Entropy

9 pages, 283 KiB

Open AccessArticle

On the Convergence Rate for the Longest at Most T-Contaminated Runs of Heads

by István Fazekas, Borbála Fazekas and László Fórián

Entropy 2025, 27(1), 33; https://doi.org/10.3390/e27010033 - 3 Jan 2025

In this paper, we study the usual coin tossing experiment. We call a run at most T-contaminated, if it contains at most T tails. We approximate the distribution of the length of the longest at most T-contaminated runs. We offer a [...] Read more.

In this paper, we study the usual coin tossing experiment. We call a run at most T-contaminated, if it contains at most T tails. We approximate the distribution of the length of the longest at most T-contaminated runs. We offer a more precise approximation than the previous one. Full article

(This article belongs to the Special Issue The Random Walk Path of Pál Révész in Probability)

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23 pages, 575 KiB

Open AccessArticle

Towards Secure Internet of Things: A Coercion-Resistant Attribute-Based Encryption Scheme with Policy Revocation

by Yuan Zhai, Tao Wang, Yanwei Zhou, Feng Zhu and Bo Yang

Entropy 2025, 27(1), 32; https://doi.org/10.3390/e27010032 - 2 Jan 2025

Abstract

With the development and application of the Internet of Things (IoT), the volume of data generated daily by IoT devices is growing exponentially. These IoT devices, such as smart wearable devices, produce data containing sensitive personal information. However, since IoT devices and users [...] Read more.

With the development and application of the Internet of Things (IoT), the volume of data generated daily by IoT devices is growing exponentially. These IoT devices, such as smart wearable devices, produce data containing sensitive personal information. However, since IoT devices and users often operate in untrusted external environments, their encrypted data remain vulnerable to potential privacy leaks and security threats from malicious coercion. Additionally, access control and management of these data remain critical issues. To address these challenges, this paper proposes a novel coercion-resistant ciphertext-policy attribute-based encryption scheme. The scheme leverages chameleon hashing to enhance deniable encryption, achieving coercion resistance, thereby enabling IoT data to resist coercion attacks. Moreover, the scheme employs attribute-based encryption to secure IoT data, enabling fine-grained access control and dynamic user access management, providing a secure and flexible solution for vast IoT data. We construct the scheme on a composite order bilinear group and provide formal proofs for its coercion resistance, correctness, and security. Finally, through experimental comparisons, we demonstrate the efficiency and feasibility of the proposed scheme. Full article

(This article belongs to the Special Issue Information Security and Data Privacy)

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13 pages, 258 KiB

Open AccessArticle

On Defining Expressions for Entropy and Cross-Entropy: The Entropic Transreals and Their Fracterm Calculus

by Jan A. Bergstra and John V. Tucker

Entropy 2025, 27(1), 31; https://doi.org/10.3390/e27010031 - 2 Jan 2025

Abstract

Classic formulae for entropy and cross-entropy contain operations

\frac{x}{0}

and

{log}_{2} x

that are not defined on all inputs. This can lead to calculations with problematic subexpressions such as

0 {log}_{2} 0

and uncertainties in large scale calculations; partiality also [...] Read more.

Classic formulae for entropy and cross-entropy contain operations

\frac{x}{0}

and

{log}_{2} x

that are not defined on all inputs. This can lead to calculations with problematic subexpressions such as

0 {log}_{2} 0

and uncertainties in large scale calculations; partiality also introduces complications in logical analysis. Instead of adding conventions or splitting formulae into cases, we create a new algebra of real numbers with two symbols

\pm \infty

for signed infinite values and a symbol named ⊥ for the undefined. In this resulting arithmetic, entropy, cross-entropy, Kullback–Leibler divergence, and Shannon divergence can be expressed without concerning any further conventions. The algebra may form a basis for probability theory more generally. Full article

(This article belongs to the Section Information Theory, Probability and Statistics)

10 pages, 4044 KiB

Open AccessArticle

Non-Orthogonality of QAM and Sunflower-like Modulated Coherent-State Signals

by Kentaro Kato

Entropy 2025, 27(1), 30; https://doi.org/10.3390/e27010030 - 1 Jan 2025

Abstract

The limitations of cloning and discriminating quantum states are related to the non-orthogonality of the states. Hence, understanding the collective features of quantum states is essential for the future development of quantum communications technology. This paper investigates the non-orthogonality of different coherent-state signal [...] Read more.

