Testing random number generators
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In two-level tests, computational errors accumulate at each level and two-level tests detect the lack-of-fit of the approximation, leading to rejection even if the generator is good.
“In this case, computational errors accumulate at each level and two-level tests detect the Lack-Of-Fit of that approximation, leading to rejection even if the generator is good [7, 10, 13, 17].”
From Checking the quality of approximation of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="mml84" display="inline" overflow="scroll" altimg="si2.gif"><mml:mi>p</mml:mi></mml:math>-values in statistical tests for random number generators by using a three-level test (2019) · cites this paper as [7]
Two-level tests permit one to apply the test with a larger total sample size to increase its power.
“Two-level tests permit one to apply the test with a larger total sample size to increase its power.”
From Checking the quality of approximation of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="mml84" display="inline" overflow="scroll" altimg="si2.gif"><mml:mi>p</mml:mi></mml:math>-values in statistical tests for random number generators by using a three-level test (2019) · cites this paper as [7]
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TestU01: A C library for empirical testing of random number generators
L'Ecuyer, P., & Simard, R. (2007) · ACM Transactions on Mathematical Software · doi:10.1145/1268776.1268777 · Cited by 1,014 · see citing works
“Several authors have advocated and/or applied a two-level (or second-order) procedure for testing RNGs (Fishman, 1996; Knuth, 1998; L’Ecuyer, 1992; Marsaglia, 1985).”
Self-citationRandom number generation and Monte Carlo methods
Gentle, J. (1998) · doi:10.1007/978-1-4757-2960-3 · Cited by 546
Uniform random number generation
L’Ecuyer, P. (1994) · Annals of Operations Research · doi:10.1007/bf02136827 · Cited by 268 · see citing works
Self-citationOn the accuracy of statistical procedures in Microsoft Excel 2003
McCullough, B., & Wilson, B. K. (1999) · Computational Statistics & Data Analysis · doi:10.1016/s0167-9473(99)00004-3 · Cited by 300 · see citing works
“One such collection of tests is given by Knuth (1981), which was programmed by Dwyer and Williams (1996a, b). Marsaglia (1993) noted that these tests are not very stringent, and later proposed DIEHARD: A battery of randomness tests (Marsaglia, 1996).”
MethodMaximally equidistributed combined Tausworthe generators
L'Ecuyer, P. (1996) · Mathematics of Computation · doi:10.1090/s0025-5718-96-00696-5 · Cited by 276 · see citing works
Self-citationGaussian random number generators
Thomas, D. B., Luk, W., Leong, P., & Villasenor, J. (2007) · CSUR · doi:10.1145/1287620.1287622 · Cited by 223 · see citing works
Matsumoto, M., & Kurita, Y. (1992) · ACM Transactions on Modeling and Computer Simulation · doi:10.1145/146382.146383 · Cited by 190 · see citing works
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The Numerical Reliability of Econometric Software
McCullough, B., & Vinod, H. (1999) · Journal of Economic Literature · doi:10.1257/jel.37.2.633 · Cited by 185 · see citing works
Good random number generators are (not so) easy to find
Hellekalek, P. (1998) · Mathematics and Computers in Simulation · doi:10.1016/s0378-4754(98)00078-0 · Cited by 185 · see citing works
“This procedure is called a two-level test, see [28,30].”
BackgroundMethodInfluentialCombined Multiple Recursive Random Number Generators
L'Ecuyer, P. (1995) · Operational Research · doi:10.1287/opre.44.5.816 · Cited by 150 · see citing works
Self-citationUniform random number generators
L’Ecuyer, P. (2002) · Winter Simulation Conference · doi:10.1109/wsc.1998.744904 · Cited by 33 · see citing works
Self-citationSchroeder, M. (2010) · doi:10.1007/978-3-540-85298-8_29 · Cited by 80
“Suppose for example, that we want a random variable X that has an exponential distribution at rate λ : The cumulative distribution function (CDF) is given by”
A new Pseudo random number generator based on generalized Newton complex map with dynamic key
Barani, M., Ayubi, P., Valandar, M. Y., & Irani, B. (2020) · Journal of Information Security and Applications · doi:10.1016/j.jisa.2020.102509 · Cited by 76 · see citing works
A Compact and Accurate Gaussian Variate Generator
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Bad Lattice Structures for Vectors of Nonsuccessive Values Produced by Some Linear Recurrences
L'Ecuyer, P. (1997) · INFORMS journal on computing · doi:10.1287/ijoc.9.1.57 · Cited by 73 · see citing works
Self-citationRandom Number Generators: Selection Criteria and Testing
L'Ecuyer, P., & Hellekalek, P. (1998) · Lecture notes in statistics · doi:10.1007/978-1-4612-1702-2_5 · Cited by 71 · see citing works
Self-citationDon't trust parallel Monte Carlo!
