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Frontiers in Computer Science

Entropy measurement and online quality control of bit streams by a true random bit generator

Cesare Gerolimetto Fabrello, Valeria Rossi, Kamil Witek, Alberto Trombetta, Mateusz Baszczyk, P. Dorosz, W. Kucewicz, M. Caccia

Published Oct 7, 2025• 1 citation
Publisher

Abstract

Generating random bit streams is required in various applications, most notably in cyber-security, which is essential for Internet of Everything applications to enable secure communication between interconnected devices. Ensuring high-quality and robust randomness is crucial to mitigate risks associated with predictability and system compromise. True random numbers provide the highest levels of unpredictability. However, known systematic biases that can emerge from physical imperfections, environmental variations, and device aging in the processes exploited for random number generation must be carefully monitored. This article reports the implementation and characterization of an online procedure for the detection of anomalies in a true random bit stream. It is based on the NIST adaptive proportion and repetition count tests, complemented by statistical analysis relying on the Monobit and RUNS tests. The procedure is implemented in firmware through dedicated hardware accelerators processing configurable-length sequences, with automated anomaly detection triggering alerts after three consecutive threshold violations. The implementation is performed simultaneously with bit stream generation and also provides an estimate of the entropy of the source. A statistical analysis of the results from the NIST procedure to evaluate the symbols of the bit-stream as independently and identically distributed is also performed, leading to a computation of the minimum entropy of the source that cross-checks the previously mentioned estimate. The experimental validation of the approach is performed up the bit streams generated by a quantum, silicon-based entropy source.

DOI
10.3389/fcomp.2025.1642566

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Generating random bit streams is required in various applications, most notably in cyber-security, which is essential for Internet of Everything applications to enable secure communication between interconnected devices. Ensuring high-quality and robust randomness is crucial to mitigate risks associated with predictability and system compromise. True random numbers provide the highest levels of unpredictability. However, known systematic biases that can emerge from physical imperfections, environmental variations, and device aging in the processes exploited for random number generation must be carefully monitored. This article reports the implementation and characterization of an online procedure for the detection of anomalies in a true random bit stream. It is based on the NIST adaptive proportion and repetition count tests, complemented by statistical analysis relying on the Monobit and RUNS tests. The procedure is implemented in firmware through dedicated hardware accelerators processing configurable-length sequences, with automated anomaly detection triggering alerts after three consecutive threshold violations. The implementation is performed simultaneously with bit stream generation and also provides an estimate of the entropy of the source. A statistical analysis of the results from the NIST procedure to evaluate the symbols of the bit-stream as independently and identically distributed is also performed, leading to a computation of the minimum entropy of the source that cross-checks the previously mentioned estimate. The experimental validation of the approach is performed up the bit streams generated by a quantum, silicon-based entropy source.
Generating random bit streams is required in various applications, most notably cyber-security. Ensuring high-quality and robust randomness is crucial to mitigate risks asso-ciated with predictability and system compromise. True random numbers provide the highest unpredictability levels. However, potential biases in the processes exploited for the random number generation must be carefully monitored. This paper reports the implementation and characterization of an on-line procedure for the detection of anomalies in a true random bit stream. It is based on the NIST Adaptive Proportion and Repetition Count tests, complemented by statistical analysis relying on the Monobit and RUNS. The procedure is firmware implemented and performed simultaneously with the bit stream generation, and providing as well an estimate of the entropy of the source. The experimental validation of the approach is performed upon the bit streams generated by a quantum, silicon-based entropy source.
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.
Availability of streams of random numbers is critical in a number of significant applications. e.g. computer security and cryptography, privacy preservation procedures,IoT\mathbf{IoT}IoTsecure communication, numerical simulation of complex phenomena, gaming and gambling. Hardware generation of random numbers, especially when based on quantum phenomena, is made unbreakable by the same laws of nature. Random Power [1] [2] is focusing on the development of a Quantum-True Random Number generation (QTRNG) platform, producing unpredictable bit streams analyzing the time series of self-amplified endogenous pulses due to stochastically generated charge carriers in a dedicated silicon device. As per NIST recommendations [3], a SHA256 conditioning function was used in order to reduce potential biases and guarantee the required level of entropy. This paper reports the firmware development and implementation of a real-time SHA256 accelerator, which is capable of generating bits in bursts at a maximum rate of 330 Mbps.
Random number generation is significant for secure communication, data security and cryptography. However, while Quantum Random Number Generators (QRNGs) rely on quantum uncertainty, environmental data can also serve as practical sources of randomness for true random number generation. Environmental data such as temperature, humidity, and wind speed exhibit continuous variability over time; these changes arise from complex weather behavior. In this paper, temperature data collected from two meteorological stations in Pakistan, Karachi and Hyderabad, are used to generate random bits. Everyday temperature values are transformed into binary sequences using a mean-based thresholding technique, followed by post-processing with the Von Neumann extractor to decrease bias and correlation. The quality of the generated random bits is evaluated using Shannon entropy, lossless compression testing with the Gzip, Bzip2, and LZMA algorithms, the NIST SP 800-22 statistical test suite and the auto-correlation analysis. The results determine that correctly processed temperature-based entropy can produce statistically usable random sequences suitable for randomness testing and security-related research.
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.
A comprehensive performance analysis of a TRNG system that is based on beat frequency is provided in this paper for secure, high-entropy applications. The proposed method generates unpredictable bit streams by leveraging the intrinsic unpredictability caused by the frequency difference between two distinct oscillators. The system employs phase noise and variations in the surrounding environment to increase entropy without the need for laborious post-processing procedures. The study evaluates statistical variance using well-known test suites such as the NIST and Diehard tests to ensure high-quality output. The entropy rate, stability, power consumption, and throughput are among the critical performance metrics that are pertinent. The experimental data firmly refutes exogenous influences and deterministic patterns.