Statistical Test Suite Research Articles

GAN-based pseudo random number generation optimized through genetic algorithms

Pseudo-random number generators (PRNGs) are deterministic algorithms that generate sequences of numbers approximating the properties of random numbers, which are widely utilized in various fields. In this paper, we present a Genetic Algorithm Optimized Generative Adversarial Network (hereinafter referred to as GAGAN), which is designed for the effective training of discrete generative adversarial networks. In situations where non-differentiable activation functions, such as the modulo operation, are employed and traditional gradient-based backpropagation methods are inapplicable, genetic algorithms are utilized to optimize the parameters of the generator network. Based on this framework, we propose a novel recursive PRNG. Given that a PRNG can be constructed from one-way functions and their associated hardcore predicates, our proposed generator consists of two neural networks that simulate these functions and serve as the state transition function and the output function, respectively. The proposed PRNG has been rigorously tested using stringent benchmarks such as the NIST Statistical Test Suite (SP800-22) and the Chinese standard for random number generation (GM/T 0005-2021). Additionally, it has demonstrated outstanding performance in terms of Hamming distance. The results indicate that the proposed GAN-based PRNG has achieved a high degree of randomness and is highly sensitive to variations in the input.

Colloidal particles as noise source for random number generation

In this work, we investigate colloidal particle patterns as a possible noise source for random number generation. We systematically analyze the minimum entropy of the noise source over different particle concentrations of {1, 3, 5, 7, 10, 12, 15} mg/ml according to the recommendations of the National Institute of Standards and Technology Special Publication 800-90B. The estimated minimum entropy of the non-independent and identically distributed particle pattern noise source is Hmin = 0.5896/1 bit at a particle amount of 5 mg/ml. For further entropy extraction on the noise source data, the secure hash algorithm is used to construct an entropy source. The randomness of the derived entropy source is verified according to the National Institute of Standards and Technology Special Publication 800-22 Rev. 1a and the accompanying statistical test suite. The entropy source passes all randomness tests of the statistical test suite and shows an estimated minimum entropy of Hmin = 0.9992/1 bit.

A robust audio steganography technique based on image encryption using different chaotic maps

The development of innovative methods for concealing critical data in multimedia files has exploded in information security in recent years. Cryptography and steganography cannot be used alone to protect data; rather, they can be combined and used in a single system. Audio steganography is among the most important information security techniques. It involves the concealment of information within audio signals to achieve covert communication. This paper introduces a comprehensive technique that integrates chaos Henon, Baker, and Arnold maps for image encryption with audio steganography to create a robust and secure audio steganography technique. First, the target image is encrypted using chaotic maps. Then, it is embeded within the high frequencies of the cover audio signal based on the Inverse Short Time Fourier Transform (ISTFT) to be transmitted to the destination through the channel. By integrating both encryption and concealment techniques, the cover audio signal quality can be preserved. Moreover, the hidden image security and robustness are improved, making the technique resistant to many types of attacks. The simulation results confirm that the suggested technique is robust in the presence of attacks. It achieves a distinct perceptual quality with an appreciated peak signal-to-noise ratio (PSNR) of 91.2 dB and a Mean Square Error (MSE) of 7.5 × 10–10. The randomness of the resulting encrypted image has successfully passed the National Institute of Standards and Technology (NIST) statistical test suite.

Autonomous three-dimensional oscillator with two and four wings attractors embedded in the microcontroller: analysis, amplitude controls, random number generator, and image encryption application

