# zbMATH — the first resource for mathematics

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
##### Software:
NIST Statistical Test Suite; OPDOE; TestU01
Full Text:
##### 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.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.