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International Bhurban Conference on Applied Sciences and Technology (IBCAST)

Robust entropy harvester for analogue noise sources in TRNG

Hina Saleem, Saba Afzal, Naveed Ahmed

Published Jan 1, 2018• 8 citations
Publisher

Abstract

Random numbers are important in diverse areas of science and technology. The requirements of randomness, however, are more stringent in cryptographic applications, where so-called true randomness is required. In particular, statistical randomness is not enough, and a degree of unpredictability stemmed in physical phenomenon is used to build a true random number generator (TRNG). A critical part in TRNG design is the entropy harvester, which extracts entropy from multiple entropy sources. Unfortunately, none of such sources provide true randomness in pure form, and the desired signal is heavily contaminated due to electrical coupling, electromagnetic interference, and other pseudo-random signals present in physical environment. Process variation and ageing affect the performance of noise sources. In this paper we propose an entropy extraction and estimation mechanism, which operates directly on raw randomness exhibited by analogue noise sources. The main strength of our design is its dynamic nature, i.e., it adapts as per the current state of source, and provides a robust mechanism to detect entropy failure. Our design can easily be implemented on commodity hardware in a cost effective manner.

DOI
10.1109/ibcast.2018.8312256

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Random numbers are important in diverse areas of science and technology. The requirements of randomness, however, are more stringent in cryptographic applications, where so-called true randomness is required. In particular, statistical randomness is not enough, and a degree of unpredictability stemmed in physical phenomenon is used to build a true random number generator (TRNG). A critical part in TRNG design is the entropy harvester, which extracts entropy from multiple entropy sources. Unfortunately, none of such sources provide true randomness in pure form, and the desired signal is heavily contaminated due to electrical coupling, electromagnetic interference, and other pseudo-random signals present in physical environment. Process variation and ageing affect the performance of noise sources. In this paper we propose an entropy extraction and estimation mechanism, which operates directly on raw randomness exhibited by analogue noise sources. The main strength of our design is its dynamic nature, i.e., it adapts as per the current state of source, and provides a robust mechanism to detect entropy failure. Our design can easily be implemented on commodity hardware in a cost effective manner.
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.
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.
True random number generation is a critical capability for fault-tolerant quantum computing at millikelvin temperatures. Yet existing Josephson-junction-based TRNGs all rest on a widely accepted but untested assumption: that reliable entropy extraction requires precisely controlled device parameters. Here we show that this assumption does not always hold. We demonstrate a counterintuitive finding: a single current-biased Josephson junction, regardless of its parameter quality, can serve as a cryptographic-grade true random number generator. To establish the universality of this conclusion, we deliberately selected the most extremely deviated devices from fabrication, with critical currents three orders of magnitude away from theoretical predictions and IcRI_cRIc​R products an order of magnitude above conventional values, as the ultimate stress test. Even under these extreme conditions, the raw Shannon entropy reaches 0.9981~bit (99.8\% of the theoretical maximum), with a min-entropy of 0.9271~bit. Using a square-wave pulsed-bias scheme, we tune the switching probability to P≈0.5P\approx0.5P≈0.5. After SHA-256 post-processing, the bitstreams pass all 15 NIST SP 800-22 tests under a conservative m=3m=3m=3 criterion that is more demanding than the standard recommendation, and this certification holds across the entire 100-700~mK operating window of a dilution refrigerator.
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.
This paper presents a novel, to our knowledge, true random number generator (TRNG) architecture based on multiple light-emitting diodes (LEDs), where each LED serves as an independent source of physical randomness. The system combines four distinct noise types: shot noise, thermal noise, flicker noise, and chaotic signals generated via a logistic map. The logistic map is selected for its computational efficiency and robust chaotic dynamics, ensuring high-entropy signal generation. A genetic algorithm optimizes the weights of these noise sources to maximize entropy and minimize autocorrelation and bias. The composite analog signal is normalized, passed through μ -law companding to enhance entropy distribution, and then digitized using median-based thresholding. A delayed XOR operation further improves randomness by reducing the residual autocorrelation. Statistical validation using NIST SP 800-22 and Dieharder test suites confirms near-ideal entropy (≈0.998), minimal bias (<0.001), and negligible autocorrelation (<9 −4 ). Normality analysis via Kolmogorov–Smirnov and Quantile–Quantile tests confirms that the noise sources are statistically consistent with normality, supporting balanced bit generation. A cryptographic security analysis demonstrates resilience against side-channel attacks, fault injection, and bias exploitation, attributed to the diversity of noise sources, robust post-processing, and optimized design parameters. These results demonstrate that the proposed TRNG is robust, high quality, and suitable for cryptographic applications.