in various fields, including components such as embedded devices and wireless sensors. However, ensuring the security of data transmission from these devices is of critical importance. In light of these challenges, a novel lightweight encryption method called DRcipher is proposed in this paper for resource-constrained IoT devices. DRcipher has a 64-bit block size and supports either 96-bit or 128-bit key sizes. In order to improve the security, DRcipher employs a pseudo-random number of encryption rounds determined by the primary key. DRcipher adopts the structure of Generalized Feistel Network (GFN) with 4 branches, and its round functions consist of F-function, FF-function and RP permutation components. In particular, there is a negative feedback mechanism between the FF-function and the overall round of encryption functions. In addition, DRcipher is synthesised using Synopsys Design Compiler version A-2007.12-SP1 and the UMCL18G212T3 standard cell library. DRcipher-96 has an area footprint of 1546 Gate Equivalents (GE), while DRcipher-128 has a slightly larger area footprint of 1646 GE. Moreover, a comprehensive security analysis shows that the proposed DRcipher ensures high-level security redundancy against differential cryptanalysis, linear cryptanalysis, and so on.

Design of a Multiple Pseudorandom Number Generator Combined Chaotic System With RNS and Its Application to Secure Image Processing

Design of a Multiple Pseudorandom Number Generator Combined Chaotic System With RNS and Its Application to Secure Image Processing

Efficient image encryption scheme using a nonlinear shift register and chaos

Powerful cryptographic systems require a qualified random number generator. This research purposes to provide a comprehensive comparative analysis done on several of the well-known pseudo-random number generators (PRNGs) regarding their efficiency and resilience against crypto-analytical threats. These generators consist of the basic 8-bit Non-Linear Feedback Shift Register (NLFSR), the logistic map (LM), and our proposed hybrid random number generator named NLFSR-LM, which combines through XOR operation the sequences of the NLFSR with the LM to achieve a high quality of randomness. The performance of the created generator is examined and subsequently compared according to statistical tests of randomness alongside cryptographic features in terms of key space, key sensitivity and resistance to numerous attacks. The proposed generator produced good results and exhibited several interesting properties, such as a high degree of security, a sufficiently large key space, and it provided better randomness than other frequently used PRNGs.

Some Properties of a Discrete Lorenz System Obtained by Variable Midpoint Method and Its Application to Chaotic Signal Modulation

Various discretization effects caused by applying numerical integration techniques to continuous chaotic systems are broadly studied in nonlinear science. Along with the negative impact on the precision of the various finite-difference schemes, such effects may have surprisingly fruitful practical applications, e.g. pseudo-random number generation, image encryption with improved diffusion and confusion properties, chaotic path planning, and many others. One such application is chaos-based communication systems which gained attention in recent decades due to their high covertness and broadband transmission capability. A crucial problem in the design of chaotic communication systems is the modulation of carrier signals. Due to the noise-like properties of chaotic signals, they can barely be modulated using the same methods as conventional harmonic signals. Thus, developing new modulation techniques is of great interest in the field of chaotic communications. In this study, we investigate the discrete model of the Lorenz oscillator obtained using controllable midpoint numerical integration and develop a novel modulation technique for chaos-based communication systems. We discover and analyze the multistability phenomenon in the dynamics of the investigated finite-difference Lorenz model through bifurcation, the basin of attraction, and Lyapunov spectrum analysis procedures. Using a specially designed testbench, we explicitly show that the proposed modulation method outperforms commonly used parametric modulation and is nearly equal to the state-of-the-art symmetry-based modulation in terms of covertness and noise resistivity. In addition, the proposed modulation technique is much easier to implement using computer arithmetics, especially in fixed-point hardware. The reported results may be efficiently applied to designing advanced chaos-based communications systems or improving the characteristics of existing communication system architectures.