Robust chaotic systems offer unpredictability, complex dynamics, noise-like properties, efficient bifurcation behavior, and the ability to model real-world phenomena, making them valuable in diverse scientific and engineering applications. This paper details on the dynamical appraisal, amplitude controls, microcontroller execution, Random number generator (RNG) of an autonomous three-dimensional (3D) oscillator with two and four wings attractors (ATDOTFWA), and its image encryption application. Thanks to the Routh-Hurwitz criteria, five steady states found in the ATDOTFWA are classified as stable or unstable, depending on its two control parameters. During the numerical simulations employing the Runge–Kutta scheme, the ATDOTFWA exhibit a wide range of dynamic behaviors, including no oscillations, Hopf bifurcation, limit cycle, five distinct presentations of two wings chaotic structures, monostable and bistable two wings chaotic structures, bistable and monostable regular oscillations, chaotic bursting characteristics, coexistence of period-2-oscillations and four wings chaotic structure, and four wings chaotic attractor which were validated experimentally by the microcontroller implementation. The total and partial controls of the amplitude are achieved in the ATDOTFWA. A RNG is designed based on the ATDOTFWA, and the generated random numbers are successfully tested using the ENT and NIST 800–22 statistical test suites, demonstrating the reliability of the ATDOTFWA-based RNG. This reliability is further confirmed through the application of the ATDOTFWA-based RNG in an efficient and secure image encryption process, where the generated random numbers are used as the encryption key. The effectiveness of the image encryption process is validated through comprehensive cryptanalysis, with an encryption time of 0.1923 s for a 512×512 image, an average normalized pixel change rate (NPCR) of 99.6126%, an average unified average changing intensity (UACI) of 33.4578%, and an average information entropy of 7.9994.

A Stealthy Communication Model with Blockchain Smart Contract for Bidding Systems

With the widespread adoption of blockchain technology, its public ledger characteristic enhances transaction transparency but also amplifies the risk of privacy breaches. Attackers can infer users’ real identities and behaviors by analyzing public transaction patterns and address relationships, posing a severe threat to users’ privacy and security, and thus hindering further advancements in blockchain applications. To address this challenge, covert communication has emerged as an effective strategy for safeguarding the privacy of blockchain users and preventing information leakage. But existing blockchain-based covert communication schemes rely solely on the immutability of blockchain itself for robustness and suffer from low transmission efficiency. To tackle these issues, this paper proposes a stealthy communication model with blockchain smart contract for bidding systems. The model initiates by preprocessing sensitive information using a secret-sharing algorithm-the Shamir (t, n) threshold scheme-and subsequently embeds this information into bidding amounts, facilitating the covert transfer of sensitive data. We implemented and deployed this model on the Ethereum platform and conducted comprehensive performance evaluations. To assess the stealthiness of our approach, we employed a suite of statistical tests including the CDF, the Kolmogorov–Smirnov test, Welch’s t-test and K–L divergence. These analyses confirmed that amounts carrying concealed information were statistically indistinguishable from regular transactions, thus validating the effectiveness of our solution in maintaining the anonymity and confidentiality of information transmission within the blockchain ecosystem.

X-ray-driven multi-bit quantum random number generator.

Random numbers are vital in cryptography, simulation modeling, and gambling. This study presents a scheme for a multi-bit quantum random number generator utilizing X-ray radiation. Using a homemade multi-pixel single-photon detector array, we extract randomness from three modes of X-ray radiation: arrival time, spatial position, and polarization direction. We employ the Toeplitz Matrix Hashing extractor for randomness distillation, resulting in the extraction of 40.4 million random bits at a rate of 33.7 bits per photon. The generated random numbers pass all test criteria in the National Institute of Standards and Technology statistical test suite. Our work paves what we believe to be a novel method for generating multi-bit quantum random numbers, promising enhanced security and reliability in various technological applications.

Fractal Tent Map with Application to Surrogate Testing

Discrete chaotic maps are a mathematical basis for many useful applications. One of the most common is chaos-based pseudorandom number generators (PRNGs), which should be computationally cheap and controllable and possess necessary statistical properties, such as mixing and diffusion. However, chaotic PRNGs have several known shortcomings, e.g., being prone to chaos degeneration, falling in short periods, and having a relatively narrow parameter range. Therefore, it is reasonable to design novel simple chaotic maps to overcome these drawbacks. In this study, we propose a novel fractal chaotic tent map, which is a generalization of the well-known tent map with a fractal function introduced into the right-hand side. We construct and investigate a PRNG based on the proposed map, showing its high level of randomness by applying the NIST statistical test suite. The application of the proposed PRNG to the task of generating surrogate data and a surrogate testing procedure is shown. The experimental results demonstrate that our approach possesses superior accuracy in surrogate testing across three distinct signal types—linear, chaotic, and biological signals—compared to the MATLAB built-in randn() function and PRNGs based on the logistic map and the conventional tent map. Along with surrogate testing, the proposed fractal tent map can be efficiently used in chaos-based communications and data encryption tasks.