Hellekalek, P. (1998) · Proceedings. Twelfth Workshop on Parallel and Distributed Simulation PADS '98 (Cat. No.98TB100233) · doi:10.1109/pads.1998.685273 · Cited by 68
Inversive and linear congruential pseudorandom number generators in empirical tests
Leeb, H., & Wegenkittl, S. (1997) · ACM Transactions on Modeling and Computer Simulation · doi:10.1145/249204.249208 · Cited by 59 · see citing works
Inversive pseudorandom number generators: concepts, results and links
Hellekalek, P. (1995) · Winter simulation conference : proceedings · doi:10.1109/wsc.1995.478732 · Cited by 59 · see citing works
On the lattice structure of the add-with-carry and subtract-with-borrow random number generators
Tezuka, S., L'Ecuyer, P., & Couture, R. (1993) · ACM Transactions on Modeling and Computer Simulation · doi:10.1145/159737.159749 · Cited by 58 · see citing works
Self-citationEdmonds, B. (2009) · Epistemological Aspects of Computer Simulation in the Social Sciences · doi:10.1007/978-3-642-01109-2_13 · Cited by 57
“by testing the outcomes is made clear in (L'Ecuyer 1992).”
BackgroundOn the lattice structure of certain linear congruential sequences related to AWC/SWB generators
Couture, R., & L'Ecuyer, P. (1994) · doi:10.2307/2153540 · Cited by 53
“Those generators looked promising at first sight, but statistical defects have quickly been discovered [2, 7].”
BackgroundSelf-citationOn the assessment of random and quasi-random point sets
Hellekalek, P. (1998) · Lecture notes in statistics · doi:10.1007/978-1-4612-1702-2_2 · Cited by 53 · see citing works
History of uniform random number generation
L’Ecuyer, P. (2017) · Winter Simulation Conference · doi:10.1109/wsc.2017.8247790 · Cited by 62 · see citing works
Self-citationSparse serial tests of uniformity for random number generators
L'Ecuyer, P., Simard, R., & Wegenkittl, S. (2002) · SIAM Journal on Scientific Computing · doi:10.1137/s1064827598349033 · Cited by 50 · see citing works
Self-citationClick, T., Kaminski, G. A., & Liu, A. (2010) · Journal of Computational Chemistry · doi:10.1002/jcc.21638 · Cited by 46
Common defects in initialization of pseudorandom number generators
Matsumoto, M., Wada, I., Kuramoto, A., & Ashihara, H. (2007) · ACM Transactions on Modeling and Computer Simulation · doi:10.1145/1276927.1276928 · Cited by 37 · see citing works
Close-Point Spatial Tests and Their Application to Random Number Generators
L'Écuyer, P., Cordeau, J.-F., & Simard, R. (2000) · Operations Research · doi:10.1287/opre.48.2.308.12385 · Cited by 38 · see citing works
Self-citationUniform random number generators
L’Ecuyer, P. (1997) · Winter Simulation Conference · doi:10.1145/268437.268461 · Cited by 26 · see citing works
“For simulations dealing with random points in space, those bad structures could have a dramatic effect (Ferrenberg, Landau, and Wong 1992; L’Ecuyer 1992).”
