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Journal of Applied Physics

Analysis of entropy source for random number generation based on optical PUFs

Kun Chen, Pidong Wang, Feng Chen Huang, Xiao Leng, Yao Yao

Published May 1, 2023• 9 citations
Publisher

Abstract

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.

DOI
10.1063/5.0147153

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AIP Advances•Oct 1, 2024•1 citation
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.
Optical physical unclonable functions (PUFs) are gaining significant attention in hardware security due to their intrinsically unpredictable quasi-chaotic behavior, rendering it particularly suitable for random key generation. However, systematic evaluation and quantitative criteria for speckle quality remain largely unexplored, with microscopic-level analyses still lacking, thereby severely hindering practical application. To address this, we conduct a comprehensive statistical and information-theoretic evaluation by extracting speckle information from diverse perspectives, with particular emphasis on the gray-level co-occurrence matrix and its higher-order statistical features. Accordingly, it is demonstrated that speckle patterns satisfying the sampling theorem reveal strong inherent randomness and are well suited for secret-key generation. Finally, we establish a quantitative speckle quality discrimination framework that integrates multiple information-theoretic means for high-quality cryptographic key generation. The resulting random bit streams successfully pass stringent Dieharder randomness tests and exhibit a verified min-entropy exceeding 0.995 bits per bit. Our results provide a potential research avenue for improving the randomness of optical PUF-based secret-key generation systems, advancing their real-world deployment in information security.
Random number generators (RNG) are fundamental to cryptographic systems, requiring high entropy, unpredictability, and resistance to cloning attacks. This work proposes RNG based on optical physical unclonable function (PUF) that uses random scattering of structured vortex beams through rough surface. The inherent disorder of the scattering medium with tunable beam parameters like vortex order, provides a rich source of physical randomness. The generated speckle patterns are processed using a post processing algorithm to produce random sequences at a rate of 1.42 Gbps. The statistical quality of the sequences is evaluated using the NIST SP 800-22, AIS-31, and Dieharder test suites, which meet the required randomness criteria. Further assessment using entropies and Kolmogorov complexity shows high entropy and algorithmic randomness. The physical unclonability and uniqueness are verified through inter-device hamming distances, Pearson correlation of sequences obtained from different spatial regions and vortex orders, revealing negligible correlations. To assess resilience against data based adversaries, machine learning modeling attacks are performed. The prediction accuracies remain close to random guessing, showing resistance to learning based cloning and response prediction attacks. These results establish the proposed optical PUF method as a high speed, physically unclonable, and machine learning resistant source of random numbers for secure cryptographic applications.
We propose an approach for fast random number generation based on homemade optical physical unclonable functions (PUFs). The optical PUF is illuminated with input laser wavefront of continuous modulation to obtain different speckle patterns. Random numbers are fully extracted from speckle patterns through a simple post-processing algorithm. Our proof-of-principle experiment achieves total random number generation rate of 0.96 Gbit/s with verified randomness, which is far faster than previous optical-PUF-based schemes. Our results demonstrate that the presented random number generator (RNG) proposal has great potential to achieve ultrafast random number generation rate up to several hundreds of Gbit/s.
Laser speckle has been proposed in a number of papers as a high entropy source of unpredictable bits for use in security applications. Bit strings derived from speckle can be used for a variety of security purposes such as in identification, authentication, anti-counterfeiting, secure key storage, random number generation and tamper protection. The choice of laser speckle as a source of random keys is quite natural, given the chaotic properties of speckle. However, this same chaotic behaviour also causes reproducibility problems. Cryptographic protocols require either zero noise or very low noise in their inputs; hence the issue of error rates is critical to applications of laser speckle in cryptography. Most of the literature uses an error reduction method based on Gabor filtering. Though the method is successful, it has not been thoroughly analysed.\nIn this paper we present a statistical analysis of Gabor-filtered speckle patterns. We introduce a model in which perturbations are described as random phase changes in the source plane. Using this model we compute the second- and fourth-order statistics of Gabor coefficients. We determine the mutual information of perturbed and unperturbed Gabor coefficients and the bit error rate in the derived bit string. The mutual information provides an absolute upper bound on the number of secure bits that can be reproducibly extracted from noisy measurements.
Laser speckle has been proposed in a number of papers as a high-entropy source of unpredictable bits for use in security applications. Bit strings derived from speckle can be used for a variety of security purposes such as identification, authentication, anti-counterfeiting, secure key storage, random number generation and tamper protection. The choice of laser speckle as a source of random keys is quite natural, given the chaotic properties of speckle. However, this same chaotic behaviour also causes reproducibility problems. Cryptographic protocols require either zero noise or very low noise in their inputs; hence the issue of error rates is critical to applications of laser speckle in cryptography. Most of the literature uses an error reduction method based on Gabor filtering. Though the method is successful, it has not been thoroughly analysed. In this paper we present a statistical analysis of Gabor-filtered speckle patterns. We introduce a model in which perturbations are described as random phase changes in the source plane. Using this model we compute the second and fourth order statistics of Gabor coefficients. We determine the mutual information between perturbed and unperturbed Gabor coefficients and the bit error rate in the derived bit string. The mutual information provides an absolute upper bound on the number of secure bits that can be reproducibly extracted from noisy measurements.
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.