Securing Data Exchange with Elliptic Curve Cryptography: A Novel Hash-Based Method for Message Mapping and Integrity Assurance

To ensure the security of sensitive data, elliptic curve cryptography (ECC) is adopted as an asymmetric method that balances security and efficiency. Nevertheless, embedding messages into elliptic curve (EC) points poses a significant challenge. The intricacies of this process can greatly affect the overall security and efficiency of the cryptosystem, reflecting security vulnerabilities observed in many existing schemes that utilize ElGamal ECC-based encryption. In this paper, we introduce an innovative hash-based technique for securely embedding messages into EC points before encryption. A random parameter and a shared secret point generated through the EC Diffie–Hellman protocol are used to bolster the scheme’s security. The security of the proposed method is evaluated against various attack models; moreover, the complexity, and sensitivity of the encryption scheme, as well as its inputs, are analyzed. The randomness assessment of the ciphertext was performed using the NIST statistical test suite. Additionally, we propose a mechanism to ensure the integrity of the message by securely appending a tag to the ciphertext. As a consequence, a comprehensive analysis of our scheme demonstrates its effectiveness in maintaining data security and integrity against various attack models. The algorithm also meets more criteria such as the strict avalanche criterion, linear complexity, and operability.

PiRATe: A Comprehensive Set of Statistical Tests for Evaluation of Quantum Random Number Generators

As true random numbers are essential for many applications, high-quality Random Number Generators (RNGs) are highly demanded. Several different statistical test suites have been developed to evaluate the quality of RNGs. However, some programming skills are required to work with these statistical tests as they are not available as self-contained software and often are without a Graphical User Interface (GUI). In this work, we have developed PiRATe (Pi Randomness Assessment Test) an easy-to-use wrapper software for the assessment of RNGs using a comprehensive set of statistical tests, including DIEHARDER, NIST SP800-22, NIST SP800-90B, Entropy-Nonlinearity-Test (ENT), Borel Normality, and four Chaitin-Schwartz-Solovay-Strassen tests. We then used PiRATe to evaluate the quality of five different (Commercial and Experimental) Quantum Random Number Generators (QRNGs).

Evaluating Urban Green Space Inequity to Promote Distributional Justice in Portland, Oregon

Access and exposure to urban green space—the combination of parks and vegetative cover in cities—are associated with various health benefits. As urban green space is often unequally distributed throughout cities, understanding how it is allocated across socio-demographic populations can help city planners and policy makers identify and address urban environmental justice and health equity issues. To our knowledge, no studies have yet combined assessments of park quality, park availability, and green cover to inform equitable urban green space planning. To this end, we developed a comprehensive methodology to identify urban green space inequities at the city scale and applied it in Portland, OR, USA. After auditing all public parks in Portland and gathering green cover data from publicly accessible repositories, we used a suite of statistical tests to evaluate distribution of parks and green cover across Census block groups, comprising race, ethnicity, income, and educational attainment characteristics. Right-of-way tree canopy cover was the most significant urban green space inequity identified in bivariate analysis (rs = −0.73). Spatial autoregressive models identified that right-of-way, private, and overall tree canopy cover (Nagelkerke pseudo-R2 = 0.66, 0.77, and 0.67, respectively) significantly decreased with the proportion of minoritized racial population and increased with median income. The results were then used to identify priority locations for specific urban green space investments. This research establishes a process to assess intra-urban green space inequities, as well as identify data-informed and spatially explicit planning priorities to promote health equity and environmental justice.