ТЕОРЕТИЧНІ АСПЕКТИ ВИКОРИСТАННЯ МЕТОДУ МОНТЕ-КАРЛО ДЛЯ МОДЕЛЮВАННЯ ОЦІНКИ ЕФЕКТИВНОСТІ ІНВЕСТИЦІЙНИХ ПРОЕКТІВ

This article is dedicated to the theoretical study of applying the Monte Carlo method for evaluating the efficiency of investment projects within enterprises. The author examines the principles and advantages of using this stochastic method in modeling economic parameters and project risks, as well as analyzing the method's capabilities in generating various scenarios for justifying investment decisions based on probabilistic calculations. The article explores methodological aspects of simulation modeling of investments, including the creation of applied mathematical models that simulation real economic processes and situations using pseudorandom numbers to generate random variables. This allows for the determination of potential financial outcomes of investment projects with varying degrees of risk and uncertainty. The historical development of the Monte Carlo method and its contemporary use in investment analysis are highlighted, emphasizing its significance in providing a deep understanding of variations in the initial data of investment projects. Particular attention is paid to the method's ability to adapt and account for uncertainty in complex investment scenarios, making it an indispensable tool for investment analysis. Efficiency indicators of investment projects, which are used to assess the economic benefits of investments, are analyzed. Key indicators include Net Present Value (NPV), Internal Rate of Return (IRR), and Profitability Index (PI). The Monte Carlo method is used to model the probabilities of various financial scenarios and influences the assessment of these indicators, providing a more detailed analysis of potential risks and returns from projects. The article emphasizes the importance of the Monte Carlo method as a foundation for developing new approaches to evaluating investment projects and managing risks. This contributes to a better understanding of how modern approaches to simulation modeling can affect the decisions of investors and managers, especially in situations where classical evaluation methods may be ineffective. Therefore, the application of the Monte Carlo method in modeling investment projects not only helps assess overall efficiency indicators but also allows for a detailed analysis of potential investment project risks, making it an indispensable tool in contemporary investment analysis.

A Hierarchical Multiscenario H.265/HEVC Video Encryption Scheme

With the pervasive application of video streaming, the security of streaming media information continually faces new challenges. Most existing encryption methods employ uniform criteria for encrypting all scenarios, leading to unnecessary mutual inhibition of algorithm security and coding efficiency. Furthermore, several encryption algorithms are inadequate for high-resolution videos. A novel, independently hierarchical video cryptosystem for H.265/high efficiency video coding (HEVC) is proposed that develops a scene-adaptive encryption strategy tailored for multiscenario videos. Additionally, we fully consider the seeds of pseudo-random number generators, syntax components in compressed codes, and scenario indicators. We analyze the visibility of encrypted videos in different scenarios and the encryption performance of various syntax parameters based on the integration of encryption for three distinct scenario categories to further enhance encryption efficiency and security. The method’s versatility is demonstrated using a diverse array of videos with significant and insignificant inter-frame motion information across varying resolutions. The experimental results from the video datasets indicate that our scheme effectively balances security and coding efficiency. Furthermore, the scene-adaptive approach can be tailored flexibly according to subscriber needs.

Design A Novel Image Encryption Algorithm Based on A PRNG with High Performance

This paper proposes a novel two-dimensional logistic map (2D-LM). Relative to the classical 2D logistic modulation map (2D-LMM), it has larger chaotic range and better chaos performance. In comparison with some 2D chaos maps, the proposed new 2D-LM also has unique advantages in the complexity of sequence. To further study its application, the novel image encryption algorithm is designed based on the proposed 2D-LM. The security tests show the higher anti-decryption ability of the design algorithm. Finally, we develop a FPGA test platform to realize the Pseudo-Random Number Generator (PRNG) based on the proposed 2D-LM. The experiment results show the feasibility of its industrial applications.

