Skip to main content
Book cover

International Symposium on Cyber Security, Cryptology, and Machine Learning

CSCML 2022: Cyber Security, Cryptology, and Machine Learning pp 153–161Cite as

Randomness for Randomness Testing

  • 172 Accesses

Part of the Lecture Notes in Computer Science book series (LNCS,volume 13301)

Abstract

Given a binary sequence, one may inquire whether it is produced by a true random source. There are several tests designed to answer this question, such as the statistical test suite of the National Institute of Standard and Technology (NIST) and the Diehard tests.

The problem is that, given deterministic tests of randomization, an adversary may know/learn, the adversary may tailor a non-random (deterministic) sequence, guided by the deterministic tests, that passes the tests.

We suggest to use a true random source for randomness tests and thus make the tests significantly harder to being misled. We design tests that use true random sources and demonstrate their ability to detect non-random sequences that NIST classifies as random.

Keywords

  • Property testing
  • Randomness testing
  • Truly random generator

D. Berend—Research supported in part by the Milken Families Foundation Chair in Mathematics and the Cyber Security Research Center at Ben-Gurion University.

S. Dolev—This research was (partially) funded by a grant from the Ministry of Science and Technology, Israel & the Japan Science and Technology Agency (JST), the German Research Funding (DFG, Grant #8767581199), Genesis Consortium, the Rita Altura trust chair in computer science, and by the Lynne and William Frankel Center for Computer Science.

This is a preview of subscription content, access via your institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • DOI: 10.1007/978-3-031-07689-3_11
  • Chapter length: 9 pages
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
eBook
USD   79.99
Price excludes VAT (USA)
  • ISBN: 978-3-031-07689-3
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book
USD   99.99
Price excludes VAT (USA)
Learn about institutional subscriptions

References

  1. Batu, T., Fortnow, L., Rubinfeld, R., Smith, W.D., White, P.: Testing that distributions are close. In: 41st Annual Symposium on Foundations of Computer Science, FOCS 2000, 12–14 November 2000, Redondo Beach, California, USA, pp. 259–269 (2000)

    Google Scholar 

  2. Batu, T., Fortnow, L., Rubinfeld, R., Smith, W.D., White, P.: Testing closeness of discrete distributions. J. ACM 60(1), 4:1–4:25 (2013)

    Google Scholar 

  3. Chan, S., Diakonikolas, I., Valiant, P., Valiant, G.: Optimal algorithms for testing closeness of discrete distributions. In: Proceedings of the Twenty-Fifth Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2014, Portland, Oregon, USA, 5–7 January 2014, pp. 1193–1203 (2014)

    Google Scholar 

  4. Diakonikolas, I., Gouleakis, T., Peebles, J., Price, E.: Collision-based testers are optimal for uniformity and closeness. Chic. J. Theor. Comput. Sci. 2019, 1–21 (2019). http://cjtcs.cs.uchicago.edu/articles/2019/1/contents.html

  5. Dolev, S., Gilboa, N., Li, X.: Accumulating automata and cascaded equations automata for communicationless information theoretically secure multi-party computation. Theor. Comput. Sci. 795, 81–99 (2019)

    MathSciNet  CrossRef  Google Scholar 

  6. Fredricksen, H., Maiorana, J.: Necklaces of beads in \(k\) colors and \(k\)-ary de Bruijn sequences. Discret. Math. 23(3), 207–210 (1978)

    MathSciNet  CrossRef  Google Scholar 

  7. Goldreich, O.: Introduction to Property Testing. Cambridge University Press, Cambridge (2017)

    Google Scholar 

  8. Goldreich, O., Goldwasser, S., Ron, D.: Property testing and its connection to learning and approximation. J. ACM 45(4), 653–750 (1998)

    MathSciNet  CrossRef  Google Scholar 

  9. Goldreich, O., Ron, D.: On testing expansion in bounded-degree graphs. In: Studies in Complexity and Cryptography. Miscellanea on the Interplay between Randomness and Computation - In Collaboration with Lidor Avigad, Mihir Bellare, Zvika Brakerski, Shafi Goldwasser, Shai Halevi, Tali Kaufman, Leonid Levin, Noam Nisan, Dana Ron, Madhu Sudan, Luca Trevisan, Salil Vadhan, Avi Wigderson, David Zuckerman, pp. 68–75 (2011)