The limitations of cloning and discriminating quantum states are related to the non-orthogonality of the states. Hence, understanding the collective features of quantum states is essential for the future development of quantum communications technology. This paper investigates the non-orthogonality of different coherent-state signal constellations used in quantum communications, namely phase-shift keying (PSK), quadrature-amplitude modulation (QAM), and a newly defined signal named the sunflower-like (SUN) coherent-state signal. The non-orthogonality index (NOI) and the average probability of correct detection (detection probability) are numerically computed. Results show that PSK NOI increases faster than QAM and SUN as the number of signals increases for a given number of signal photons. QAM and SUN exhibit similar NOI and detection probability, behaving similarly to randomly generated signals for a larger number of signals. Approximation formulas are provided for the detection probability as a function of NOI for each signal type. While similar to QAM, SUN signal offers potential advantages for applications requiring uniform signal-space distribution. The findings provide valuable insights for designing useful quantum signal constellations. Full article

(This article belongs to the Special Issue Quantum Communication, Quantum Radar, and Quantum Cipher, 2nd Edition)

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44 pages, 751 KiB

Open AccessReview

Unique Information Through the Lens of Channel Ordering: An Introduction and Review

by Pradeep Kr. Banerjee

Entropy 2025, 27(1), 29; https://doi.org/10.3390/e27010029 - 1 Jan 2025

Abstract

The problem of constructing information measures with a well-defined interpretation is of fundamental significance in information theory. A good definition of an information measure entails certain desirable properties while also providing answers to operational problems. In this work, we investigate the properties of [...] Read more.

The problem of constructing information measures with a well-defined interpretation is of fundamental significance in information theory. A good definition of an information measure entails certain desirable properties while also providing answers to operational problems. In this work, we investigate the properties of the unique information, an information measure that quantifies a deviation from the Blackwell order. Beyond providing an accessible introduction to the topic from a channel ordering perspective, we present a novel resource-theoretic characterization of unique information in a cryptographic task related to secret key agreement. Our operational view of unique information entails rich physical intuition that leads to new insights into secret key agreement in the context of non-negative decompositions of the mutual information into redundant and synergistic contributions. Through this lens, we illuminate new directions for research in partial information decompositions and information-theoretic cryptography. Full article

(This article belongs to the Special Issue Synergy and Redundancy Measures: Theory and Applications to Characterize Complex Systems and Shape Neural Network Representations)

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15 pages, 664 KiB

Open AccessArticle

Few-Shot Graph Anomaly Detection via Dual-Level Knowledge Distillation

by Xuan Li, Dejie Cheng, Luheng Zhang, Chengfang Zhang and Ziliang Feng

Entropy 2025, 27(1), 28; https://doi.org/10.3390/e27010028 - 1 Jan 2025

Abstract

Graph anomaly detection is crucial in many high-impact applications across diverse fields. In anomaly detection tasks, collecting plenty of annotated data tends to be costly and laborious. As a result, few-shot learning has been explored to address the issue by requiring only a [...] Read more.

