{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,18]],"date-time":"2025-12-18T19:46:31Z","timestamp":1766087191516},"reference-count":25,"publisher":"Walter de Gruyter GmbH","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2017,6,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>Generating pseudorandom numbers is a prerequisite for many areas including Monte Carlo simulation and randomized algorithms. The performance of pseudorandom number generators (PRNGs) depends on the quality of the generated random sequences. They must be generated quickly and have good statistical properties. Several statistical test suites have been developed to evaluate a single stream of random numbers such as those from the TestU01 library, the DIEHARD test suite, the tests from the SPRNG package, and a set of tests designed to evaluate bit sequences developed at NIST. This paper presents a new pseudorandom number generation scheme that produces pseudorandom sequences with good statistical properties via a scrambling procedure motivated by cryptographic transformations. We will specifically apply this to a popular set of PRNGs called the Linear Congruential generators (LGCs). The scrambling technique is based on a simplified version of a Feistel network. The proposed method seeks to improve the quality of the LCGs output stream. We show that this Feistel-inspired scrambling technique breaks up the regularities that are known to exist in LCGs. The Feistel-inspired scrambling technique is modular, and can be applied to any 64-bit PRNG, and so we believe that it can serve as an inexpensive model for a scrambler that can be used with most PRNGs via post-processing.<\/jats:p>","DOI":"10.1515\/mcma-2017-0105","type":"journal-article","created":{"date-parts":[[2017,6,2]],"date-time":"2017-06-02T13:21:55Z","timestamp":1496409715000},"page":"89-99","source":"Crossref","is-referenced-by-count":2,"title":["Feistel-inspired scrambling improves the quality of linear congruential generators"],"prefix":"10.1515","volume":"23","author":[{"given":"Asia","family":"Aljahdali","sequence":"first","affiliation":[{"name":"Department of Computer Science , Florida State University , Tallahassee , FL 32306\u20134530 , USA ; and Faculty of Computing and Information Technology, King Abdulaziz University, P.O. Box 80221, Jeddah 21589, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Michael","family":"Mascagni","sequence":"additional","affiliation":[{"name":"Departments of Computer Science, Mathematics, Computational Science, and Institute for MolecularBiophysics , Florida State University , Tallahassee , FL 32306\u20134530 , USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"374","published-online":{"date-parts":[[2017,5,20]]},"reference":[{"key":"2023040102052504796_j_mcma-2017-0105_ref_001_w2aab2b8d692b1b7b1ab2ab1Aa","unstructured":"J. Banks, J. S. Carson II and L. Barry,\nDiscrete-Event System Simulation,\nPrentice Hall, Upper Saddle River, 2001."},{"key":"2023040102052504796_j_mcma-2017-0105_ref_002_w2aab2b8d692b1b7b1ab2ab2Aa","doi-asserted-by":"crossref","unstructured":"C. Bays and S. Durham,\nImproving a poor random number generator,\nACM Trans. Math. Software (TOMS) 2 (1976), no. 1, 59\u201364.","DOI":"10.1145\/355666.355670"},{"key":"2023040102052504796_j_mcma-2017-0105_ref_003_w2aab2b8d692b1b7b1ab2ab3Aa","unstructured":"J. Beizer,\nSpeeding up TestU01 with the use of HTCondor,\npreprint (2017), https:\/\/arxiv.org\/abs\/1703.08212."