BackgroundSelf-citationOn Independence and Sensitivity of Statistical Randomness Tests
Turan, M. S., Doğanaksoy, A., & Boztaş, S. (2008) · Sequences and Their Applications · doi:10.1007/978-3-540-85912-3_2 · Cited by 37 · see citing works
“Multi Level Testing In [14], to increase the power of tests, it is proposed to apply the test N times to disjoint parts of the sequence, yielding N different test statistics, t1, t2, .”
MethodImplementation of high-order particle-tracking schemes in a water column model
Gräwe, U. (2011) · doi:10.1016/j.ocemod.2010.10.002 · Cited by 35
Microsoft Excel's 'Not The Wichmann-Hill' random number generators
McCullough, B. D. (2008) · Computational Statistics & Data Analysis · doi:10.1016/j.csda.2008.03.006 · Cited by 34
Portable random number generators
Dwyer, G., & Williams, K. (2003) · Journal of Economic Dynamics and Control · doi:10.1016/s0165-1889(01)00065-3 · Cited by 30 · see citing works
Random Number Generators and Empirical Tests
L'Ecuyer, P. (1998) · doi:10.1007/978-1-4612-1690-2_7 · Cited by 26
Self-citationNumerical Issues in Statistical Computing for the Social Scientist
Altman, M., Gill, J., & McDonald, M. P. (2003) · doi:10.18637/jss.v012.b05 · Cited by 24
The accurary of Mathematica 4 as a statistical package
McCullough, B. (2000) · Computational statistics (Zeitschrift) · doi:10.1007/pl00022713 · Cited by 23
True Random Number Generator Using GPUs and Histogram Equalization Techniques
Chan, J., Sharma, B., Lv, J., Thomas, G., Thulasiram, R., & Thulasiraman, P. (2011) · IEEE International Conference on High Performance Computing and Communications · doi:10.1109/hpcc.2011.30 · Cited by 22 · see citing works
“In these situations, the use of PRNGs can become unreliable since its sequence becomes predictable due to its geometrical properties [7, 8, 9 ]. Because of these reasons and the more frequent use of GPUs in today’s computational systems, in this work we highlight the benefits of implementing a parallel and completely…”
BackgroundRadix-b extensions to some common empirical tests for pseudorandom number generators
Johnson, B. C. (1996) · ACM Transactions on Modeling and Computer Simulation · doi:10.1145/240896.240906 · Cited by 18
Genetic algorithm based key sequence generation for cipher system
Sudeepa, K. B., Aithal, G., Rajinikanth, V., & Satapathy, S. C. (2020) · Pattern Recognition Letters · doi:10.1016/j.patrec.2020.03.015 · Cited by 16 · see citing works
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Tests based on sum-functions of spacings for uniform random numbers
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Self-citationSeveral extensively tested multiple recursive random number generators
Chiang, K., & Tang, H.-C. (1998) · doi:10.1016/s0898-1221(98)00166-7 · Cited by 13
Study on the Effects of Pseudorandom Generation Quality on the Performance of Differential Evolution
Tirronen, V., Äyrämö, S., & Weber, M. (2011) · International Conference on Adaptive and Natural Computing Algorithms · doi:10.1007/978-3-642-20282-7_37 · Cited by 12
“Marsaglia, to complex spectral and theoretical tests (for a survey, see [8]).”
BackgroundA Reinforcement Learning System for Generating Instantaneous Quality Random Sequences
Almardeny, Y., Benavoli, A., Boujnah, N., & Naredo, E. (2023) · IEEE Transactions on Artificial Intelligence · doi:10.1109/tai.2022.3161893 · Cited by 11 · see citing works
“For a PRNG to be suitable for cryptographic applications, it should initially pass the next bit test [22], [23], in addition to a large number of statistical tests [24].”
BackgroundAutomation of Statistical Tests on Randomness to Obtain Clearer Conclusion
Haramoto, H. (2009) · Springer eBooks · doi:10.1007/978-3-642-04107-5_26 · Cited by 11 · see citing works
“Thus, if the p-values of the first level tests has 1% error in the same direction, and if the second level test uses a large number of these p-values (say, k = 10000 times), then the second level may detect the systematic computing error, which may lead to a false rejection [5] [13].”