Graph anomaly detection is crucial in many high-impact applications across diverse fields. In anomaly detection tasks, collecting plenty of annotated data tends to be costly and laborious. As a result, few-shot learning has been explored to address the issue by requiring only a few labeled samples to achieve good performance. However, conventional few-shot models may not fully exploit the information within auxiliary sets, leading to suboptimal performance. To tackle these limitations, we propose a dual-level knowledge distillation-based approach for graph anomaly detection, DualKD, which leverages two distinct distillation losses to improve generalization capabilities. In our approach, we initially train a teacher model to generate prediction distributions as soft labels, capturing the entropy of uncertainty in the data. These soft labels are then employed to construct the corresponding loss for training a student model, which can capture more detailed node features. In addition, we introduce two representation distillation losses—short and long representation distillation—to effectively transfer knowledge from the auxiliary set to the target set. Comprehensive experiments conducted on four datasets verify that DualKD remarkably outperforms the advanced baselines, highlighting its effectiveness in enhancing identification performance. Full article

(This article belongs to the Special Issue Robustness of Graph Neural Networks)

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16 pages, 782 KiB

Open AccessArticle

Suppressing Polarization Mode Dispersion with the Quantum Zeno Effect

by Ian Nodurft, Alejandro Rodriguez Perez, Naveed Naimipour and Harry C. Shaw

Entropy 2025, 27(1), 27; https://doi.org/10.3390/e27010027 - 1 Jan 2025

Abstract

Polarization mode dispersion can introduce quantum decoherence in polarization encoded information, limiting the range of quantum communications protocols. Therefore, strategies to nullify the effect would reduce quantum decoherence and potentially increase the operational range of such technology. We constructed a quantum model of [...] Read more.

Polarization mode dispersion can introduce quantum decoherence in polarization encoded information, limiting the range of quantum communications protocols. Therefore, strategies to nullify the effect would reduce quantum decoherence and potentially increase the operational range of such technology. We constructed a quantum model of polarization mode dispersion alongside a two-level absorbing material. The two-level material serves to destructively measure one of two orthogonal polarization modes, thus projecting the polarization onto the other state. The theoretical results are supported by a numerical simulation in Mathematica Documentation where we compare the evolution of the polarization state with and without the absorbing material. We find that this strategy is effective in suppressing the effects of polarization mode dispersion, and that this method produces a global phase shift related to the waveguide’s birefringent properties. Full article

(This article belongs to the Section Quantum Information)

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36 pages, 2178 KiB

Open AccessArticle

Density Classification with Non-Unitary Quantum Cellular Automata

by Elisabeth Wagner, Federico Dell'Anna, Ramil Nigmatullin and Gavin K. Brennen

Entropy 2025, 27(1), 26; https://doi.org/10.3390/e27010026 - 31 Dec 2024

Abstract

The density classification (DC) task, a computation which maps global density information to local density, is studied using one-dimensional non-unitary quantum cellular automata (QCAs). Two approaches are considered: one that preserves the number density and one that performs majority voting. For number-preserving DC, [...] Read more.

The density classification (DC) task, a computation which maps global density information to local density, is studied using one-dimensional non-unitary quantum cellular automata (QCAs). Two approaches are considered: one that preserves the number density and one that performs majority voting. For number-preserving DC, two QCAs are introduced that reach the fixed-point solution in a time scaling quadratically with the system size. One of the QCAs is based on a known classical probabilistic cellular automaton which has been studied in the context of DC. The second is a new quantum model that is designed to demonstrate additional quantum features and is restricted to only two-body interactions. Both can be generated by continuous-time Lindblad dynamics. A third QCA is a hybrid rule defined by both discrete-time and continuous-time three-body interactions that is shown to solve the majority voting problem within a time that scales linearly with the system size. Full article

(This article belongs to the Special Issue Recent Advances and Challenges in Quantum Cellular Automata)

38 pages, 663 KiB

Open AccessArticle

Comparing Statistical and Machine Learning Methods for Time Series Forecasting in Data-Driven Logistics—A Simulation Study

by Lena Schmid, Moritz Roidl, Alice Kirchheim and Markus Pauly

Entropy 2025, 27(1), 25; https://doi.org/10.3390/e27010025 - 31 Dec 2024

Abstract

Many planning and decision activities in logistics and supply chain management are based on forecasts of multiple time dependent factors. Therefore, the quality of planning depends on the quality of the forecasts. We compare different state-of-the-art forecasting methods in terms of forecasting performance. [...] Read more.

