Pseudorandom Number Generator Research Articles

MAXEM: A New Pseudo-Random Number Generating Algorithm with Implementation of Modulo Arithmetic, XORShift, and Entropy Modulation

This paper introduces a novel pseudo-random number generation algorithm incorporating modulo arithmetic, XORShift, and entropy modulation. The method is designed to enhance randomness and unpredictability by utilizing bitwise manipulations and dynamic entropy modulation. Experimental results demonstrate the algorithm’s performance across various test sets. The algorithm seeks to resolve two of the most common problems of common PRNGs, which are the quality of randomness with selection of an arbitrary seed and the presence of periodic cycles. The findings suggest potential applications in cryptography and statistical simulations.

A predecessor value XOR method for improving chaotic maps and its application in pseudo-random bit generators

Abstract With the increasing requirements for the quality of pseudo-random sequences in fields such as cryptography, researchers continue to propose new chaotic map improvement schemes to meet these needs. However, these schemes still have some limitations in terms of randomness, stability and security. In order to solve these problems, we propose a method named predecessor value XOR (PVX), and then use this method to improve chaotic maps and construct a pseudo-random bit generator (PRBG). The PVX method aims to select a delayed chaotic state, make a specific change to its bit sequence, and finally use the changed state to perform an XOR operation with the output value. This method does not destroy the original formulation of chaotic map and is universal. Numerous numerical experiments have confirmed the effectiveness of the PVX method. For example, when the computational precision was only 6 bits, the approximate entropy (1.799), permutation entropy (0.99), and cycle length (183,680) of the improved Logistic Map. Concurrently, the approximate entropy (2.042), permutation entropy (0.983), and cycle length (undetected) of the x-dimension sequence of the improved Hénon Map, all achieved excellent results. Additionally, the PRBG constructed by us is formed by a parallel connection of two improved Logistic Maps and one improved Hénon Map. Experimental results show that the proposed PRBG exhibits excellent randomness, good stability, and high security. It is worth noting that the improved chaotic maps using the PVX method outperform many recent improved schemes in several dimensions, especially in the low-precision computational scenarios, and the method effectively solves the problem of degradation of the chaotic map dynamics, and provides a more reliable technological support for cryptography and other fields.

A refined sine-derived chaotic map for securing medical image encryption in telemedicine.

A refined sine-derived chaotic map for securing medical image encryption in telemedicine.

Applicability and Design Considerations of Chaotic and Quantum Entropy Sources for Random Number Generation in IoT Devices

This article presents a comparative analysis of two types of generators of random sequences: one based on a discrete chaotic system being the logistic map, and the other being a commercial quantum random number generator QUANTIS-USB-4M. The results of the conducted analysis serve as a guide for selecting the type of generator that is more suited for a specific IoT solution, depending on the functional profile of the target application and the amount of random data required in the cryptographic process. This article discusses both the theoretical foundations of chaotic phenomena underlying the pseudorandom number generator based on the logistic map, as well as the theoretical principles of photon detection used in the quantum random number generators. A hardware IP Core implementing the logistic map was developed, suitable for direct implementation either as a standalone ASIC using the SkyWater PDK process or on an FPGA. The generated bitstreams from the implemented IP Core were evaluated for randomness. The analysis of the entropy levels and evaluation of randomness for both the logistic map and the quantum random number generator were performed using the ent tool and NIST test suite.

High- and Low-Rank Optimization of SNOVA on ARMv8: From High-Security Applications to IoT Efficiency

The increasing threat of quantum computing to traditional cryptographic systems has prompted intense research into post-quantum schemes. Despite SNOVA’s potential for lightweight and secure digital signatures, its performance on embedded devices (e.g., ARMv8 platforms) remains underexplored. This research addresses this gap by presenting the optimal SNOVA implementations on embedded devices. This paper presents a performance-optimized implementation of the SNOVA post-quantum digital signature scheme on ARMv8 processors. SNOVA is a multivariate cryptographic algorithm under consideration in the NIST’s additional signature standardization. Our work targets the performance bottlenecks in the SNOVA scheme. Specifically, we employ matrix arithmetic over GF16 and AES-CTR-based pseudorandom number generation by exploiting the NEON SIMD extension and tailoring the computations to the matrix rank. At a low level, we develop rank-specific SIMD kernels for addition and multiplication. Rank 4 matrices (i.e., 16 bytes) are handled using fully vectorized instructions that align with 128-bit-wise registers, while rank 2 matrices (i.e., 4 bytes) are processed in batches of four to ensure full SIMD occupancy. At the high level, core routines such as key generation and signature evaluation are structurally refactored to provide aligned memory layouts for batched execution. This joint optimization across algorithmic layers reduces the overhead and enables seamless hardware acceleration. The resulting implementation supports 12 SNOVA parameter sets and demonstrates substantial efficiency improvements compared to the reference baseline. These results highlight that fine-grained SIMD adaptation is essential for the efficient deployment of multivariate cryptography on modern embedded platforms.