},{"key":"2023040102052504796_j_mcma-2017-0105_ref_004_w2aab2b8d692b1b7b1ab2ab4Aa","doi-asserted-by":"crossref","unstructured":"J. Daemen and V. Rijmen,\nThe design of Rijndael: AES \u2013 The advanced encryption standard,\nJ. Cryptology 4 (1991), no. 1, 3\u201372.","DOI":"10.1007\/978-3-662-60769-5_1"},{"key":"2023040102052504796_j_mcma-2017-0105_ref_005_w2aab2b8d692b1b7b1ab2ab5Aa","unstructured":"K. Donald,\nThe Art of Computer Programming. Volume 2: Semi-Numerical Algorithms,\nAddison-Wesley, Boston, 1998."},{"key":"2023040102052504796_j_mcma-2017-0105_ref_006_w2aab2b8d692b1b7b1ab2ab6Aa","unstructured":"N. Ferguson, S. Lucks, B. Schneier, D. Whiting, M. Bellare, T. Kohno, J. Callas and J. Walker,\nThe skein hash function family,\nSubmission to NIST (round 3) (2010), http:\/\/www.skein-hash.info\/sites\/default\/files\/skein1.3.pdf."},{"key":"2023040102052504796_j_mcma-2017-0105_ref_007_w2aab2b8d692b1b7b1ab2ab7Aa","unstructured":"N. Fips,\n46-3: The official document describing the DES standard,\nTechnical Report, 1999."},{"key":"2023040102052504796_j_mcma-2017-0105_ref_008_w2aab2b8d692b1b7b1ab2ab8Aa","doi-asserted-by":"crossref","unstructured":"G. S. Fishman and I. L. R. Moore,\nAn exhaustive analysis of multiplicative congruential random number generators with modulus 231-12^{31}-1,\nSIAM J. Sci. Stat. Comput. 7 (1986), no. 1, 24\u201345.","DOI":"10.1137\/0907002"},{"key":"2023040102052504796_j_mcma-2017-0105_ref_009_w2aab2b8d692b1b7b1ab2ab9Aa","unstructured":"J. E. Gentle,\nRandom Number Generation and Monte Carlo Methods,\nSpringer, New York, 2003."},{"key":"2023040102052504796_j_mcma-2017-0105_ref_010_w2aab2b8d692b1b7b1ab2ac10Aa","doi-asserted-by":"crossref","unstructured":"P. Hellekalek,\nGood random number generators are (not so) easy to find,\nMath. Comput. Simulation 46 (1998), no. 5, 485\u2013505.","DOI":"10.1016\/S0378-4754(98)00078-0"},{"key":"2023040102052504796_j_mcma-2017-0105_ref_011_w2aab2b8d692b1b7b1ab2ac11Aa","doi-asserted-by":"crossref","unstructured":"J. Katz and Y. Lindell,\nIntroduction to Modern Cryptography: Principles and Protocols,\nChapman Hall\/CRC, London, 2008.","DOI":"10.1201\/9781420010756"},{"key":"2023040102052504796_j_mcma-2017-0105_ref_012_w2aab2b8d692b1b7b1ab2ac12Aa","unstructured":"L. Keliher,\nSubstitution-permutation network cryptosystems using key-dependent S-boxes,\npreprint (1998), https:\/\/pdfs.semanticscholar.org\/df81\/08646ba9242c9c337dabc293125ba8f5a8ff.pdf."},{"key":"2023040102052504796_j_mcma-2017-0105_ref_013_w2aab2b8d692b1b7b1ab2ac13Aa","doi-asserted-by":"crossref","unstructured":"P. L\u2019Ecuyer,\nTables of linear congruential generators of different sizes and good lattice structure,\nMath. Comp. 68 (1999), no. 225, 249\u2013260.","DOI":"10.1090\/S0025-5718-99-00996-5"},{"key":"2023040102052504796_j_mcma-2017-0105_ref_014_w2aab2b8d692b1b7b1ab2ac14Aa","doi-asserted-by":"crossref","unstructured":"P. L\u2019Ecuyer and R. Simard,\nOn the performance of birthday spacings tests with certain families of random number generators,\nMath. Comput. Simulation 55 (2001), no. 1, 131\u2013137.","DOI":"10.1016\/S0378-4754(00)00253-6"},{"key":"2023040102052504796_j_mcma-2017-0105_ref_015_w2aab2b8d692b1b7b1ab2ac15Aa","doi-asserted-by":"crossref","unstructured":"P. L\u2019Ecuyer and R. Simard,\nTestU01: A C library for empirical testing of random number generators,\nACM Trans. Math. Software (TOMS) 33 (2007), no. 4, Article No. 22.","DOI":"10.1145\/1268776.1268777"},{"key":"2023040102052504796_j_mcma-2017-0105_ref_016_w2aab2b8d692b1b7b1ab2ac16Aa","doi-asserted-by":"crossref","unstructured":"G. Marsaglia,\nRandom numbers fall mainly in the planes,\nProc. Natl. Acad. Sci. USA 61 (1968), no. 1, 25\u201328.","DOI":"10.1073\/pnas.61.1.25"},{"key":"2023040102052504796_j_mcma-2017-0105_ref_017_w2aab2b8d692b1b7b1ab2ac17Aa","unstructured":"G. Marsaglia,\nA current view of random number generators,\nComputer Science and Statistics. Sixteenth Symposium on the Interface,\nNorth-Holland, Amsterdam (1985), 3\u201310."},{"key":"2023040102052504796_j_mcma-2017-0105_ref_018_w2aab2b8d692b1b7b1ab2ac18Aa","unstructured":"G. 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Shaw,\nParallel random numbers: As easy as 1, 2, 3,\n2011 International Conference for High Performance Computing, Networking, Storage and Analysis,\nIEEE Press, Piscataway (2011), 1\u201312.","DOI":"10.1145\/2063384.2063405"},{"key":"2023040102052504796_j_mcma-2017-0105_ref_022_w2aab2b8d692b1b7b1ab2ac22Aa","doi-asserted-by":"crossref","unstructured":"C. E. Shannon,\nCommunication theory of secrecy systems,\nBell Labs Tech. J. 28 (1949), no. 4, 656\u2013715.","DOI":"10.1002\/j.1538-7305.1949.tb00928.x"},{"key":"2023040102052504796_j_mcma-2017-0105_ref_023_w2aab2b8d692b1b7b1ab2ac23Aa","unstructured":"J. Soto,\nStatistical testing of random number generators,\nProceedings of the 22nd National Information Systems Security Conference,\nNational Institute of Standards and Technology, Gaithersburgh (1999), 1\u201312."},{"key":"2023040102052504796_j_mcma-2017-0105_ref_024_w2aab2b8d692b1b7b1ab2ac24Aa","doi-asserted-by":"crossref","unstructured":"S. Tzeng and L.-Y. Wei,\nParallel white noise generation on a GPU via cryptographic hash,\nProceedings of the 2008 Symposium on Interactive 3D Graphics and Games,\nACM, New York (2008), 79\u201387.","DOI":"10.1145\/1342250.1342263"},{"key":"2023040102052504796_j_mcma-2017-0105_ref_025_w2aab2b8d692b1b7b1ab2ac25Aa","unstructured":"F. Zafar, M. Olano and A. Curtis,\nGpu random numbers via the tiny encryption algorithm,\nProceedings of the Conference on High Performance Graphics,\nEurographics Association, Aire-la-Ville (2010), 133\u2013141."}],"container-title":["Monte Carlo Methods and Applications"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/www.degruyter.com\/view\/j\/mcma.2017.23.issue-2\/mcma-2017-0105\/mcma-2017-0105.xml","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/mcma-2017-0105\/xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/mcma-2017-0105\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,4,1]],"date-time":"2023-04-01T23:39:38Z","timestamp":1680392378000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/mcma-2017-0105\/html"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,5,20]]},"references-count":25,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2017,5,20]]},"published-print":{"date-parts":[[2017,6,1]]}},"alternative-id":["10.1515\/mcma-2017-0105"],"URL":"https:\/\/doi.org\/10.1515\/mcma-2017-0105","relation":{},"ISSN":["0929-9629","1569-3961"],"issn-type":[{"value":"0929-9629","type":"print"},{"value":"1569-3961","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,5,20]]}}}