BackgroundMethodDesign of low-power random number generator using signal quantization error in Smart Grid
Fujdiak, R., Mlýnek, P., Misurec, J., & Mašek, P. (2016) · International Conference on Telecommunications and Signal Processing · doi:10.1109/tsp.2016.7760819 · Cited by 10 · see citing works
“If the generator not pass the tests then it is here a reason for being suspicious as described in [26].”
BackgroundMcFarland, C. D. (2014) · Journal of Statistical Computation and Simulation · doi:10.1080/00949655.2015.1060234 · Cited by 10
“Journal of Statistical Computation and Simulation, 2016 Vol. 86, No. 7, 1281–1294, http://dx.doi.org/10.1080/00949655.2015.1060234”
InfluentialPseudo-random number generator based on irrational numbers
Milinkovic, L., Antic, M., & Čiča, Z. (2011) · International Conference on Telecommunication in Modern Satellite, Cable and Broadcasting Services · doi:10.1109/telsks.2011.6143212 · Cited by 10
“For example, it must have the long period, and it should be efficient (run fast and use only a small amount of memory), unpredictable and portable [5], [6].”
BackgroundRandom Number Generation with +-NFAs
van Zijl, L. (2001) · International Conference on Implementation and Application of Automata · doi:10.1007/3-540-36390-4_23 · Cited by 9
“Our technique is adapted from LFSR random number generation (see [6, 7, 8] for a description of random number generators based on LFSRs).”
MethodHaramoto, H., & Matsumoto, M. (2019) · Mathematics and Computers in Simulation · doi:10.1016/j.matcom.2018.08.005 · Cited by 8 · see citing works
“In order to avoid such difficulties, a two-level test is often used, see [6, 7].”
BackgroundMethodParallel random number generators for sequences uniformly distributed over any range of integers
Kuehnel, R., Theiler, J. P., & Wang, Y. (2006) · IEEE Transactions on Circuits and Systems I Fundamental Theory and Applications · doi:10.1109/tcsi.2006.877884 · Cited by 8 · see citing works
The MERLin Environment Applied to *-NFAs
van Zijl, L., Harper, J., & Olivier, F. (2000) · International Conference on Implementation and Application of Automata · doi:10.1007/3-540-44674-5_28 · Cited by 8
“It was shown for LFSRs [ 8 ] that characteristic polynomials of the form q k q s 1 must be combined to obtain pseudorandom sequences with good statistical properties.”
MethodA note on pseudorandom number generators
Hellekalek, P. (1997) · doi:10.1016/s0928-4869(97)84227-9 · Cited by 8
A bibliography of algorithm experimentation
McGeoch, C. C. (1999) · Data Structures, Near Neighbor Searches, and Methodology · doi:10.1090/dimacs/059/12 · Cited by 8
Design and implementation of a novel cryptographically secure pseudorandom number generator
Mauro, J. D., Salazar, E., & Scolnik, H. (2022) · Journal of Cryptographic Engineering · doi:10.1007/s13389-022-00297-8 · Cited by 7 · see citing works
Modulus of Linear Congruential Random Number Generator
Tang, H.-C. (2005) · doi:10.1007/s11135-004-6788-6 · Cited by 7
Random number generators with long period and sound statistical properties
Chiang, K., & Wong, J. (1998) · doi:10.1016/s0898-1221(98)00133-3 · Cited by 6
Testing the Tests: Using Random Number Generators to Improve Empirical Tests
Leopardi, P. C. (2009) · doi:10.1007/978-3-642-04107-5_32 · Cited by 6
“The use of two-level testing with such empirical tests and “known good” random number generators can reveal the goodness of fit between the empirical distribution of the test statistic and the approximate theoretical distribution [10, Section 3.1] [11, Section 3].”
BackgroundMethodInfluentialStudy on upper limit of sample size for a two-level test in NIST SP800-22
Haramoto, H. (2021) · Japan Journal of Industrial and Applied Mathematics · doi:10.1007/s13160-020-00434-y · Cited by 5 · see citing works
“Further descriptions and explanations of two-level tests can be found in [6, 7, 8, 9, 14, 15] However, NIST recommends that the sample size at the second level should be on the order of the inverse of the significance level, without any mathematical justifications.”