A three-dimensional memristor-based hyperchaotic map for pseudorandom number generation and multi-image encryption.

The resistance state of a memristor can be influenced by external stimuli, and these variations can be converted into a pseudorandom sequence through appropriate circuitry and control mechanisms. By leveraging this property, a reliable and complex pseudorandom number generator suitable for encryption can be designed. To enhance the chaotic complexity of memristor-based discrete systems, this paper introduces a three-dimensional hyperchaotic map based on a memristor (3D-HMBM), which integrates a sine-function nonlinearity with a discrete memristor model. Analyzing its dynamical properties via Lyapunov exponents, the 3D-HMBM exhibits evolution from periodicity to chaos and hyperchaos. The complexity of its iterated sequences is verified through metrics such as Spectral Entropy and C0 complexity. Furthermore, the 3D-HMBM displays a unique phenomenon of infinite coexisting attractors. As initial values vary, the system generates attractors at different positions, suggesting that-in theory-an infinite number of attractors exist. Finally, the simulation results are validated via digital-circuit implementation. Building on this foundation, we propose a multi-image encryption algorithm based on the 3D-HMBM, offering a more secure solution for encrypting large volumes of data. Through statistical testing and cryptographic analysis, we confirm the significant potential of the keystream generated by the 3D-HMBM for cryptographic applications.

Design and FPGA implementation of a novel cryptographic secure pseudo random number generator based on artificial neural networks and chaotic systems

Design and FPGA implementation of a novel cryptographic secure pseudo random number generator based on artificial neural networks and chaotic systems

Conic curve encryption and digital signature based on complex number theory for cybersecurity applications

Secure image transmission requires robust algorithms to ensure authentication, integrity, non-repudiation, and confidentiality. Addressing emerging security challenges necessitates continuous advancements in cryptographic design. This paper presents an authenticated and encrypted image scheme that achieves all essential security services. While Elliptic curve cryptography (ECC) remains a fundamental component of recent encryption schemes, it is vulnerable to side-channel and inherent ECC-specific attacks. To overcome these vulnerabilities, the proposed scheme replaces ECC with Conic curve cryptography (CCC), offering enhanced security and performance. The integration of complex number theory with CCC enables a secure complex key exchange and incorporates a robust Iterative conic curve pseudorandom number generator (ICC-PRNG) to thwart all known attack types. The system is a public key cryptosystem based on multi-hard problems, including the Gaussian conic curve integer factorization problem (GCC-IFP), Conic curve discrete logarithm problem (CC-DLP), and Conic curve integer factorization problem (CC-IFP), combined with XOR operations for image encryption. Additionally, the scheme introduces a novel complex digital signature for encrypted images, leveraging complex arithmetic to enhance security. Experimental results demonstrate high entropy 7.999, correlation near 0.0001, key space {2}^{688}$$\\end{document}]]>, and average PSNR of 8.51 dB, ensuring resilience against brute-force and statistical attacks. Additionally, the scheme achieves encryption times of 25 ms, making it suitable for real-time applications. Security analysis validates robustness against various attacks, with NIST statistical tests confirming ICC-PRNG effectiveness. By leveraging complex numbers over conic curves, the proposed method improves security and computational efficiency, establishing it as a promising solution for advanced image encryption.

Extreme multistability in a double-memristors-based chaotic system

Abstract A novel double-memristor-based chaotic system (DMCS) is proposed in this paper to address limitations in traditional chaos generation methods. Two identical memristors are introduced into the first and third dimensions of a chaotic system, creating a unique platform for investigating extreme multi-stability induced by the memory characteristics of the memristors. Diverse coexisting attractors are observed, with variations in initial conditions resulting in shifts in both the position and size of the attractors. Additionally, cross-dimensional control of multistability is achieved, where the stability in one dimension is influenced by initial values in other dimensions, leading to symmetric attractor arrangements under specific conditions. An inverse regulation of the attractor oscillation range is enabled by adjusting the memristor coupling strength, providing a novel chaotic signal tuning mechanism. The system’s chaotic dynamics are validated through a circuit implementation in Multisim, where fundamental behaviors predicted by theoretical analysis are confirmed. A pseudo-random number generator (PRNG) based on the DMCS is developed, demonstrating exceptional randomness as verified by rigorous testing.

