Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
129 tokens/sec
GPT-4o
28 tokens/sec
Gemini 2.5 Pro Pro
42 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

Statistical testing of random number generators and their improvement using randomness extraction (2403.18716v1)

Published 27 Mar 2024 in cs.CR and quant-ph

Abstract: Random number generators (RNGs) are notoriously hard to build and test, especially in a cryptographic setting. Although one cannot conclusively determine the quality of an RNG by testing the statistical properties of its output alone, running numerical tests is both a powerful verification tool and the only universally applicable method. In this work, we present and make available a comprehensive statistical testing environment (STE) that is based on existing statistical test suites. The STE can be parameterised to run lightweight (i.e. fast) all the way to intensive testing, which goes far beyond what is required by certification bodies. With it, we benchmark the statistical properties of several RNGs, comparing them against each other. We then present and implement a variety of post-processing methods, in the form of randomness extractors, which improve the RNG's output quality under different sets of assumptions and analyse their impact through numerical testing with the STE.

Definition Search Book Streamline Icon: https://streamlinehq.com
References (65)
  1. A statistical test suite for random and pseudorandom number generators for cryptographic applications, volume 22. US Department of Commerce, Technology Administration, National Institute of Standards and Technology, 2001.
  2. George Marsaglia. The Marsaglia random number CDROM including the Diehard battery of tests of randomness. http://www.stat.fsu.edu/pub/diehard, 2008.
  3. Dieharder. Duke University Physics Department Durham, NC, pages 27708–0305, 2018.
  4. TestU01: AC library for empirical testing of random number generators. ACM Transactions on Mathematical Software (TOMS), 33(4):1–40, 2007.
  5. John Walker. A Pseudorandom Number Sequence Test Program.
  6. Chris Doty-Humphrey. PractRand official site. http://pracrand.sourceforge.net, 2018.
  7. Cryptomite: A versatile and user-friendly library of randomness extractors. arXiv preprint arXiv:2402.09481, 2024.
  8. Juan Soto. Statistical testing of random number generators. In Proceedings of the 22nd national information systems security conference, volume 10, page 12. NIST Gaithersburg, MD, 1999.
  9. E. A. Tsvetkov. Empirical tests for statistical properties of some pseudorandom number generators. Mathematical Models and Computer Simulations, 3:697–705, 2011.
  10. Analysis of Intel’s Ivy Bridge digital random number generator. http://www.cryptography.com/public/pdf/Intel_TRNG_Report_20120312.pdf, 2012.
  11. The Intel random number generator. Cryptography Research Inc. white paper, 27:1–8, 1999.
  12. High performance physical random number generator. IET computers & digital techniques, 1(4):349–352, 2007.
  13. 640-Gbit/s fast physical random number generation using a broadband chaotic semiconductor laser. Scientific Reports, 7(1):45900, 2017.
  14. Fast physical random number generator using amplified spontaneous emission. Optics express, 18(23):23584–23597, 2010.
  15. Random number generation using inertial measurement unit signals for on-body IoT devices. 2018.
  16. Random number generator using sensors for drone. IEEE Access, 8:30343–30354, 2020.
  17. High speed continuous variable source-independent quantum random number generation. Quantum Science and Technology, 4(2):025013, 2019.
  18. Operation of an electrical-only-contact photonic integrated chip for quantum random number generation using laser gain-switching. Optics, 4(4):551–562, 2023.
  19. Quantum generators of random numbers. Scientific Reports, 11(1):16108, 2021.
  20. A 3.3-gb/s spad-based quantum random number generator. IEEE Journal of Solid-State Circuits, 2023.
  21. Quantum leap and crash: Searching and finding bias in quantum random number generators. ACM Transactions on Privacy and Security (TOPS), 23(3):1–25, 2020.
  22. ID Quantique. Quantis: Quantum random number generator, 2004.
  23. Review of methodologies and metrics for assessing the quality of random number generators. Electronics, 12(3):723, 2023.
  24. Classification of random number generator applications in iot: A comprehensive taxonomy. Journal of Information Security and Applications, 71:103365, 2022.
  25. Ronen Shaltiel. An introduction to randomness extractors. In International colloquium on automata, languages, and programming, pages 21–41. Springer, 2011.
  26. A comparison of post-processing techniques for biased random number generators. In Information Security Theory and Practice. Security and Privacy of Mobile Devices in Wireless Communication: 5th IFIP WG 11.2 International Workshop, WISTP 2011, Heraklion, Crete, Greece, June 1-3, 2011. Proceedings 5, pages 175–190. Springer, 2011.
  27. Postprocessing for quantum random-number generators: Entropy evaluation and randomness extraction. Physical Review A, 87(6):062327, 2013.
  28. Ran Canetti. Universally composable security: A new paradigm for cryptographic protocols. In Proceedings 42nd IEEE Symposium on Foundations of Computer Science, pages 136–145. IEEE, 2001.