BackgroundMalik, K., Pulikkotil, J., & Sharma, A. (2021) · MAPAN · doi:10.1007/s12647-021-00443-3 · Cited by 5
On testing pseudorandom generators via statistical tests based on the arcsine law
Lorek, P., Los, G., Gotfryd, K., & Zagórski, F. (2019) · Journal of Computational and Applied Mathematics · doi:10.1016/j.cam.2020.112968 · Cited by 5 · see citing works
“, in [3]) or second level (a term used e.”
BackgroundInfluentialAnalysis of random number generator from texas instrument in MSP430 x5xx families
Fujdiak, R., Misurec, J., Mlýnek, P., & Raso, O. (2015) · International Conference on Telecommunications and Signal Processing · doi:10.1109/tsp.2015.7296344 · Cited by 5 · see citing works
Analysis of chaotic maps applied to self-organizing maps for the Traveling Salesman Problem
Ryter, R., Stauffer, M., Hanne, T., & Dornberger, R. (2015) · IEEE Congress on Evolutionary Computation · doi:10.1109/cec.2015.7257094 · Cited by 5
ShoveRand: A model-driven framework to easily generate random numbers on GP-GPU
Passerat-Palmbach, J., Mazel, C., Bachelet, B., & Hill, D. (2011) · International Symposium on High Performance Computing Systems and Applications · doi:10.1109/hpcsim.2011.5999805 · Cited by 5
“It misses some classics statistical tests such as BirthdaySpacing according to [7].”
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Entacher, K., Schell, T., & Uhl, A. (2005) · Computing · doi:10.1007/s00607-004-0105-z · Cited by 5 · see citing works
“generator are given in [5], [63], empirical results in [37].”
BackgroundRecent advances in uniform random number generation
L’Ecuyer, P. (2005) · Winter Simulation Conference · doi:10.1109/wsc.1994.717114 · Cited by 5 · see citing works
“Again, those generators turned out to have bad structural and statistical properties (L’Ecuyer 1992; Tezuka 1992).”
BackgroundInfluentialSelf-citationClassification and development of mathematical models and simulation for industrial ecology
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Symmetry property of multiplicative congruential random number generator in chi-square test
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B., S. K., & Aithal, G. (2019) · Concurrency and Computation · doi:10.1002/cpe.5181 · Cited by 4
Monkeys, gambling, and return times: assessing pseudorandomness
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“I6;’2;1 equals the ordinary chisquare statistic, whereas ’1.u/ VD 1 uCu ln.u/ yields the I-Divergence of Kullback and Leibler (1951) , G2. O P.N/; P/ D 2nPm iD1 O”
BackgroundPorównanie generatorów liczb pseudolosowych
Sulewski, P. (2019) · Wiadomości Statystyczne The Polish Statistician · doi:10.5604/01.3001.0013.7605 · Cited by 3 · see citing works
Pseudo-random number generator analysis based on the set of quadratic irrationals
Milinkovic, L., & Malešević, B. (2012) · Telecommunications Forum · doi:10.1109/telfor.2012.6419266 · Cited by 3
Testing Stream Ciphers by Finding the Longest Substring of a Given Density
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“Randomness testing has been investigated by various authors in the past: Knuth [8] has a good overview of such tests, L’Ecuyer [4] has also considered the same problem, from a different point of view.”
BackgroundA new heuristic for second-order multiple recursive random number generator
Kung, C.-J., & Tang, H.-C. (2005) · doi:10.1080/02522667.2005.10699634 · Cited by 3
“To increase the power of empirical tests, a two-level test proposed by L’Ecuyer [6] is adopted.”
MethodTang, H.-C. (2003) · Math. Methods Oper. Res. · doi:10.1007/s001860200237 · Cited by 3
“To increase the power of empirical tests, a two-level test proposed by L’Ecuyer [ 13 ] is used.”