Study of the set of initial values of pseudorandom number generators based on floating point arithmetic

Study of the set of initial values of pseudorandom number generators based on floating point arithmetic

Modelling the Lengths of Quantitative Motifs in Pseudorandom Integer Sequences

This study explores the behaviour of quantitative motifs in random numerical data, focussing on the property of length. One hundred and twenty sequences of pseudorandom integers were generated and segmented into quantitative motifs using the standard definition. The length–frequency relationship was modelled in each case using the Zipf-Alekseev function. Different combinations of sequence length, integer range, and pseudorandom number generator were trialled. The model-fitting was successful in all cases (𝑅2 1 > 0.9 in 118/120 cases and > 0.8 in 2/120), and the model parameters fell in the same range as those obtained in a previous textual study of motifs. Integer range was the main factor affecting the parameter values, with sequence length affecting the degree of spread. Further comparisons between textual and random data are needed, as well as a theoretical explanation of why motifs in random data demonstrate lawful behaviour. In future textual motif studies, particular attention needs to be paid to possible dependencies on value range and text length.

A New Memristive System with Extreme Multistability and Hidden Chaotic Attractors and with Application to Image Encryption

Chaotic systems have proven highly beneficial in engineering applications. Pseudo-random numbers produced by chaotic systems have been used for secure communication, notably image encryption. Specific characteristics can increase the chaotic behavior of the system by adding complexity and nonlinearity. The three most well-known characteristics are memristive properties, multistability (coexisting attractors), and hidden attractors. These characteristics strengthen the produced time series’ unpredictability and randomness, strengthening an encryption algorithm’s resistance to many attacks. This study introduces a unique four-dimensional chaotic system with extreme multistability with respect to three initial conditions (including the memristor initial condition) and all previously known properties. It is rare to find an extreme multistable system like this. This system is coupled with a quadratic flux-controlled memristor based on the well-known Sprott J system. This system has a line of unstable equilibrium points with hidden attractors. The memristor displays the characteristic pinched hysteresis loops, where the area inside a loop and the voltage frequency are inversely related. A comprehensive dynamical analysis thoroughly examines all system characteristics and initial conditions. The numerical findings are carefully verified, and an analog circuit is successfully built and simulated. The chaotic sequences generated by this system are combined with deoxyribonucleic acid (DNA) operations and the global bit scrambling (GBS) technique to create an image encryption algorithm that has strong resistance to a variety of potential attacks, including noise, statistical, exhaustive, differential, and cropping attacks.

Hardware random numbers generator based on microcontroller

The work considers the principles of development and organization of the random number generation system using a hardware generator of true random numbers. An analysis of noise sources for a hardware generator of true random numbers has been carried out. The architecture of the random and pseudo-random number generation system, the structure of the hardware part, and the interaction protocol of the system elements have been developed. Hardware and software of the system are implemented. An analysis of numbers sequences randomness degree obtained in different modes was carried out using a NIST statistical tests suite and visual tests. Recommendations for using the system are given.

IOOA: A multi-strategy fusion improved Osprey Optimization Algorithm for global optimization

<abstract><p>With the widespread application of metaheuristic algorithms in engineering and scientific research, finding algorithms with efficient global search capabilities and precise local search performance has become a hot topic in research. The osprey optimization algorithm (OOA) was first proposed in 2023, characterized by its simple structure and strong optimization capability. However, practical tests have revealed that the OOA algorithm inevitably encounters common issues faced by metaheuristic algorithms, such as the tendency to fall into local optima and reduced population diversity in the later stages of the algorithm's iterations. To address these issues, a multi-strategy fusion improved osprey optimization algorithm is proposed (IOOA). First, the characteristics of various chaotic mappings were thoroughly explored, and the adoption of Circle chaotic mapping to replace pseudo-random numbers for population initialization improvement was proposed, increasing initial population diversity and improving the quality of initial solutions. Second, a dynamically adjustable elite guidance mechanism was proposed to dynamically adjust the position updating method according to different stages of the algorithm's iteration, ensuring the algorithm maintains good global search capabilities while significantly increasing the convergence speed of the algorithm. Lastly, a dynamic chaotic weight factor was designed and applied in the development stage of the original algorithm to enhance the algorithm's local search capability and improve the convergence accuracy of the algorithm. To fully verify the effectiveness and practical engineering applicability of the IOOA algorithm, simulation experiments were conducted using 21 benchmark test functions and the CEC-2022 benchmark functions, and the IOOA algorithm was applied to the LSTM power load forecasting problem as well as two engineering design problems. The experimental results show that the IOOA algorithm possesses outstanding global optimization performance in handling complex optimization problems and broad applicability in practical engineering applications.</p></abstract>

