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Colloidal particles as noise source for random number generation

Alexander Stefan Scholz, Pooja Arya, Jasmin Aghassi‐Hagmann

Published Oct 1, 2024• 1 citation
Publisher

Abstract

In this work, we investigate colloidal particle patterns as a possible noise source for random number generation. We systematically analyze the minimum entropy of the noise source over different particle concentrations of {1, 3, 5, 7, 10, 12, 15} mg/ml according to the recommendations of the National Institute of Standards and Technology Special Publication 800-90B. The estimated minimum entropy of the non-independent and identically distributed particle pattern noise source is Hmin = 0.5896/1 bit at a particle amount of 5 mg/ml. For further entropy extraction on the noise source data, the secure hash algorithm is used to construct an entropy source. The randomness of the derived entropy source is verified according to the National Institute of Standards and Technology Special Publication 800-22 Rev. 1a and the accompanying statistical test suite. The entropy source passes all randomness tests of the statistical test suite and shows an estimated minimum entropy of Hmin = 0.9992/1 bit.

DOI
10.1063/5.0223329

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In this work, we investigate colloidal particle patterns as a possible noise source for random number generation. We systematically analyze the minimum entropy of the noise source over different particle concentrations of {1, 3, 5, 7, 10, 12, 15} mg/ml according to the recommendations of the National Institute of Standards and Technology Special Publication 800-90B. The estimated minimum entropy of the non-independent and identically distributed particle pattern noise source is Hmin = 0.5896/1 bit at a particle amount of 5 mg/ml. For further entropy extraction on the noise source data, the secure hash algorithm is used to construct an entropy source. The randomness of the derived entropy source is verified according to the National Institute of Standards and Technology Special Publication 800-22 Rev. 1a and the accompanying statistical test suite. The entropy source passes all randomness tests of the statistical test suite and shows an estimated minimum entropy of Hmin = 0.9992/1 bit.
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.
In this paper, we present an in-depth analysis for entropy source based on optical physical unclonable functions (PUFs). The randomness of speckle patterns is elaborated essentially according to its statistical characteristics. Various factors affecting the source of entropy have been analyzed in detail, including wavefront modulation, sensitivity, and universality of the optical PUF, and bit-depth settings of captured speckle patterns. In view of the above considerations, we demonstrate that the entropy source can achieve an ultra-high min-entropy (>0.985 bits/bit) while maintaining a high extraction rate of 75% and also verify its independent and identically distributed nature. These results provide an in-depth and comprehensive understanding of the developed entropy source and offer a firm foundation for its practical use.
Abstract Random numbers have significant applications in fundamental science, high-level scientific research, cryptography and several other areas where there is a pressing need for high-quality random numbers. We present an experimental demonstration of a non-deterministic random bit generator from a quantum entropy source and a deterministic random bit generator mechanism to provide high quality random numbers of 1 GB data size. Quantum entropy is realized by a series of quantum chips based on radioactive isotope Americium-241. The extracted raw random numbers are further post-processed to generate a high-entropy seed for the hash based deterministic random bit generator. We discuss the implementation of randomness extraction algorithm and Hash-DRBG algorithm in detail. The random numbers pass all the randomness measures provided in standard statistical test suites.
Abstract Pseudo-random number generators are predominantly utilised as entropy sources in encryption and seeding processes, however, they are deterministic by nature. This paper presents the analysis and design methodology of an on-chip quantum noise source that may suitably be used as an entropy source in true random number generators. Quantum tunnelling is achieved through the strong biasing of a MOS structure to generate gate-referred shot noise. Structures are fabricated in a commercial 40 nm process and the sampled noise is tested against the NIST SP800-90B and SP800-22 test suites, showing a maximal entropy of 0.985 at a bias current of 1500 µA with a consistent pass rate across all NIST tests.
The never-ending quest to improve the security of digital information combined with recent improvements in hardware technology has caused the field of random number generation to undergo a fundamental shift from relying solely on pseudo-random algorithms to employing optical entropy sources. Despite these significant advances on the hardware side, commonly used statistical measures and evaluation practices remain ill-suited to understand or quantify the optical entropy that underlies physical random number generation. We review the state of the art in the evaluation of optical random number generation and recommend a new paradigm: quantifying entropy generation and understanding the physical limits of the optical sources of randomness. In order to do this, we advocate for the separation of the physical entropy source from deterministic post-processing in the evaluation of random number generators and for the explicit consideration of the impact of the measurement and digitization process on the rate of entropy production. We present the Cohen-Procaccia estimate of the entropy rate h(𝜖,τ) as one way to do this. In order to provide an illustration of our recommendations, we apply the Cohen-Procaccia estimate as well as the entropy estimates from the new NIST draft standards for physical random number generators to evaluate and compare three common optical entropy sources: single photon time-of-arrival detection, chaotic lasers, and amplified spontaneous emission.
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.