Many planning and decision activities in logistics and supply chain management are based on forecasts of multiple time dependent factors. Therefore, the quality of planning depends on the quality of the forecasts. We compare different state-of-the-art forecasting methods in terms of forecasting performance. Differently from most existing research in logistics, we do not perform this in a case-dependent way but consider a broad set of simulated time series to give more general recommendations. We therefore simulate various linear and nonlinear time series that reflect different situations. Our simulation results showed that the machine learning methods, especially Random Forests, performed particularly well in complex scenarios, with the differentiated time series training significantly improving the robustness of the model. In addition, the time series approaches proved to be competitive in low noise scenarios. Full article

(This article belongs to the Section Multidisciplinary Applications)

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24 pages, 2985 KiB

Open AccessArticle

Algorithms for Solving the Equilibrium Composition Model of Arc Plasma

by Zhongyuan Chi, Yuzhang Ji, Ningning Liu, Tianchi Jiang, Xin Liu and Weijun Zhang

Entropy 2025, 27(1), 24; https://doi.org/10.3390/e27010024 - 31 Dec 2024

Abstract

In the present study, the Homotopy Levenberg−Marquardt Algorithm (HLMA) and the Parameter Variation Levenberg–Marquardt Algorithm (PV–LMA), both developed in the context of high-temperature composition, are proposed to address the equilibrium composition model of plasma under the condition of local thermodynamic and chemical equilibrium. [...] Read more.

In the present study, the Homotopy Levenberg−Marquardt Algorithm (HLMA) and the Parameter Variation Levenberg–Marquardt Algorithm (PV–LMA), both developed in the context of high-temperature composition, are proposed to address the equilibrium composition model of plasma under the condition of local thermodynamic and chemical equilibrium. This model is essentially a nonlinear system of weakly singular Jacobian matrices. The model was formulated on the basis of the Saha and Guldberg–Waage equations, integrated with Dalton’s law of partial pressures, stoichiometric equilibrium, and the law of conservation of charge, resulting in a nonlinear system of equations with a weakly singular Jacobian matrix. This weak singularity primarily arises due to significant discrepancies in the coefficients between the Saha equation and the Guldberg–Waage equation, attributed to differing chemical reaction energies. By contrast, the coefficients in the equations derived from the other three principles within the equilibrium composition model are predominantly single−digit constants, further contributing to the system’s weak singularity. The key to finding the numerical solution to nonlinear equations is to set reasonable initial values for the iterative solution process. Subsequently, the principle and process of the HLMA and PV–LMA algorithms are analyzed, alongside an analysis of the unique characteristics of plasma equilibrium composition at high temperatures. Finally, a solving method for an arc plasma equilibrium composition model based on high temperature composition is obtained. The results show that both HLMA and PV–LMA can solve the plasma equilibrium composition model. The fundamental principle underlying the homotopy calculation of the (n−1) −th iteration, which provides a reliable initial value for the n−th LM iteration, is particularly well suited for the solution of nonlinear equations. A comparison of the computational efficiency of HLMA and PV–LMA reveals that the latter exhibits superior performance. Both HLMA and PV–LMA demonstrate high computational accuracy, as evidenced by the fact that the variance of the system of equations ||F|| < 1 × 10⁻¹⁵. This finding serves to substantiate the accuracy and feasibility of the method proposed in this paper. Full article

(This article belongs to the Section Statistical Physics)

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30 pages, 2836 KiB

Open AccessArticle

Analysis of the Spatiotemporal Heterogeneity and Influencing Factors of Regional Economic Resilience in China

by Qiuyue Zhang, Yili Lin, Yu Cao and Long Luo

Entropy 2025, 27(1), 23; https://doi.org/10.3390/e27010023 - 31 Dec 2024

Abstract

This study estimates regional economic resilience in China from 2000 to 2022, focusing on economic resistance resilience, recovery resilience, and reorientation resilience. The entropy method, kernel density estimation, and spatial Durbin model are applied to examine the spatiotemporal evolution and influencing factors. The [...] Read more.