Comparative Analysis of Pseudorandom Number Generators: Mersenne Twister, Middle Square Method, and Linear Congruential Generator through Dieharder Tests

Comparative Analysis of Pseudorandom Number Generators: Mersenne Twister, Middle Square Method, and Linear Congruential Generator through Dieharder Tests

On a Vernam cipher scheme based on elliptic curve L-functions

In this paper, we present a new Vernam-like cryptosystem based on the L-functions attached to elliptic curves. Actually, we show that for infinitely many elliptic curves, the coefficients of the L-series can be considered as a secure cryptographic cipher key when combined with linear and classical pseudo-random number generators. Hence, fast and widely known classical generators, like linear congruential generators, should be reintroduced into our list of cryptographic design choices.

Pseudo-Random Number Generators for Stochastic Computing (SC): Design and Analysis

Pseudo-Random Number Generators for Stochastic Computing (SC): Design and Analysis

Four Novel Dual Discrete Memristor-Coupled Hyperchaotic Maps

Unlike the high-dimensional hyperchaotic system based on a continuous memristor, the low-dimensional map coupled by discrete memristor (DM) and traditional chaotic map can also generate hyperchaos. However, the hyperchaotic map constructed by two DMs has not attracted much attention. To this end, a generalized two-dimensional dual DM-coupled hyperchaotic mapping model is reported in this paper, and four specific maps are provided. The proposed maps have line invariant points, which can be interpreted as allowing arbitrary real values for the initial condition associated with the DM, and the stability is investigated in detail. Furthermore, the coupling strength-dependent and initial condition-dependent complex dynamics of four maps are studied by numerical simulations, and the dynamical performance is evaluated from the perspective of quantitative analysis. It is shown that the considered maps are capable of exhibiting the three characteristic fingerprints of memristors in arbitrary parameter spaces, and this characteristic has gained attention for the first time. In particular, the complete control of the considered maps by variable substitution is performed, which can generate arbitrary switched hyperchaotic behaviors. In addition, four pseudo-random number generators are designed based on the proposed maps, and the randomness is tested by using the NIST SP800-22 software. In general, the proposed maps can not only generate abundant dynamical behaviors, but also enrich the DM circuits and provide a reference for applications based on chaos. Finally, the developed digital hardware circuit implementation platform verifies the results of the numerical method.

Method for the Simultaneous Generation of Two Nonlinear Pseudo Random Sequences: 5-ary and Binary

Multi-level signals and sequences have become a significant aspect of modern high-speed communication systems. Hence, to ensure the confidentiality and integrity of the transmitted information, advanced methods and devices are necessary to produce strong cryptographic properties for not only binary but also for nonbinary keystreams, which can be used in resource-constrained microcontrollers. The proposed method and apparatus generate both a balanced nonlinear 5-ary pseudo-random sequence and a binary keystream sequence. The nonlinearity is determined by applying shrinking and multiplexing techniques to the generated linear 5-ary pseudo-random sequence and the running zero in its conversion to a binary balanced sequence.

A Process based Algorithm for Random Number Generation

Background: Random number generation plays a crucial role in various scientific, computational, cryptographic applications and stochastic processes. This paper introduces a novel algorithm designed to address the demand for high-quality random numbers with improved statistical properties. The proposed Algorithm uses the elements of hardware-based entropy to generate random numbers for efficiency and unpredictability. Methods: Pseudo-random numbers are sequences derived from algorithms known as pseudo-random number generators (PRNGs). These generators use an initial value, or seed, to produce sequences that exhibit statistical properties akin to truly random numbers.Results:For the z-test statistic and the corresponding p-value in the above five samples we found that p-value is not less than α = 0.05, therefore we fail to reject the null hypothesis. Conclusions: Module U behaves as a Random number generation algorithm. Further, we can test the module U for large samples and we can use module U for simulation of different Random processes to verify it’s correctness.