Enhancing Visual Data Security: A Novel FSM-Based Image Encryption and Decryption Methodology

The paper presents a comprehensive exploration of a novel image encryption and decryption methodology, leveraging finite state machines (FSM) for the secure transformation of visual data. The study meticulously evaluates the effectiveness of the proposed encryption algorithm using a diverse image dataset. The encryption algorithm demonstrates high proficiency in obfuscating the original content of images, producing cipher images that resemble noise, thereby substantiating the encryption’s effectiveness. The robustness of the proposed methodology is further evidenced by its performance in the National Institute of Standards and Technology Statistical Test Suite (NIST STS). Such achievements highlight the algorithm’s capability to maintain the stochastic integrity of encrypted data, a critical aspect of data security and confidentiality. Histogram analysis revealed that the encryption process achieves a uniform distribution of pixel values across the encrypted images, masking any identifiable patterns and enhancing the security level. Correlation analysis corroborated the success of the encryption technique, showing a substantial reduction in the correlation among adjacent pixel values, thereby disrupting spatial relationships essential for deterring unauthorized data analysis. This improvement indicates the algorithm’s efficiency in altering pixel patterns to secure image data. Additionally, a comparative analysis of correlation coefficients using various encryption methods on the Lenna image offered insights into the relative effectiveness of different techniques, emphasizing the importance of method selection based on specific security requirements and data characteristics.

Blood-inspired random bit generation using microfluidics system

The development of random number generators (RNGs) using speckle patterns is pivotal for secure encryption key generation, drawing from the recent statistical properties identified in speckle-based imaging. Speckle-based RNG systems generate a sequence of random numbers through the unpredictable and reproducible nature of speckle patterns, ensuring a source of randomness that is independent of algorithms. However, to guarantee their effectiveness and reliability, these systems demand a meticulous and rigorous approach. In this study, we present a blood-inspired RNG system with a microfluidics device, designed to generate random numbers at a rate of 5.5 MHz and a high-speed of 1250 fps. This process is achieved by directing a laser beam through a volumetric scattering medium to procure speckle patterns. Additionally, designed microfluidic device requires only a minimal blood sample of 5 µl to capture these speckle patterns effectively. After implementing the two-pass tuple-output von Neumann debiasing algorithm to counteract statistical biases, we utilized the randomness statistical test suite from the National Institute of Standards and Technology for validation. The generated numbers successfully passed these tests, ensuring their randomness and unpredictability. Our blood-inspired RNG, utilizing whole blood, offers a pathway for affordable, high-output applications in fields like encryption, computer security, and data protection.

A secure fingerprint hiding technique based on DNA sequence and mathematical function.

DNA steganography is a technique for securely transmitting important data using DNA sequences. It involves encrypting and hiding messages within DNA sequences to prevent unauthorized access and decoding of sensitive information. Biometric systems, such as fingerprinting and iris scanning, are used for individual recognition. Since biometric information cannot be changed if compromised, it is essential to ensure its security. This research aims to develop a secure technique that combines steganography and cryptography to protect fingerprint images during communication while maintaining confidentiality. The technique converts fingerprint images into binary data, encrypts them, and embeds them into the DNA sequence. It utilizes the Feistel network encryption process, along with a mathematical function and an insertion technique for hiding the data. The proposed method offers a low probability of being cracked, a high number of hiding positions, and efficient execution times. Four randomly chosen keys are used for hiding and decoding, providing a large key space and enhanced key sensitivity. The technique undergoes evaluation using the NIST statistical test suite and is compared with other research papers. It demonstrates resilience against various attacks, including known-plaintext and chosen-plaintext attacks. To enhance security, random ambiguous bits are introduced at random locations in the fingerprint image, increasing noise. However, it is important to note that this technique is limited to hiding small images within DNA sequences and cannot handle video, audio, or large images.