MethodColin, E., & Jit, T. (1997) · doi:10.11606/d.3.1997.tde-09122003-143854 · Cited by 3
Combination of multiplicative congruential random-number generators with safe prime modulus
Sakamoto, M.-A., & Morito, S. (1995) · Winter simulation conference : proceedings · doi:10.1109/wsc.1995.478740 · Cited by 3
“..> ~(~) (cf. lemma Q in Section 3.2.1.2 of Knuth 1969 ).”
BackgroundMethodInfluentialSelecting Input Models and Random Variate Generation
Cheng, R. C. H. (1993) · Online World Conference on Soft Computing in Industrial Applications · doi:10.1145/256563.256577 · Cited by 3
LS-14 Test Suite for Long Sequences
Akcengi̇z, Z., Aslan, M., Doğanaksoy, A., Sulak, F., & Uğuz, M. (2023) · Hacettepe Journal of Mathematics and Statistics · doi:10.15672/hujms.1190807 · Cited by 2 · see citing works
“P. L’Ecuyer introduced some statistical tests in [21].”
BackgroundAnalysis and improvements of the pseudorandom number generation in passive UHF-RFID tags
Blanco, J., García, A., & Cañas, V. (2019) · Future generations computer systems · doi:10.1016/j.future.2019.04.021 · Cited by 2 · see citing works
The cycle length, statistical and key sensitivity properties of a perturbed couple chaotic PRBG
Hong, S., Li, C.-T., Chen, H.-K., & Chen, C.-H. (2011) · 2011 International Conference on Multimedia Technology · doi:10.1109/icmt.2011.6003042 · Cited by 2
“We can say that the cycle length is long enough [2].”
BackgroundA parallel unpredictable random number generator
Marton, K., Suciu, A., & Petricean, D. (2011) · 2011 RoEduNet International Conference 10th Edition: Networking in Education and Research · doi:10.1109/roedunet.2011.5993701 · Cited by 2 · see citing works
“The recurrence formula for the simplest LCGs is: ( ) mcaxx nn mod1 += − , and the period length cannot exceed the modulus.”
BackgroundInfluentialOptimization of Prime Modules Multiplicative Linear Congruential Generators for Genetic Algorithms
Xu, X.-Z., Pan, L.-J., & Yang, X.-H. (2010) · 2010 Sixth International Conference on Natural Computation · doi:10.1109/icnc.2010.5583677 · Cited by 2
“When 1 = n , (4) becomes M ax x i i mod ) ( 1 = + , that is exactly (1).”
BackgroundMethodology for DNS Cache Poisoning Vulnerability Analysis of DNS 64 Implementations
Lencse, G., & Kadobayashi, Y. (2018) · doi:10.36244/icj.2018.2.3 · Cited by 2
“There are a high nu ber of methods described for testing randomness both in university lecture notes [36] and research papers [37].”
MethodInfluentialGao, P., Zhang, B., Wang, Z., & Li, C. (2026) · Scientific Reports · doi:10.1038/s41598-026-38020-w · Cited by 1 · see citing works
“Existing methods fail to effectively validate the consistency of test implementation and threshold settings, nor do they adequately conduct in-depth validation of test robustness and consistency under near-failure conditions 5,35 .”
Modeling Particle Randomness: A Pseudorandom Number Generator
Dunmire, C., & Wagner, A. (2023) · ACM Southeast Regional Conference · doi:10.1145/3564746.3587025 · Cited by 1
“The Runs Test is another important test to analyze sequential randomness [4, 7].”
BackgroundMethodAnalysis randomness properties of basic components of SNOW 3G cipher in mobile systems
Jasim, K., & Alshaikhli, I. A. (2016) · International Journal on Perceptive and Cognitive Computing · doi:10.31436/ijpcc.v2i2.36 · Cited by 1 · see citing works
“For all the statistical tests in this research, level of significance (α = 0.01) [18, 19].”
