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Randomness Quality and Trade-Offs for CA Random String Generators

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Reachability Problems (RP 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14235))

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Abstract

We present classical theories for randomness, starting from mathematical ones to others focusing on randomness testing, more useful in computer science. Those characterisations are made by bounding the computational resources required for testing. Next, we present some suitable practical randomness testing suites designed to measure the quality of random strings that can be efficiently generated. Finally, random string generation by binary uniform cellular automata of increasing quality illustrates the improvements of the randomness testing suites.

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References

  1. Blum, M., Micali, S.: How to generate cryptographically strong sequences of pseudo-random bits. SIAM J. Comput. 13, 850–864 (1984)

    Article  MathSciNet  MATH  Google Scholar 

  2. Carlet, C.: Boolean functions for cryptography and error-correcting codes. Technical report, University of Paris 8 (2011)

    Google Scholar 

  3. Davie, G.: Characterising the Martin-Löf random sequences using computably enumerable sets of measure one. Inf. Process. Lett. 92(3), 157–160 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  4. Goldreich, O.: Pseudorandomness. Not. AMS 46(10), 1209–1216 (1999)

    MathSciNet  MATH  Google Scholar 

  5. Goldreich, O., Levin, L.A.: A hard core predicate for any one way function. In: 21st STOC, pp. 25–32 (1989)

    Google Scholar 

  6. Goldwasser, S., Micali, S.: Probabilistic encryption. JCSS 28(2), 270–299 (1984)

    MathSciNet  MATH  Google Scholar 

  7. Gruska, J.: Foundations of Computing. International Thomson Publishing, London (1997)

    Google Scholar 

  8. Knuth, D.: Seminumerical Algorithms. Addison Wesley, Boston (1969)

    MATH  Google Scholar 

  9. Kolmogorov, A.: Three approaches to the quantitative definition of information. Problemy Pederachi Informatsii 1, 3–11 (1965)

    MATH  Google Scholar 

  10. Li, M., Vitányi, P.: An Introduction to Kolmogorov Complexity and Its Applications. TCS, Springer, New York (2008). https://doi.org/10.1007/978-0-387-49820-1

    Book  MATH  Google Scholar 

  11. Marsaglia, G.: A current view of random number generators. In: Computer Sciences and Statistics, pp. 3–10 (1985)

    Google Scholar 

  12. Marsaglia, G.: Diehard (1995). http://www.stat.fsu.edu/pub/diehard/

  13. Martin, B.: A Walsh exploration of elementary CA rules. J. Cell. Autom. 3(2), 145–156 (2008)

    MathSciNet  MATH  Google Scholar 

  14. Formenti, E., Imai, K., Martin, B., Yunès, J.-B.: Advances on random sequence generation by uniform cellular automata. In: Calude, C.S., Freivalds, R., Kazuo, I. (eds.) Computing with New Resources. LNCS, vol. 8808, pp. 56–70. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-13350-8_5

    Chapter  Google Scholar 

  15. Martin-Löf, P.: The definition of random sequences. Inf. Control 9, 602–619 (1966)

    Article  MathSciNet  MATH  Google Scholar 

  16. Ryan, C., Kshirsagar, M., Vaidya, G., Cunningham, A., Sivaraman, R.: Design of a cryptographically secure pseudo random number generator with grammatical evolution. Sci. Rep. 12(1), 8602 (2022). https://doi.org/10.1038/s41598-022-11613-x

    Article  Google Scholar 

  17. Seredynski, F., Bouvry, P., Zomaya, A.Y.: Cellular automata computations and secret key cryptography. Parallel Comput. 30(5–6), 753–766 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  18. Shackleford, B., Tanaka, M., Carter, R.J., Snider, G.: FPGA implementation of neighborhood-of-four cellular automata random number generators. In: Proceedings of the 2002 ACM/SIGDA Tenth International Symposium on Field-programmable Gate Arrays, pp. 106–112. FPGA 2002, ACM (2002)

    Google Scholar 

  19. Shannon, C., Weaver, W.: The mathematical theory of communication. University of Illinois Press (1964)

    Google Scholar 

  20. Wang, Q., Yu, S., Ding, W., Leng, M.: Generating high-quality random numbers by cellular automata with PSO. In: 2008 Fourth International Conference on Natural Computation, vol. 7, pp. 430–433 (2008)

    Google Scholar 

  21. Wertheimer, M.: The mathematics community and the NSA. Not. Am. Math. Soc. 62(2), 165–167 (2015)

    MATH  Google Scholar 

  22. Wolfram, S.: Cryptography with cellular automata. In: Williams, H.C. (ed.) CRYPTO 1985. LNCS, vol. 218, pp. 429–432. Springer, Heidelberg (1986). https://doi.org/10.1007/3-540-39799-X_32

    Chapter  Google Scholar 

  23. Wolfram, S.: Random sequence generation by cellular automata. Adv. Appl. Math. 7, 123–169 (1986)

    Article  MathSciNet  MATH  Google Scholar 

  24. Xiao, G.Z., Massey, J.L.: A spectral characterization of correlation-immune combining functions. IEEE Trans. Inf. Theory 34(3), 569–571 (1988)

    Article  MathSciNet  MATH  Google Scholar 

  25. Yao, A.: Theory and application of trapdoor functions. In: 23d Symposium on Foundations of Computer Science (1982)

    Google Scholar 

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Author information

Authors and Affiliations

  1. Université Côte d’Azur, CNRS, I3S, Sophia Antipolis, France

    Bruno Martin

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  1. Bruno Martin
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Correspondence to Bruno Martin .

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Editors and Affiliations

  1. École Polytechnique, Paris, France

    Olivier Bournez

  2. Université Côte d’Azur, Nice, France

    Enrico Formenti

  3. University of Liverpool, Liverpool, UK

    Igor Potapov

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Martin, B. (2023). Randomness Quality and Trade-Offs for CA Random String Generators. In: Bournez, O., Formenti, E., Potapov, I. (eds) Reachability Problems. RP 2023. Lecture Notes in Computer Science, vol 14235. Springer, Cham. https://doi.org/10.1007/978-3-031-45286-4_1

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  • DOI: https://doi.org/10.1007/978-3-031-45286-4_1

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-45285-7

  • Online ISBN: 978-3-031-45286-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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