A High-Quality Random Number Generator Using Multistage Ring Oscillators and Fast Fourier Transform-Based Noise Extraction

Random Numbers are widely employed in cryptography and security applications. This paper presents a novel approach to generate high-quality random bitstreams by harnessing the inherent noise properties of ring oscillators. We implemented ring oscillators with varying numbers of stages (3, 5, and 7), different geometries and different startup voltages in Cadence and recorded their total output power, which includes the cumulative noise effects. Subsequently, we exported these power measurements to MATLAB, where we applied a Fast Fourier Transform (FFT)-based technique to extract the total noise characteristics for each ring oscillator. Using the obtained noise data, we generated separate random bitstreams of 10 million bits for the 3-stage, 5-stage, and 7-stage ring oscillators. The final random bitstream, consisting of 10 million bits, was created by performing a bitwise XOR operation on the bitstreams generated by each ring oscillator. The degree of randomness of the generated bitstreams was assessed using the NIST 800-22 statistical test suite. Remarkably, the final random bitstream exhibited strong robustness and suitability for cryptographic applications. This innovative approach leverages the noise properties of ring oscillators to create reliable random bitstreams, offering potential applications in secure communications and cryptography. The results highlight the feasibility of using ring oscillators as noise sources for random bit generation and underscore their effectiveness in meeting stringent randomness criteria.

Towards accurate keyspace analysis of chaos-based image ciphers

In recent years, there has been a surge in new chaos-based cryptographic algorithms, many of which claim to have unusually large keyspaces. Although cryptographic primitives such as symmetric-key ciphers should have a secret keyspace large enough to resist brute force attacks, simply increasing the size of a secret key may not lead to improved security margins. An n-bit key may not necessarily have a keyspace of 2n-1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$2^n-1$$\\end{document} due to the key scheduling algorithm or how the key is used. In this paper, we cryptanalyse several chaos-based algorithms from the perspective of their key schedules. Our numerical analysis is based on the known-plaintext attack model, Kerckhoff’s principle and considers the number representations used for real number computation. Our analysis reveals that the actual security margins for these ciphers are significantly lower, some by a factor of over 2100\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$2^{100}$$\\end{document} than what was claimed. We then provide accurate keyspace estimates for these ciphers. Finally, we highlight alternative solutions for how secret keys can be used in the context of chaos-based cryptography and propose a simple key schedule as a proof of concept. Despite its simplicity, the proposed key schedule not only ensures that the keyspace matches the key length but also passes both the NIST and ENT statistical test suites, making it a viable option for generating secure cryptographic keys. Our work contributes towards addressing one of the fundamental problems in chaos-based cryptography that limits its real-world impact and reputation within the cryptographic community.

Lorenz Kaotik Devre Tabanlı Entropi Kaynağı ile Özgün Gerçek Rasgele Sayı Üretimi ve Ses Şifreleme Uygulaması

This paper introduces a methodology for generating secure cryptographic key bits from analog values obtained from the Lorenz chaotic circuit. The analog values are transferred from the chaotic circuit to the computer via an Analog Discovery-2 device and then post-processed by using a fixed-point number representation format and Von-Neumann corrector for the sampled values on the MATLAB program. By employing this method, the analog values are digitized and randomized as the main idea is to obtain secure and efficient statistically random bits. Furthermore, the generated random bits are utilized for secure audio transmission by demonstrating a practical application of the proposed methodology. In addition to the classical randomness test criteria, and NIST 800.22 statistical test suite, the throughput bit stream is also subjected to Chi-square and FIPS 140-1 tests to further evaluate its effectiveness. The results of these comprehensive tests confirm the successful performance of the proposed system in generating statistically random bits and its secure audio encryption system. The utilization of the Lorenz chaotic circuit as an entropy source in generating true random bits for secure audio transmission applications showcases the potential of the proposed system.

Secure post-processing for non-ideal photon arrival time based quantum random number generator

Utilizing the inherently unpredictable nature of quantum mechanics, quantum random number generators (QRNGs) can provide randomness for applications where quality entropy (like in the case of cryptography) is essential. We present a post-processing scheme utilizing min-entropy estimation and hashing for optical QRNGs based on measuring individual photon arrival times. Our method allows for the handling of possible errors due to non-ideal components or even a potential attacker, given some basic assumptions to reliably produce a safe, good quality, uniformly distributed bitstream as output. We validate our results with an intentionally non-ideal measurement setup to show robustness, while also statistically testing our final output with four popular statistical test suites.