Joint Data Hiding and Partial Encryption of Compressive Sensed Streams

This paper proposes a method to secure Compressive Sensing (CS) streams. It involves protecting part of the measurements with a secret key and inserting code into the remaining measurements. The secret key is generated via a cryptographically secure pseudorandom number generator (CSPRNG) and XORed with the measurements to be inserted. For insertion, we use a reversible data hiding (RDH) scheme, which is a prediction error expansion algorithm modified to match the statistics of CS measurements. The reconstruction from the embedded stream results in a visibly distorted image. The image distortion is controlled by the number of embedded levels. In our tests, embedding on 10 levels results in ≈18 dB distortion for images of 256×256 pixels reconstructed with the Fast Iterative Shrinkage-Thresholding Algorithm (FISTA). A particularity of the presented method is on-the-fly insertion, which makes it appropriate for the sequential acquisition of measurements with a single-pixel camera. On-the-fly insertion avoids the buffering of CS measurements for the subsequent standard encryption and generation of a thumbnail image.

Design and analysis of a 2D discrete memristive map

Abstract This study proposes a novel 2D memristive hyperchaotic map (2DMHM) with hyperbolic tangent and absolute value functions. The 2DMHM exhibits an infinite of fixed points in a set of lines on the y-axis, with stability characteristics partitioned across memristor parameters and initial condition planes. System dynamics are systematically investigated through bifurcation analysis, Lyapunov exponent spectra, and basin of attraction, trajectory plots, revealing remarkable multistability and initial-sensitive chaotic behavior. The map demonstrates superior spectral entropy (SE) complexity across critical parameter ranges, significantly outperforming conventional chaotic systems. A microcontroller-based digital implementation validates the physical realizability of 2DMHM, while the NIST test success rate demonstrates its exceptional performance in pseudorandom number generation. These results establish 2DMHM as a promising candidate for secure communication systems and cryptographic applications.

2D logistic map with unit transfer function and modulus operation based pseudorandom number generation for image encryption

This study presents a novel approach to generating high-quality random numbers using a two-dimensional logistic map with a unit transfer function (2DLMUTF). The method is built upon the chaotic dynamics of the logistic map, where the parameter governs the system’s behavior, exhibiting chaotic nature in the range of 3.57 to 4. By applying a unit transfer function and modulus operation, the system’s output is constrained within the [0, 1] range, altering the phase space dynamics compared to traditional 2D logistic maps. Numerical simulations in MATLAB, with parameters =4, =3.8, and initial seed values =0.2350 and =0.3500, were run for iterations. Statistical testing using the NIST SP 800 − 22 test suite showed superior randomness, with the method passing all 15 tests. Additionally, uniformity, autocorrelation, cross-correlation, and entropy analyses confirmed the method’s suitability for cryptographic applications. The generated random numbers were used to create substitution boxes (S-boxes) for image encryption, demonstrating strong encryption performance. Overall, 2DLMUTF offers a computationally efficient and secure solution for random number generation which is suitable for cryptographic and image encryption applications.

ACURATE neo2 valve versus commercially available transcatheter heart valves in patients with severe aortic stenosis (ACURATE IDE): a multicentre, randomised, controlled, non-inferiority trial.

ACURATE neo2 valve versus commercially available transcatheter heart valves in patients with severe aortic stenosis (ACURATE IDE): a multicentre, randomised, controlled, non-inferiority trial.