InfluentialAn Efficiency Optimization Scheme for the On-the-Fly Statistical Randomness Test
Chen, T., Ma, Y., Lin, J.-Q., Wang, Z., & Jing, J.-W. (2015) · 2015 IEEE 2nd International Conference on Cyber Security and Cloud Computing · doi:10.1109/cscloud.2015.10 · Cited by 1 · see citing works
Weierstrass Function-based Uniform Random Number Generator
Zhu, H.-G., Zhang, X., & Yang, L.-P. (2009) · Global Congress on Intelligent Systems · doi:10.1109/gcis.2009.177 · Cited by 1 · see citing works
“All these discussions show that WFU-RNG not only extends possibilities of obtaining absolutely unpredictable random number automatically, but also provides random number in simple and portable way, Consequently, it can enhance security of the intelligent systems.”
BackgroundAre there hyperbolas in the scatter plots of inversive congruential pseudorandom numbers
Wegenkittl, S. (1998) · doi:10.1016/s0377-0427(98)00077-6 · Cited by 1
Results from statistical analysis of popular pseudorandom number generators for simulation
Labbé, P., & Bureau, M. (1993) · Proceedings of Canadian Conference on Electrical and Computer Engineering · doi:10.1109/ccece.1993.332218 · Cited by 1
Simulation of Asian options delta using a quadratic congruential pseudo-random numbers generator
Moussi, A., Lidouh, A., & Nqi, F. Z. (2013) · doi:10.12988/ams.2013.36294 · Cited by 1
“this generator kind was done, either to improve their performance, or to study their properties (see [28], [21], [22], [23], [31], [33] and [34]).”
BackgroundOccupancy Numbers in Testing Random Number Generators
Figotin, A., Gordon, A., Molchanov, S., Quinn, J., & Stavrakas, N. (2002) · SIAM Journal on Applied Mathematics · doi:10.1137/s0036139900366869 · Cited by 1 · see citing works
A lightweight secure communication protocol in smart homes
Chang, M.-X., Ye, T., Wang, K., Jiang, H., Yan, Y.-H., & Yang, H. (2026) · Array · doi:10.1016/j.array.2026.101237
Randomness of encryption keys generated by super H-antimagic total labeling
Prihandoko, A., Auliya, Y. A., Firmansyah, D. M., & Slamin, S. (2020) · doi:10.19184/ijc.2020.4.1.3
A better lower bound on the family complexity of binary Legendre sequencePreprint
Çakıroğlu, Y., & Yayla, O. (2018) · arXiv.org · doi:10.48550/arxiv.1812.06140
“Finite pseudorandom binary sequences are used in many areas such as telecommunication, simulation, spectroscopy and in several areas of cryptography, see [14, 16, 20].”
MethodNon-Recurring Improved Random Number Generator- a new step to improve cryptographic algorithms
Annam, T. A., & Varghese, P. (2018) · EAI Endorsed Transactions on Energy Web · doi:10.4108/eai.12-6-2018.154813
“KS test can be used to check the randomness of the numbers generated by a RNG that is allowed to take on any value within a certain interval, leading to a continuous cdf [16].”
Method
- Authors
- L'Ecuyer, P.
- Venue
- Proceedings of the 24th conference on Winter simulation - WSC '92
- Publisher
- ACM Press
- Published
- 1992
- Pages
- 305-313
- ISSN
- 0891-7736 (ISSN-L)
- OpenAlex
- W2114833710
- Cited by
- 115
- References
- 0
- Citations by year
- 2024: 1 · 2022: 2 · 2020: 6 · 2019: 3 · 2018: 5 · 2017: 1 · 2016: 4 · 2015: 4 · 2014: 4 · 2013: 2 · 2012: 2
- FWCI
- 17.33
- Type
- conference paper
- Language
- en
- Open access
- closed
- Locations
- Winter Simulation Conference (publishedVersion)
- NCSU Libraries Repository (North Carolina State University Libraries) (submittedVersion)
- Topics
- Physical Sciences › Mathematics › Statistics and Probability › Probability and Statistical Research
- Physical Sciences › Mathematics › Numerical Analysis › Mathematical Approximation and Integration
- Physical Sciences › Computer Science › Software › Software Testing and Debugging Techniques
- Keywords
- random number generators, randomness testing
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
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