Lightweight encryption with data and device integrity using NLFSR and PUF for the Internet of Medical Things

Nowadays the Internet of Medical Things (IoMT) is in top demand; they communicate with each other in an IoT network, but there are various security issues including privacy preservation, data and device integrity, and authentication. The IoMT devices have challenges like limited computational power and resources, so conventional techniques are not suitable for them. This paper presents a lightweight stream cipher to ensure privacy protection, data integrity, and device integrity using a message authentication code (MAC). The stream cipher is designed using a nonlinear feedback shift register (NLFSR). The cipher is associated with a MAC generated by concatenating a physical unclonable function (PUF) response and the hash of the plaintext to protect the device and data integrity. The use of NLFSR and PUF makes the proposed scheme robust and lightweight for resource-constrained devices like MIoT. To evaluate the quality of the cipher the NIST 800-22 statistical test suite (NIST STS) is used, and results are compared with existing stream ciphers like Rivest cipher 4 (RC4), RC4 based on chaotic mapping (RCCM), and product algebra RCCM (PARCCM). All the tests and comparisons were performed using a Heart Disease Dataset. The scheme ensures the confidentiality and integrity of sensitive medical data which are critical for protecting patient privacy and regulatory compliance. The proposed scheme can also resist cloning attacks on the IoMT devices.

Land Use and Land Cover Trends and Their Impact on Streamflow and Sediment Yield in a Humid Basin of Brazil’s Atlantic Forest Biome

Understanding the trends in land use and land cover (LULC) is crucial for modeling streamflow and sediment yield, particularly in hydrological basins. This study examined the impact of LULC on the dynamics of streamflow and sediment yield within a humid tropical basin of the Atlantic Forest biome in Brazil, focusing on the period from 2000 to 2016. Changes in LULC were analyzed using annual MapBiomas data products for the same period. The Soil and Water Assessment Tool (SWAT) model was deployed to simulate streamflow and sediment yield based on LULC changes. To investigate temporal trends in LULC, a suite of non-parametric statistical tests, including the Mann–Kendall, Pettitt, and Sen’s slope estimator tests, was employed. Ecological diversity indices such as Shannon–Weaver, Simpson, and Pielou were applied to assess forest fragmentation, along with the Forest Fragmentation Index. The results revealed a growing trend in urban and sugarcane areas, coupled with a decline in dense vegetation, mangroves, and other forms of dense vegetation. With regard to the correlation between land uses and hydrological variables, the findings indicate minor variations in hydrological balance, attributable to the not-so-significant changes among the studied land-use scenarios, except for sediment yield estimates, which showed more considerable alterations. Notably, the estimates for 2000 and 2013–2016 were the most divergent. In a broader scientific context, this research conclusively establishes that the incorporation of dynamic LULC data into the SWAT model augments the precision and robustness of simulations pertaining to agricultural watersheds, thereby enabling a more comprehensive hydrological characterization of the study area.

Critical Analysis of Beta Random Variable Generation Methods

The fast generation of values of the beta random variable is a subject of great interest and multiple applications, ranging from purely mathematical and statistical ones to applications in management and production, among others. There are several methods for generating these values, with one of the essential points for their design being the selection of random seeds. Two interesting aspects converge here: the use of sequences as inputs (and the need for them to verify properties such as randomness and uniformity, which are verified through statistical test suites) and the design of the algorithm for the generation of the variable. In this paper, we analyse, in detail, the algorithms that have been developed in the literature, both from a mathematical/statistical and computational point of view. We also provide empirical development using R software, which is currently in high demand and is one of the main novelties with respect to previous comparisons carried out in FORTRAN. We establish which algorithms are more efficient and in which contexts, depending on the different values of the parameters, allowing the user to determine the best method given the experimental conditions.