ЗАСТОСУВАННЯ ГЕНЕРАТОРІВ ПСЕВДОВИПАДКОВИХ ЧИСЕЛ У МАШИННОМУ НАВЧАННІ

The paper analyzes the role of pseudorandom number generators in ensuring the efficiency and stability of machine learning algorithms. The key areas and forms of such application are identified. Particular attention is paid to the impact of the quality of PRNGs on the performance of models, in particular in the tasks of initializing neural networks, synthetic data augmentation, stochastic optimization, and reproducibility of results. The problems of periodicity, predictability, and low adaptability of generators to specific ML tasks are considered. Modern approaches to assessing the quality of PRNGs, including empirical, theoretical, and applied tests, are analyzed. The study also highlights the prospects of using deep learning to analyze PRNGs and identify patterns in pseudo-random sequences. Recommendations for improving the efficiency of machine learning systems by optimizing the use of PRNGs are proposed. The results of the study contribute to a deeper understanding of the role of PRNGs in modern machine learning and identify new directions for improving model performance. Keywords: pseudorandom number generators, machine learning, neural network initialization, stochastic optimization, reproducibility.

NTRU-MCF: A Chaos-Enhanced Multidimensional Lattice Signature Scheme for Post-Quantum Cryptography

To address the growing threat of quantum computing to classical cryptographic primitives, this study introduces NTRU-MCF, a novel lattice-based signature scheme that integrates multidimensional lattice structures with fractional-order chaotic systems. By extending the NTRU framework to multidimensional polynomial rings, NTRU-MCF exponentially expands the private key search space, achieving a key space size for dimensions and rendering brute-force attacks infeasible. By incorporating fractional-order chaotic masks generated via a hyperchaotic Lü system, the scheme introduces nonlinear randomness and robust resistance to physical attacks. Fractional-order chaotic masks, generated via a hyperchaotic Lü system validated through NIST SP 800-22 randomness tests, replace conventional pseudorandom number generators (PRNGs). The sensitivity to initial conditions ensures cryptographic unpredictability, while the use of a fractional-order L hyperchaotic system—instead of conventional pseudorandom number generators (PRNGs)—leverages multiple Lyapunov exponents and initial value sensitivity to embed physically unclonable properties into key generation, effectively mitigating side-channel analysis. Theoretical analysis shows that NTRU-MCF’s security reduces to the Ring Learning with Errors (RLWE) problem, offering superior quantum resistance compared to existing NTRU variants. While its computational and storage complexity suits high-security applications like military and financial systems, it is less suitable for resource-constrained devices. NTRU-MCF provides robust quantum resistance and side-channel defense, advancing PQC for classical computing environments.

Artificial Complex-Valued Neural Processing Using Memristive Hyperchaotic Synchronization

This study intends to boost the communication security in Industrial Internet of Things (IIoT) by addressing the alteration challenges of secure key exchange over public network. The objectives are to propose a cognitive Artificial Neural Network (ANN) synchronization combined with memristive hyperchaotic systems towards obtaining better synchronization performance, accuracy, random behaviour and overall security. The proposed method makes use of complex-valued ANN synchronization assisted with memristive hyperchaotic system that has dimensions 4D, 5D and 6D to produce high-entropy cryptographic keys. In this paper, Pseudo-Random Number Generation (PRNG) based on hyperchaotic is used to generate an input vector for ANN synchronization. A bi-directional learning approach is applied in the process of synchronization to improve the distribution of neuronal keys in a public channel between ANNs. A series of experiments were conducted using synchronized speed rate, entropy test as well as accuracy dominant test and performance key extraction phase using precision and recall and also F1-score. The proposed approach outperforms the existing traditional methods. It improves synchronization speed by 15%, synchronization accuracy by 93.8%, precision by 92.0% and F1 score by 93.3%. Therefore, and it can produce higher reliable key generation without any errors because the proposed system is generating high-entropy cryptographic keys with more than 7.5 bits that are able to strengthen IIoT communication against attacks by providing more randomness and security. Besides that, this faster and secured key exchange is possible due to memristive hyperchaotic structures that provide an excellent PRNG support, whereby they produced a remarkable reduction in error rate generated in key synchronization as well as low latency was achieved during key exchange process. An ANN-synchronized key exchange scheme is proposed in this research as the solution for secure IIoT communication problem. The proposed synchronization method uses hyperchaotic systems and coordination of two ANNs, which provides low-latency synchronization with high precision and high F1 score in comparison to the existing methods published in literature. The proposed key generation grows linearly with the number of nodes utilized in a network. Thus, it can also be used for IIoT real-time applications without privacy concerns.

