Abstract Random numbers play a crucial role in cryptography since the security of cryptographic protocols relies on the assumption of the availability of uniformly distributed and unpredictable random numbers to generate secret keys, nonce, salt, etc. However, real-world random number generators sometimes fail and produce outputs with low entropy, leading to security vulnerabilities. The NIST Special Publication (SP) 800-90 series provides guidelines and recommendations for generating random numbers for cryptographic applications and describes 10 black-box entropy estimation methods. This paper evaluates the effectiveness and limitations of the SP 800-90 methods by exploring the accuracy of these estimators using simulated random numbers with known entropy, investigating the correlation between entropy estimates, and studying the impacts of deterministic transformations on the estimators.
Abstract Random numbers play a crucial role in cryptography since the security of cryptographic protocols relies on the assumption of the availability of uniformly distributed and unpredictable random numbers to generate secret keys, nonce, salt, etc. However, real-world random number generators sometimes fail and produce outputs with low entropy, leading to security vulnerabilities. The NIST Special Publication (SP) 800-90 series provides guidelines and recommendations for generating random numbers for cryptographic applications and describes 10 black-box entropy estimation methods. This paper evaluates the effectiveness and limitations of the SP 800-90 methods by exploring the accuracy of these estimators using simulated random numbers with known entropy, investigating the correlation between entropy estimates, and studying the impacts of deterministic transformations on the estimators.
Random numbers play a crucial role in cryptography since the security of cryptographic protocols relies on the assumption of the availability of uniformly distributed and unpredictable random numbers to generate secret keys, passwords, initialization vectors, nonces, salt, etc. True Random Number Generators (TRNGs) extract random numbers from physical processes (such as radioactive decay, thermal noise, and atmospheric noise) that are inherently unpredictable. However, real-world random number generators sometimes fail and produce outputs with low entropy, leading to security vulnerabilities. It is commonly observed that the TRNG outputs have statistical biases and dependencies that make them unsuitable to be directly used for cryptographic purposes. There are some standards and guidelines on generating and testing random numbers that are suitable for cryptographic applications. The National Institute of Standards and Technology (NIST) Special Publication (SP) 800-90 series provide guidelines and recommendations for generating random numbers for cryptographic applications and describes statistical randomness testing, estimating min-entropy with 10 black-box entropy estimation methods. In this thesis, we evaluate the effectiveness and limitations of the SP 800-90B methods by exploring the accuracy of these estimators using simulated random numbers with known entropy, investigating the correlation between entropy estimates, and studying the impacts of deterministic transformations on the estimators. To understand the unpredictability of the outputs, it is important to estimate their entropy accurately. The National Institute of Standards and Technology (NIST) Special Publication (SP) 800-90B specifies ten min-entropy estimators ranging from simple frequency-based estimators to more advanced approaches. Each estimator has specific assumptions, making them suitable for different types of sources. The minimum of these estimates is assumed to be the min-entropy of the TRNG. We propose a new entropy estimator (estimates min-entropy and also Shannon entropy) called index-value coincidence estimate that is suitable for outputs that might include some dependencies and we also provide some experimental results that demonstrate the effectiveness of the estimator. Additionally, TRNGs may be affected by outside conditions such as temperature, humidity, etc. Health tests are an integral part of the noise source of TRNG, defined to detect unexpected changes in the working process and dramatic changes in the amount of entropy generated by the noise source. Existing health test suites are examined, and a health test suite for cryptographic TRNGs is introduced by using random variables weight, run, runs of length 1 and overlapping templates. Some suggested parameters and experimental results are given.
Random number generators (RNGs) are essential for cryptographic applications. In most practical applications, the randomness of RNGs is provided by entropy sources. If the randomness is less than the expected, the security of cryptographic applications could be undermined. Accurate entropy estimation is a critical method for the evaluation of RNG security, and significant overestimation and underestimation are both inadvisable. The NIST Special Publication 800-90B is one of the most common certifications for entropy estimation. It makes no assumption of the entropy source and provides min-entropy estimation results by a set of entropy estimators. It estimates the entropy sources in two tracks: the IID (independent and identically distributed) track and non-IID track. In practice, non-IID entropy sources are more common, as physical phenomenon, sampling process or external perturbation could cause the dependency of the outputs. In this paper, we prove that the Collision Estimate and the Compression Estimate in non-IID track could provide significant underestimates in theory. In order to accurately estimate the min-entropy of non-IID sources, we provide a formula of minentropybased on conditional probability, and propose a new estimator to approximate the result of this formula. Finally, we perform experiments to compare our estimator with the NIST estimators using simulated non-IID data. Results show that our estimator gives close estimates to the real min-entropy.