This study estimates regional economic resilience in China from 2000 to 2022, focusing on economic resistance resilience, recovery resilience, and reorientation resilience. The entropy method, kernel density estimation, and spatial Durbin model are applied to examine the spatiotemporal evolution and influencing factors. The results show significant spatial clustering, with stronger resilience in the east and weaker resilience in the west. While economic resilience has generally improved, regional disparities persist. Key factors such as human capital, urban hospitals, financial development, market consumption, and environmental quality have a positive effect on resilience, with spatial spillover effects. However, human capital and urban hospitals also show a negative indirect impact on surrounding regions. The influence of these factors varies across regions and periods, indicating strong spatiotemporal heterogeneity. Full article

(This article belongs to the Special Issue Entropy-Based Applications in Economics, Finance and Management, 3rd Edition)

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33 pages, 3930 KiB

Open AccessArticle

The Second Law of Infodynamics: A Thermocontextual Reformulation

by Harrison Crecraft

Entropy 2025, 27(1), 22; https://doi.org/10.3390/e27010022 - 30 Dec 2024

Abstract

Vopson and Lepadatu recently proposed the Second Law of Infodynamics. The law states that while the total entropy increases, information entropy declines over time. They state that the law has applications over a wide range of disciplines, but they leave many key questions [...] Read more.

Vopson and Lepadatu recently proposed the Second Law of Infodynamics. The law states that while the total entropy increases, information entropy declines over time. They state that the law has applications over a wide range of disciplines, but they leave many key questions unanswered. This article analyzes and reformulates the law based on thermocontextual interpretation (TCI). The TCI generalizes Hamiltonian mechanics by defining states and transitions thermocontextually with respect to an ambient-temperature reference state. The TCI partitions energy into exergy, which can do work on the ambient surroundings, and entropic energy with zero work potential. The TCI is further generalized here to account for a reference observer’s actual knowledge. This enables partitioning exergy into accessible exergy, which is known and accessible for use, and configurational energy, which is knowable but unknown and inaccessible. The TCI is firmly based on empirically validated postulates. The Second Law of thermodynamics and its information-based analog, MaxEnt, are logically derived corollaries. Another corollary is a reformulated Second Law of Infodynamics. It states that an external agent seeks to increase its access to exergy by narrowing its information gap with a potential exergy source. The principle is key to the origin of self-replicating chemicals and life. Full article

(This article belongs to the Special Issue Thermodynamics of Dissipative Structures and Related Emergent Phenomena)

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5 pages, 197 KiB

Open AccessArticle

A Simple Wide Range Approximation of Symmetric Binomial Distribution

by Tamás Szabados

Entropy 2025, 27(1), 21; https://doi.org/10.3390/e27010021 - 30 Dec 2024

Abstract

The paper gives a wide range, uniform, local approximation of symmetric binomial distribution. The result clearly shows how one has to modify the classical de Moivre–Laplace normal approximation in order to give an estimate at the tail as well as to minimize the [...] Read more.

The paper gives a wide range, uniform, local approximation of symmetric binomial distribution. The result clearly shows how one has to modify the classical de Moivre–Laplace normal approximation in order to give an estimate at the tail as well as to minimize the relative error. Full article

(This article belongs to the Special Issue The Random Walk Path of Pál Révész in Probability)

16 pages, 7577 KiB

Open AccessArticle

Lattice Boltzmann Modeling of Additive Manufacturing of Functionally Graded Materials

by Dmytro Svyetlichnyy

Entropy 2025, 27(1), 20; https://doi.org/10.3390/e27010020 - 30 Dec 2024

Abstract

Functionally graded materials (FGMs) show continuous variations in properties and offer unique multifunctional capabilities. This study presents a simulation of the powder bed fusion (PBF) process for FGM fabrication using a combination of Unity-based deposition and lattice Boltzmann method (LBM)-based process models. The [...] Read more.

