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.
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.
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.
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 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.
잡음원(Noise source)의 안전성 평가에 사용되는 대표적인 표준으로는 미국 NIST의 SP 800-90B가 있다. 최근 SP 800-90B가 2차 안(Second Draft)으로 개정되면서 Non-IID 트랙의 최소 엔트로피 추정에 프레딕터(predictor)를 이용한 추정 방법이 새롭게 추가되었다. 프레딕터는 잡음원의 주기적인 특성을 검출하기에 용이하다고 알려져 있지만, 그 특성에 대한 구체적인 언급은 하지 않고 있다. 이에 본 논문에서는 프레딕터가 검출해낼 수 있는 잡음원의 주기적 특성을 명확히 밝히기 위한 실험을 진행한다. 먼저 주기적 성질을 갖는 잡음원에 대하여 Non-IID 트랙의 추정을 실시했을 때, 잡음원의 최소 엔트로피가 대체적으로 프레딕터보다는 Non-IID 트랙의 다른 추정 방법에 의해서 결정되고 있음을 실험적으로 확인한다. 다음으로 프레딕터를 이용한 추정법이 검출해낼 수 있는 주기적 특성을 밝혀내기 위한 다양한 실험 결과를 제시함으로써, 프레딕터 추정 방법의 의미와 그 역할을 실험적으로 규명한다. NIST SP 800-90B is developed to evaluate the security of entropy sources. As SP 800-90B was updated to Second Draft, Estimators with predictors were added at Non-IID track. Though the predictors are known as detecting periodic property of noise sources, periodic properties which are detected by predictor are not clearly known. In this paper, we experiment to find properties of predictors. Once, by experiments we have a result that the min-entropy of Non-IID noise sources is generally determined by tests except for estimators with predictors. And then through presenting various experimental results for clarifying periodic properties detected by predictor, we experimentally analyze on its meaning and role of predictor estimation.
In physical-layer key generation (PLKG), researchers often assess key security using randomness tests or secret key capacity analysis. However, randomness tests can be misleading, as low-entropy inputs may still pass when obscured by hash functions or extractors. While key capacity captures the theoretical upper limit of secret bits from raw channels, it overlooks the impact of practical preprocessing. Recent studies have explored min-entropy as a more practical security metric. However, commonly used min-entropy estimators, such as those in NIST SP 800-90B (90B), may yield inaccurate results for complex sources, even overestimating entropy and thereby undermining security. Their applicability to PLKG also remains unverified. To address the above research gap, this paper focuses on modeling the received signal envelope, a common feature extracted for key generation. Leveraging typical wireless fading scenarios considered in key capacity analysis, we adopt the more general Weibull distribution to characterize the envelope statistics, which generalizes the Rayleigh model and better captures diverse propagation conditions. We first derive an explicit expression for the min-entropy in the absence of preprocessing, and then systematically analyze the impact of typical preprocessing operations on the statistical properties of the observed channel. Building on this foundation, we further establish theoretical upper and lower bounds on the min-entropy under representative preprocessing strategies. We further evaluate all 90B entropy estimators using both simulations and real-world channel measurements, comparing their estimates with our analytical results. While some estimators work well on raw data, they often fail or overestimate entropy after preprocessing, compromising security. In contrast, our conservative lower bound remains robust across all tested scenarios and preprocessing conditions. It offers a reliable fallback when standard estimators break down, providing a stronger theoretical foundation for secure key extraction in PLKG systems.
Semiconductor superlattice true random number generator (SSL-TRNG) has an outstanding practical property on high-throughput and high-security cryptographic applications. Security in random number generators is closely related to the min-entropy of the raw output because feeding cryptographic applications with insufficient entropy leads to poor security and vulnerability to malicious attacks. However, no research has focused on the min-entropy estimation based on the stochastic model for SSL-TRNG, which is a highly recommended method for evaluating the security of a specific TRNG structure. A min-entropy estimation method is proposed in this paper for the SSL-TRNG by extending the Markov stochastic model derived from the memory effects. By calculating the boundary of the transition matrix, the min-entropy result is the average value of each sample (1 bit) is 0.2487. Moreover, the experimental results show that the estimator is accurate enough to adjust compression rate dynamically in post-processing to reach the required security level, estimating entropy on the fly rather than off-line.