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Assessing the statistical quality of RNGs. (English) Zbl 07216554
Kollmitzer, Christian (ed.) et al., Quantum random number generation. Theory and practice. Cham: Springer (ISBN 978-3-319-72594-9/hbk; 978-3-319-72596-3/ebook). Quantum Science and Technology, 45-64 (2020).
Summary: There has and still is an ongoing discourse on how to measure the quality of random numbers generated by Random Number Generators (RNGs).
For the entire collection see [Zbl 1443.65001].
Reviewer: Reviewer (Berlin)
MSC:
65C10 Random number generation in numerical analysis
11K45 Pseudo-random numbers; Monte Carlo methods
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References:
[1] Federal information processing standards publication (FIPS 197). (2001). Advanced Encryption Standard (AES).
[2] Amrhein, V., Korner-Nievergelt, F., & Roth, T. (2017). The earth is flat (p \(>0.05)\): significance thresholds and the crisis of unreplicable research. PeerJ, 5, e3544 . https://doi.org/10.7717/peerj.3544.
[3] Barker, E., & Kelsey, J. (2010). Recommendation for random number generation using deterministic random bit generators. National Institute of Standards and Technology (NIST), Tech-Rep.
[4] Baron, M., & Rukhin, A.L. (1999). Distribution of the number of visits of a random walk. Communications in Statistics Stochastic Models, 15(3), 593-597. https://doi.org/10.1080/15326349908807552. · Zbl 0930.60039
[5] Berlekamp, E. (2015). Algebraic Coding Theory. World Scientific Publishing Co Pte Ltd. · Zbl 1320.94001
[6] Blackburn, S., Carter, G., Gollmann, D., Murphy, S., Paterson, K., Piper, F., Wild, P. (1994). Aspects of Linear Complexity (pp. 35-42). Boston, MA: Springer US. https://doi.org/10.1007/978-1-4615-2694-0_4. · Zbl 0835.68035
[7] Bundschuh, P., & Zhu, Y. (1993). A method for exact calculation of the discrepancy of low-dimensional finite point sets i. In Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg (Vol. 63, no. 1, pp. 115-133). https://doi.org/10.1007/BF02941337. · Zbl 0789.11041
[8] Erdmann, E.D. (1992). Empirical tests of binary keystreams.
[9] Fang, K.T., & Sudjianto, L.R. (2015). Design and modeling for computer experiments. · Zbl 1093.62117
[10] Földes, A. (1979). The limit distribution of the length of the longest head-run. Periodica Mathematica Hungarica, 10(4), 301-310. https://doi.org/10.1007/BF02020027. · Zbl 0349.60021
[11] Good, I. J. (1953). The serial test for sampling numbers and other tests for randomness. Mathematical Proceedings of the Cambridge Philosophical Society, 49(2), 276284. https://doi.org/10.1017/S030500410002836X. · Zbl 0051.36203
[12] Gordon, L., Schilling, M.F., & Waterman, M.S. (1986). An extreme value theory for long head runs. Probability Theory and Related Fields, 72(2), 279-287. https://doi.org/10.1007/BF00699107. · Zbl 0587.60031
[13] Hickernell, F.J. (1998). A generalized discrepancy and quadrature error bound. Mathematics of Computation, 67(221), 299-322. https://doi.org/10.1090/S0025-5718-98-00894-1. · Zbl 0889.41025
[14] Hoenig, J.M., & Heisey, D.M. (2001). The abuse of power. The American Statistician, 55(1), 19-24. https://doi.org/10.1198/000313001300339897.
[15] ID Quantique: IDQ Random Number Generator White Paper (2017)
[16] Kendall, M.G., & Babington-Smith, B. (1939). Second paper on random sampling numbers. Supplement to the Journal of the Royal Statistical Society6(1), 51-61. http://www.jstor.org/stable/2983623
[17] Knuth, D.E. (1997). The Art of Computer Programming, vol. 2: Seminumerical Algorithms (3rd ed.,). Addison-Westley Professional. · Zbl 0895.68055
[18] L’Ecuyer, P., & Simard, R. (2007). Testu01: AC library for empirical testing of random number generators. ACM Transactions on Mathematical Software, 33(4), 22:1-22:40. https://doi.org/10.1145/1268776.1268777 · Zbl 1365.65008
[19] Li, N., Kim, B., Chizhevsky, V.N., Locquet, A., Bloch, M., Citrin, D.S., et al. (2014). Two approaches for ultrafast random bit generation based on the chaotic dynamics of a semiconductor laser. Optics Express, 22(6), 6634-6646. https://doi.org/10.1364/OE.22.006634, http://www.opticsexpress.org/abstract.cfm?URI=oe-22-6-6634.
[20] Panneton, F., L’Ecuyer, P., & Matsumoto, M. (2006). Improved long-period generators based on linear recurrences modulo 2. ACM Transactions on Mathematical Software (TOMS), 32(1), 1-16. · Zbl 1346.94089
[21] Rasch, D., Pilz, J., Verdooren, R., & Gebhardt, A. (2011). Optimal experimental design with R. Taylor & Francis Group: CRC Press. · Zbl 1237.62096
[22] Révész, P. (2013). Random walk in random and non-random environments. World Scientific,. https://doi.org/10.1142/8678. · Zbl 1283.60007
[23] Robert G.B. Dieharder: A random number test suite. http://webhome.phy.duke.edu/ rgb/General/dieharder.php.
[24] Rukhin, A., Soto, J., Nechvatal, J., Smid, M., Barker, E., Leigh, S., et al. (2010). A statistical test suite for random and pseudorandom number generators for cryptographic applications. National Institute of Standards and Technology (NIST): Tech-Rep.
[25] Vollert, N., Ortner, M., & Pilz, J. (2017). Benefits and application of tree structures in Gaussian process models to optimize magnetic field shaping problems (pp. 159-168). Berlin: Springer. · Zbl 1397.62616
[26] Vollert, N., Ortner, M., & Pilz, J. (2018). Robust additive gaussian process models using reference priors and cut-off-designs. Applied Mathematical Modeling. · Zbl 07183356
[27] Warnock, T.T. (1972). Computational investigations of low-discrepancy point sets*. In S. Zaremba (Ed.) Applications of number theory to numerical analysis (pp. 319 - 343). Academic Press. https://doi.org/10.1016/B978-0-12-775950-0.50015-7. https://www.sciencedirect.com/science/article/pii/B9780127759500500157 · Zbl 0248.65018
[28] Wegenkittl, S. (1998). Generalized \(\phi \)-divergence and frequency analysis in Markov chains. Ph.D. thesis, University of Salzburg. · Zbl 0935.65002
[29] Winker, P.
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