Functionally graded materials (FGMs) show continuous variations in properties and offer unique multifunctional capabilities. This study presents a simulation of the powder bed fusion (PBF) process for FGM fabrication using a combination of Unity-based deposition and lattice Boltzmann method (LBM)-based process models. The study introduces a diffusion model that allows for the simulation of material mixtures, in particular AISI 316L austenitic steel and 18Ni maraging 300 martensitic steel. The Unity-based model simulates particle deposition with controlled distribution, incorporating variations in particle size, friction coefficient, and chamber wall rotation angles. The LBM model that simulated free-surface fluid flow, heat flow, melting, and solidification during the PBF process was extended with diffusion models for mixture fraction and concentration-dependent properties. Comparison of the results obtained in simulation with the experimental data shows that they are consistent. Future research may be connected with further verification and validation of the model, by modeling different materials. The presented model can be used for the simulation, study, modeling, and optimization of the production of functionally graded materials in PBF processes. Full article

(This article belongs to the Special Issue 180th Anniversary of Ludwig Boltzmann)

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11 pages, 695 KiB

Open AccessArticle

Persistent Homology Combined with Machine Learning for Social Network Activity Analysis

by Zhijian Zhang, Yuqing Sun, Yayun Liu, Lin Jiang and Zhengmi Li

Entropy 2025, 27(1), 19; https://doi.org/10.3390/e27010019 - 30 Dec 2024

Abstract

Currently, the rapid development of social media enables people to communicate more and more frequently in the network. Classifying user activities in social networks helps to better understand user behavior in social networks. This paper first creates an ego network for each user, [...] Read more.

Currently, the rapid development of social media enables people to communicate more and more frequently in the network. Classifying user activities in social networks helps to better understand user behavior in social networks. This paper first creates an ego network for each user, encodes the higher-order topological features of the ego network as persistence diagrams using persistence homology, and computes the persistence entropy. Then, based on the persistence entropy, this paper defines the Norm Entropy-NE(X) to represent the complexity of the topological features of the ego network, a larger NE(X) indicates a higher topological complexity, i.e., the higher the activity of the nodes, thus indicating the degree of activity of the nodes. The paper uses the extracted set of feature vectors to train the machine learning model to classify the users in the social network. Numerical experiments are conducted to evaluate the performance of clustering quality metrics such as profile coefficients. The results show that the proposed algorithm can effectively classify social network users into different groups, which provides a good foundation for further research and application. Full article

(This article belongs to the Special Issue Spreading Dynamics in Complex Networks)

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17 pages, 658 KiB

Open AccessArticle

Heat Transport Hysteresis Generated Through Frequency Switching of a Time-Dependent Temperature Gradient

by Renai Chen and Galen T. Craven

Entropy 2025, 27(1), 18; https://doi.org/10.3390/e27010018 - 30 Dec 2024

Abstract

A stochastic energetics framework is applied to examine how periodically shifting the frequency of a time-dependent oscillating temperature gradient affects heat transport in a nanoscale molecular model. We specifically examine the effects that frequency switching, i.e., instantaneously changing the oscillation frequency of the [...] Read more.

A stochastic energetics framework is applied to examine how periodically shifting the frequency of a time-dependent oscillating temperature gradient affects heat transport in a nanoscale molecular model. We specifically examine the effects that frequency switching, i.e., instantaneously changing the oscillation frequency of the temperature gradient, has on the shape of the heat transport hysteresis curves generated by a particle connected to two thermal baths, each with a temperature that is oscillating in time. Analytical expressions are derived for the energy fluxes in/out of the system and the baths, with excellent agreement observed between the analytical expressions and the results from nonequilibrium molecular dynamics simulations. We find that the shape of the heat transport hysteresis curves can be significantly altered by shifting the frequency between fast and slow oscillation regimes. We also observe the emergence of features in the hysteresis curves such as pinched loops and complex multi-loop patterns due to the frequency shifting. The presented results have implications in the design of thermal neuromorphic devices such as thermal memristors and thermal memcapacitors. Full article