The paper proposes a hybrid entropy-controlled random number generator for information security systems that combines physical entropy sources, cryptographic conditioning, and adaptive feedback control. A comparative analysis of traditional pseudo-random and quantum generators was conducted, and experimental testing was performed in accordance with NIST SP 800-90B, NIST SP 800-90C, and ISO/IEC 18031:2025. According to statistical analysis of a large volume of bit sequences, minimum entropy close to unity was observed, with only a slight deviation, confirming the high randomness. The throughput of the hardware implementation is ~ 600 Mbit/s (over 500 Mbit/s) with an energy consumption of E ≈ 0.29 mJ/Mbit. Compared to classical generators on an uncontrolled cypher counter or hardware generators on ring oscillators without pre-mixing, a reduction in correlation and mean shift of more than a third has been achieved. The proposed architecture demonstrates resistance to source manipulation, fault injection, and side-channel attacks, confirming the effectiveness of the entropy approach for modern cryptographic systems, Internet of Things platforms, and security modules.
Random number generators (RNGs) are foundational to modern cryptographic systems.While quantum random number generators (QRNGs) leverage inherently stochastic quantum measurements, practical deployments still exhibit implementation artifacts (e.g., detector dead time, afterpulsing, drift) that can introduce bias, correlation, and non-stationarity.This paper presents a unified validation framework for both CMOS true random number generators (TRNGs) and QRNGs under NIST SP 800-90B entropy source validation.Rather than simulating quantum physics, we model observable raw-output behaviors of practical implementations and evaluate them using a consistent pipeline: raw capture constraints, IID screening, conservative min-entropy bounding, and online health testing (repetition count test and adaptive proportion test).Using synthetic sources that emulate typical CMOS and QRNG failure modes, we demonstrate how similar artifacts drive the IID versus non-IID decision and tighten entropy bounds, motivating a vendor-agnostic, reproducible validation methodology.
Generators of random sequences used in high-end applications such as cryptography rely on entropy sources for their indeterminism. Physical processes governed by the laws of quantum mechanics are excellent sources of entropy available in nature. However, extracting enough entropy from such systems for generating truly random sequences is challenging while maintaining the feasibility of the extraction procedure for real-world applications. Here, we present a compact and an all-electronic van der Waals heterostructure-based device capable of detecting discrete charge fluctuations for extracting entropy from physical processes and use it for the generation of independent and identically distributed true random sequences. We extract a record-high value (>0.98 bits/bit) of min-entropy using the proposed scheme. We demonstrate an entropy generation rate tunable over multiple orders of magnitude and show the persistence of the underlying physical process for temperatures ranging from cryogenic to ambient conditions. We verify the random nature of the generated sequences using tests such as NIST SP 800-90B standard and other statistical measures and verify the suitability of our random sequence for cryptographic applications using the NIST SP 800-22 standard. The generated random sequences are then used in implementing various randomized algorithms without any preconditioning steps.
Quantum devices offer a highly useful function - that is generating random numbers in a non-deterministic way since the measurement of a quantum state is not deterministic. This means that quantum devices can be constructed that generate qubits in a uniform superposition and then measure the state of those qubits. If the preparation of the qubits in a uniform superposition is unbiased, then quantum computers can be used to create high entropy, secure random numbers. Typically, preparing and measuring such quantum systems requires more time compared to classical pseudo random number generators (PRNGs) which are inherently deterministic algorithms. Therefore, the typical use of quantum random number generators (QRNGs) is to provide high entropy secure seeds for PRNGs. Quantum annealing (QA) is a type of analog quantum computation that is a relaxed form of adiabatic quantum computation and uses quantum fluctuations in order to search for ground state solutions of a programmable Ising model. Here we present extensive experimental random number results from a D-Wave 2000Q quantum annealer, totaling over 20 billion bits of QA measurements, which is significantly larger than previous D-Wave QA random number generator studies. Current quantum annealers are susceptible to noise from environmental sources and calibration errors, and are not in general unbiased samplers. Therefore, it is of interest to quantify whether noisy quantum annealers can effectively function as an unbiased QRNG. The amount of data that was collected from the quantum annealer allows a comprehensive analysis of the random bits to be performed using the NIST SP 800-22 Rev 1a testsuite, as well as min-entropy estimates from NIST SP 800-90B. The randomness tests show that the generated random bits from the D-Wave 2000Q are biased, and not unpredictable random bit sequences. With no server-side sampling post-processing, the 1 microsecond annealing time measurements had a min-entropy of 0.824.