    Google Scholar 

  10. jmviz: random-debruijn (2020). https://github.com/jmviz/random-debruijn/blob/master/debruijn.py

  11. Kendall, M.G., Smith, B.B.: Randomness and random sampling numbers. J. R. Stat. Soc. 101(1), 147–166 (1938). http://www.jstor.org/stable/2980655

  12. Knuth, D.E.: The Art of Computer Programming, Seminumerical Algorithms, vol. 2, 3rd edn. Addison-Wesley Longman Publishing Co., Inc., Boston (1997)

    Google Scholar 

  13. Kumar, M.: Randomness test of sequences (2022). https://github.com/manishkk/Randomness-Test-of-Sequences

  14. Lehmann, E.L., Romano, J.P.: Testing Statistical Hypotheses. STS, Springer, New York (2005). https://doi.org/10.1007/0-387-27605-X

    CrossRef  MATH  Google Scholar 

  15. Neyman, J., Pearson, E.S.: On the problem of the most efficient tests of statistical hypotheses. Philos. Trans. R. Soc. London Ser. A 231, 289–337 (1933). http://www.jstor.org/stable/91247

  16. Rubinfeld, R., Sudan, M.: Robust characterizations of polynomials with applications to program testing. SIAM J. Comput. 25(2), 252–271 (1996)

    MathSciNet  CrossRef  Google Scholar 

  17. Rukhin, A., Soto, J., Nechvatal, J., Smid, M., Barker, E.: A statistical test suite for random and pseudorandom number generators for cryptographic applications. Technical report, Booz-Allen and Hamilton Inc. McLean VA (2001)

    Google Scholar 

  18. Sawada, J., Williams, A., Wong, D.: A surprisingly simple de Bruijn sequence construction. Discret. Math. 339(1), 127–131 (2016)

    MathSciNet  CrossRef  Google Scholar 

  19. Siu, M., Tong, P.: Generation of some de Bruijn sequences. Discret. Math. 31(1), 97–100 (1980)

    MathSciNet  CrossRef  Google Scholar 

  20. Soto, J., Bassham, L.: Randomness testing of the advanced encryption standard finalist candidates, 1 April 2000

    Google Scholar 

  21. Sýs, M., Říha, Z.: Faster randomness testing with the NIST statistical test suite. In: Chakraborty, R.S., Matyas, V., Schaumont, P. (eds.) SPACE 2014. LNCS, vol. 8804, pp. 272–284. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-12060-7_18

    CrossRef  Google Scholar 

  22. Turan, M.S., Barker, E., Kelsey, J., McKay, K.A., Baish, M.L., Boyle, M., et al.: Recommendation for the entropy sources used for random bit generation. NIST Special Publication 800(90B), 102 (2018)

    Google Scholar 

Download references

Acknowledgment

We thank Dean Doron for many interesting discussion related to this research.

Author information

Authors and Affiliations

  1. Ben-Gurion University of the Negev, Be’er Sheva, Israel

    Daniel Berend, Shlomi Dolev & Manish Kumar

Authors
  1. Daniel Berend
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Shlomi Dolev
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Manish Kumar
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Manish Kumar .

Editor information

Editors and Affiliations

  1. Ben-Gurion University of the Negev, Be’er Sheva, Israel

    Shlomi Dolev

  2. University of Maryland, College Park, MD, USA

    Jonathan Katz

  3. Ben-Gurion University of the Negev, Be’er Sheva, Israel

    Amnon Meisels

Rights and permissions

Reprints and Permissions

Copyright information

© 2022 Springer Nature Switzerland AG

About this paper

Verify currency and authenticity via CrossMark

Cite this paper

Berend, D., Dolev, S., Kumar, M. (2022). Randomness for Randomness Testing. In: Dolev, S., Katz, J., Meisels, A. (eds) Cyber Security, Cryptology, and Machine Learning. CSCML 2022. Lecture Notes in Computer Science, vol 13301. Springer, Cham. https://doi.org/10.1007/978-3-031-07689-3_11

Download citation

  • DOI: https://doi.org/10.1007/978-3-031-07689-3_11

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-07688-6

  • Online ISBN: 978-3-031-07689-3

  • eBook Packages: Computer ScienceComputer Science (R0)