A 4D memristive chaotic system with multiple amplitude and offset controllers

Abstract This paper constructs a novel 4D memristive chaotic system based on the classical Lorenz-like system. The study reveals that, despite the system’s asymmetric nature, it can exhibit coexisting attractor basins with quasi-symmetric structures under specific parameter configurations. Further analysis shows that the system possesses two independent amplitude control parameters, one can simultaneously regulate the scaling of three state variables, while the other can regulate the amplitude of the memristor variable. Notably, offset control of the memristive variable can also be achieved, and only under the condition of the offset boosting of the memristive variable, changing the memristive coupling coefficient can induce offset in another system variable. Finally, the effectiveness of the system’s amplitude and offset control characteristics is verified through analog circuit experiments, which provides a new theoretical basis and technical support for application to pseudo-random number generators.

Spin-Wheel: A Fast and Secure Chaotic Encryption System with Data Integrity Detection

The increasing demand for real-time multimedia communications has driven the need for highly secure and computationally efficient encryption schemes. In this work, we present a novel chaos-based encryption system that provides remarkable levels of security and performance. It leverages the benefits of applying fast-to-evaluate chaotic maps, along with a 2-Dimensional Look-Up Table approach (2D-LUT), and simple but powerful periodic perturbations. The foundation of our encryption system is a Pseudo-Random Number Generator (PRNG) that consists of a fully connected random graph with M vertices representing chaotic maps that populate the 2D-LUT. In every iteration of the system, one of the M chaotic maps in the graph and the corresponding trajectories are randomly selected from the 2D-LUT using an emulated spin-wheel picker game. This approach exacerbates the complexity in the event of an attack, since the trajectories may come from the same or totally different maps in a non-sequential time order. We additionally perform two levels of perturbation, at the map and trajectory level. The first perturbation (map level) produces new trajectories that are retrieved from the 2D-LUT in non-sequential order and with different initial conditions. The second perturbation applies a p-point crossover scheme to combine a pair of trajectories retrieved from the 2D-LUT and used in the ciphering process, providing higher levels of security. As a final process in our methodology, we implemented a simple packet-based data integrity scheme that detects with high probability if the received information has been modified (for example, by a man-in-the-middle attack). Our results show that our proposed encryption scheme is robust to common cryptanalysis attacks, providing high levels of security and confidentiality while supporting high processing speeds on the order of gigabits per second. To the best of our knowledge, our chaotic cipher implementation is the fastest reported in the literature.

Probabilistic photonic computing for AI.

Probabilistic computing excels in approximating combinatorial problems and modeling uncertainty. However, using conventional deterministic hardware for probabilistic models is challenging: (pseudo) random number generation introduces computational overhead and additional data shuffling. Therefore, there is a pressing need for different probabilistic computing architectures that achieve low latencies with reasonable energy consumption. Physical computing offers a promising solution, as these systems do not rely on an abstract deterministic representation of data but directly encode the information in physical quantities, enabling inherent probabilistic architectures utilizing entropy sources. Photonic computing is a prominent variant of physical computing due to the large available bandwidth, several orthogonal degrees of freedom for data encoding and optimal properties for in-memory computing and parallel data transfer. Here, we highlight key developments in physical photonic computing and photonic random number generation. We further provide insights into the realization of probabilistic photonic processors and their impact on artificial intelligence systems and future challenges.

A hybrid security protocol based on honey encryption and hyperchaotic systems for improving security in internet of things

Communication security in the internet of things (IoT) is essential to prevent devices and data from being vulnerable to cyber-attacks and possible abuses. In IoT systems, some sensors transmit critical data, so maintaining the security of these data and preventing their unauthorized interpretation is of great importance. For this reason, it is necessary to use advanced and complex encryption methods. The proposed research method consists of two phases: in the first phase, we use a hyperchaotic system to generate a complex sequence of pseudo-random numbers, and then by applying this system, we covertly replace the data. After that, we use the honey encryption technique to increase the security and obfuscation of the information, which helps us to improve the security of the data and prevent unauthorized interpretation. The proposed method has several key advantages, including the enhanced security that results from the combination of honey cryptography and chaotic systems, and this combination provides higher security than previous methods. In addition, the flexibility of the proposed protocol ensures its adaptability in various IoT applications, especially in cases where data security is required. These advantages help us to improve the security and efficiency of IoT systems in various situations. The proposed method is able to reduce the energy consumption caused by calculations and reduce the delay to the values of 21.8 and 0.34, respectively. Also, in terms of security, this method has been able to improve the security of information, which has achieved values of 1.041 and 0.49, respectively, using the Mean Squared Error and Bit Error Ratio criteria.