  29. Kerry McKay et al. Users guide to running the draft NIST SP 800-90B entropy estimation suite. NIST, Gaithersburg, MD, USA, Tech. Rep. SP, 2016.
  30. Certifiably biased: An in-depth analysis of a common criteria EAL4+ certified TRNG. IEEE Transactions on Information Forensics and Security, 13(4):1031–1041, 2017.
  31. Heartbeats do not make good pseudo-random number generators: An analysis of the randomness of inter-pulse intervals. Entropy, 20(2):94, 2018.
  32. A provable-security analysis of Intel’s secure key RNG. In Annual International Conference on the Theory and Applications of Cryptographic Techniques, pages 77–100. Springer, 2015.
  33. A systematic approach of NIST statistical tests dependencies. Journal of Electrical Engineering, Electronics, Control and Computer Science, 5(1):1–6, 2019.
  34. Correction of overlapping template matching test included in NIST randomness test suite. IEICE transactions on fundamentals of electronics, communications and computer sciences, 90(9):1788–1792, 2007.
  35. On the revision of NIST 800-22 test suites. Cryptology ePrint Archive, 2022.
  36. On the interpretation of results from the NIST statistical test suite. Science and Technology, 18(1):18–32, 2015.
  37. Markku-Juhani O Saarinen. NIST SP 800-22 and GM/T 0005-2012 tests: Clearly obsolete, possibly harmful.
  38. A bad day to die hard: Correcting the Dieharder battery. Journal of Cryptology, 35(1):1–20, 2022.
  39. Statistical analysis of the LFSR generators in the NIST STS test suite. Computer applications in electrical engineering, 11, 2013.
  40. Discussion on the full entropy assumption of the SP 800-90 series. Technical report, National Institute of Standards and Technology, 2022.
  41. Analysis and improvement of entropy estimators in NIST SP 800-90B for non-IID entropy sources. IACR Transactions on Symmetric Cryptology, pages 151–168, 2017.
  42. John Von Neumann. Various techniques used in connection with random digits. John von Neumann, Collected Works, 5:768–770, 1963.
  43. Randomness extraction from somewhat dependent sources. In 13th Innovations in Theoretical Computer Science Conference (ITCS 2022). Schloss Dagstuhl-Leibniz-Zentrum für Informatik, 2022.
  44. Quantum-proof multi-source randomness extractors in the Markov model. arXiv preprint arXiv:1510.06743, 2015.
  45. A reference for randomness beacons: Format and protocol version 2. Technical report, National Institute of Standards and Technology, 2019.
  46. Practical randomness amplification and privatisation with implementations on quantum computers. Quantum, 7:969, 2023.
  47. True randomness from realistic quantum devices (2013). URL http://arxiv. org/abs/1311.4547.
  48. Improved randomness extraction from two independent sources. In Approximation, randomization, and combinatorial optimization. Algorithms and techniques, pages 334–344. Springer, 2004.
  49. Hugo Krawczyk. LFSR-based hashing and authentication. In Annual International Cryptology Conference, pages 129–139. Springer, 1994.
  50. Luca Trevisan. Construction of extractors using pseudo-random generators. In Proceedings of the thirty-first annual ACM symposium on Theory of computing, pages 141–148, 1999.
  51. Salil P Vadhan. Pseudorandomness. Foundations and Trends® in Theoretical Computer Science, 7(1–3):1–336, 2012.
  52. Bell nonlocality. Reviews of modern physics, 86(2):419, 2014.
  53. Certified randomness in quantum physics. Nature, 540(7632):213–219, 2016.
  54. Quantinuum. H1-1. https://www.quantinuum.com/, 1-4 Nov, 2021.
  55. Algorithm 806: SPRNG: A scalable library for pseudorandom number generation. ACM Transactions on Mathematical Software (TOMS), 26(3):436–461, 2000.
  56. A computer package for measuring the strength of encryption algorithms. Computers & Security, 13(8):687–697, 1994.
  57. Julio Hernandez-Castro Jamie Pont, Calvin Brierley. BitReps. https://github.com/jjp31/bitreps-1/tree/master.
  58. Cristiano Piras. RaBiGeTe—Random Bit Generators Tester. http://cristianopi.altervista.org/RaBiGeTe_MT/.
  59. Recommendation for the entropy sources used for random bit generation. NIST Special Publication, 800(90B):102, 2018.
  60. Design and implementation of multibit LFSR on FPGA to generate pseudorandom sequence number. In 2017 Devices for Integrated Circuit (DevIC), pages 346–349. IEEE, 2017.
  61. Implementation of random number generator using LFSR for high secured multi purpose applications. International Journal of Computer Science and Information Technologies, 3(1):3287–3290, 2012.
  62. Patrik Ekdahl. On LFSR based Stream Ciphers-analysis and design. Lund University, 2003.
  63. FPGA implementation of 8, 16 and 32 bit LFSR with maximum length feedback polynomial using VHDL. In 2012 International Conference on Communication Systems and Network Technologies, pages 769–773. IEEE, 2012.
  64. N David Mermin. Extreme quantum entanglement in a superposition of macroscopically distinct states. Physical Review Letters, 65(15):1838, 1990.
  65. Randomness versus nonlocality in the Mermin-Bell experiment with three parties. Quantum, 2:82, 2018.
Citations (2)
View on Semantic Scholar

Summary

We haven't generated a summary for this paper yet.

Ai Sparkles Streamline Icon: https://streamlinehq.com Summarize Now