(This article belongs to the Special Issue Stochastic Thermodynamics of Microscopic Systems)

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3 pages, 134 KiB

Open AccessEditorial

Updates on Information Theory and Network Coding

by Shenghao Yang and Kenneth W. Shum

Entropy 2025, 27(1), 17; https://doi.org/10.3390/e27010017 - 30 Dec 2024

Abstract

Around the year 2000, network coding introduced the concept that coding can replace the basic packet forwarding operation used in traditional network communication systems [...] Full article

(This article belongs to the Special Issue Information Theory and Network Coding II)

15 pages, 5103 KiB

Open AccessArticle

Relationship Between the 2019 Ridgecrest, California, M_W7.1 Earthquake and Its M_W6.4 Foreshock Sequence

by Jianchang Zheng, Zhengshuai Zhang and Xiaohan Li

Entropy 2025, 27(1), 16; https://doi.org/10.3390/e27010016 - 28 Dec 2024

Abstract

The 2019 Ridgecrest M_W7.1 earthquake has received significant attention due to its complex fault activity. It is also noticeable for its M_W6.4 foreshock sequence. There are intricate dynamic relationships between earthquakes in such vigorous sequences. Based on the relocated [...] Read more.

The 2019 Ridgecrest M_W7.1 earthquake has received significant attention due to its complex fault activity. It is also noticeable for its M_W6.4 foreshock sequence. There are intricate dynamic relationships between earthquakes in such vigorous sequences. Based on the relocated catalogue, we adopt the nearest neighbour algorithm to analyze its foreshock and aftershock sequences. Detailed links and family structures of the sequence are obtained. The results show that a M_W5.0 event at 03:16 (UTC) on 6 July is a direct foreshock of the M_W7.1 mainshock. It is likely related to barriers on the northwest-striking fault. The M_W6.4 event on 4 July is characterized as a complex conjugate rupture. Notably, a magnitude 4.0 event occurred on the northwest-striking fault before the M_W6.4 event, establishing it as a direct foreshock. The Ridgecrest sequence is predominantly influenced by northwest fault activity. It first caused small fractures on the northwest-striking fault. Then, it triggered conjugate slips on the southwest-striking fault. Lastly, it led to larger ruptures on the northwest-striking fault. Full article

(This article belongs to the Special Issue Time Series Analysis in Earthquake Complex Networks)

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16 pages, 3804 KiB

Open AccessArticle

Ring Oscillators with Additional Phase Detectors as a Random Source in a Random Number Generator

by Łukasz Matuszewski, Mieczysław Jessa and Jakub Nikonowicz

Entropy 2025, 27(1), 15; https://doi.org/10.3390/e27010015 - 28 Dec 2024

Abstract

In this paper, we propose a method to enhance the performance of a random number generator (RNG) that exploits ring oscillators (ROs). Our approach employs additional phase detectors to extract more entropy; thus, RNG uses fewer resources to produce bit sequences that pass [...] Read more.

In this paper, we propose a method to enhance the performance of a random number generator (RNG) that exploits ring oscillators (ROs). Our approach employs additional phase detectors to extract more entropy; thus, RNG uses fewer resources to produce bit sequences that pass all statistical tests proposed by National Institute of Standards and Technology (NIST). Generating a specified number of bits is on-demand, eliminating the need for continuous RNG operation. This feature enhances the security of the produced sequences, as eavesdroppers are unable to observe the continuous random bit generation process, such as through monitoring power lines. Furthermore, our research demonstrates that the proposed RNG’s perfect properties remain unaffected by the manufacturer of the field-programmable gate arrays (FPGAs) used for implementation. This independence ensures the RNG’s reliability and consistency across various FPGA manufacturers. Additionally, we highlight that the tests recommended by the NIST may prove insufficient in assessing the randomness of the output bit streams produced by RO-based RNGs. Full article

(This article belongs to the Section Signal and Data Analysis)

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