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Recent Contributions to Physics

Characterizing Environmental Thermal Fluctuations for Use in True Random Number Generators

Roohi Zafar, Muhammad Kamran, Tahir Malik, Kousar Shaheen

Published Jun 18, 2026• 0 citations
Publisher

Abstract

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.

DOI
10.26577/rcph972202612

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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.
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.
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 numbers are one of the key foundations of cryptography. This work implements a discrete quantum random number generator (QRNG) based on the tunneling effect of electrons in an avalanche photo diode. Without any post-processing and conditioning, this QRNG can output raw sequences at a rate of 100 Mbps. Remarkably, the statistical min-entropy of the 8,000,000 bits sequence reaches 0.9944 bits/bit, and the min-entropy validated by NIST SP 800-90B reaches 0.9872 bits/bit. This metric is currently the highest value we have investigated for QRNG raw sequences. Moreover, this QRNG can continuously and stably output raw sequences with high randomness over extended periods. The system produced a continuous output of 1,174 Gbits raw sequence for a duration of 11,744 s, with every 8 Mbits forming a unit to obtain a statistical min-entropy distribution with an average value of 0.9892 bits/bit. The statistical min-entropy of all data (1,174 Gbits) achieves the value of 0.9951 bits/bit. This QRNG can produce high-quality raw sequences with good randomness and stability. It has the potential to meet the high demand in cryptography for random numbers with high quality.
Random numbers are of vital importance in today’s world and used for example in many cryptographical protocols to secure the communication over the internet. The generators producing these numbers are Pseudo Random Number Generators (PRNGs) or True Random Number Generators (TRNGs). A subclass of TRNGs are the Quantum based Random Number Generators (QRNGs) whose generation processes are based on quantum phenomena. However, the achievable quality of the numbers generated from a practical implementation can differ from the theoretically possible. To ease this negative effect post-processing can be used, which contains the use of extractors. They extract as much entropy as possible from the original source and produce a new output with better properties. The quality and the different properties of a given output can be measured with the help of statistical tests. In our work we examined the effect of different extractors on two QRNG outputs and found that witg the right extractor we can improve their quality.
Topicality. Reliable random number generation is one of the key requirements for modern cryptographic systems and cybersecurity applications. Traditional pseudo-random number generators are based on deterministic algorithms and may exhibit limited entropy and predictability, which can negatively affect information security. The subject of study in the article is methods of quantum random number generation and approaches to evaluating the quality of generated random sequences. The purpose of the article is to analyze modern methods of quantum random number generation, develop a software tool for obtaining quantum random numbers based on the ANU Quantum Random Number Generator service, perform statistical testing of the generated sequences, and analyze the obtained results. The following results were obtained. Modern quantum random number generation systems were analyzed and compared. A software tool was implemented in Python for automatic retrieval of quantum random numbers through the ANU QRNG API. The generated binary sequences were evaluated using Frequency Test and Block Frequency Test from the NIST SP 800-22 statistical test suite. The obtained p-values were 0.977181 and 0.200659 respectively, confirming successful completion of both tests. Additionally, visual analysis of the generated sequences revealed no noticeable patterns or repetitive structures. Conclusion. The obtained results confirm the high quality of quantum random sequences generated using ANU QRNG and demonstrate the applicability of the developed software tool for cryptographic and cybersecurity applications requiring high-quality randomness.
Random numbers play a central role in cryptography, cyber security, and gaming applications. Extracting bits from some random natural activity is one of the primitive ways to generate random numbers. True random number generator(TRNG) and quantum random number generator(QRNG) are examples of this random number sequence. The development of quantum technology made it possible to extract random sequences from quantum entropy sources. This sequence is called quantum random numbers and the whole setup is named a quantum random number generator. A suitable sampling and a physical device for the entropy source are the building blocks for a TRNG. Here we present a comparative analysis of two random number generators. Apart from the conventional statistical test for randomness, here we introduce a straightforward coefficient based on the concept of non-linearity of the Boolean function to determine the availability of any linearity in a chosen random binary sequence. It reveals the cryptographic suitability of the generated sequence w.r.t any correlation attack. A comparison of the nonlinearity of two Boolean sequences generated from two different random sources is presented.