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Chhikara}, title = {Robustness of Some Random Variate Generators}, journal = {Statistica Neerlandica}, year = {1992}, volume = {46}, number = {2--3}, pages = {195--207}, OPTannote = {} } @Article{rDEN94a, author = {L.-Y. Deng and K. H. Chan and Y. Yuan}, title = {Design and Implementation of Random Number Generators for Multiprocessor Systems}, journal = {International Journal of Modeling and Simulation}, year = {1994}, volume = {14}, number = {4}, pages = {185--191}, OPTannote = {} } @Article{rDEN97a, author = {L.-Y. Deng and D. K. J. Lin and J. Wang and Y. Yuan}, title = {Statistical Justification of Combination Generators}, journal = {Statistica Sinica}, year = {1997}, volume = {7}, pages = {993--1003}, OPTannote = {} } @Article{rDEN00a, author = {L.-Y. Deng and D. K. J. 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Niederreiter}, address = {Berlin}, publisher = {Springer-Verlag}, } @article{rEDM60a, author = {A. R. Edmonds}, title = {The Generation of Pseudorandom Numbers on Electronic Digital Computers}, journal = {The Computer Journal}, volume = {2}, pages = {181--185}, year = {1960} } @ARTICLE {rEIC86a, AUTHOR="J. Eichenauer and J. Lehn", TITLE="A Nonlinear Congruential Pseudorandom Number Generator", JOURNAL={Statistische Hefte}, VOLUME={27}, YEAR={1986}, PAGES={315--326} } @ARTICLE {rEIC87a, AUTHOR="J. Eichenauer and J. Lehn", TITLE="On the Structure of Quadratic Congruential Sequences", JOURNAL={Manuscripta Mathematica}, VOLUME={58}, YEAR={1987}, PAGES={129--140} } @ARTICLE {rEIC87b, AUTHOR="J. Eichenauer and H. Grothe and J. Lehn and A. Topuz{\v{o}}glu", TITLE="A Multiple Recursive Nonlinear Congruential Pseudorandom Number Generator", JOURNAL={Manuscripta Mathematica}, VOLUME={59}, YEAR={1987}, PAGES={331--346} } @ARTICLE {rEIC88a, AUTHOR="J. Eichenauer and J. Lehn and A. 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Grothe", TITLE="A New Inversive Congruential Pseudorandom Number Generator with Power of Two Modulus", JOURNAL={ACM Transactions on Modeling and Computer Simulation}, VOLUME={2}, NUMBER={1}, YEAR={1992}, PAGES={1--11} } @ARTICLE {rEIC93a, AUTHOR="J. {Eichenauer-Herrmann}", TITLE="Statistical Independence of a New Class of Inversive Congruential Pseudorandom Numbers", JOURNAL={Mathematics of Computation}, VOLUME={60}, YEAR={1993}, PAGES={375--384} } @ARTICLE {rEIC94a, AUTHOR="J. {Eichenauer-Herrmann}", TITLE="Improved Lower Bounds for the Discrepancy of Inversive Congruential Pseudorandom Numbers", JOURNAL={Mathematics of Computation}, VOLUME={62}, NUMBER={206}, YEAR={1994}, PAGES={783--786} } @ARTICLE {rEIC94b, AUTHOR="J. {Eichenauer-Herrmann} and K. Ickstadt", TITLE="Explicit Inversive Congruential Pseudorandom Numbers with Power of Two Modulus", JOURNAL={Mathematics of Computation}, VOLUME={62}, NUMBER={206}, YEAR={1994}, PAGES={787--797} } @ARTICLE {rEIC94c, AUTHOR="J. {Eichenauer-Herrmann}", TITLE="On Generalized Inversive Congruential Pseudorandom Numbers", JOURNAL={Mathematics of Computation}, VOLUME={63}, YEAR={1994}, PAGES={293--299} } @ARTICLE {rEIC94d, AUTHOR="J. {Eichenauer-Herrmann} and H. Niederreiter", TITLE="Bounds for Exponential Sums and their Applications to Pseudorandom Numbers", JOURNAL={Acta Arithmetica}, VOLUME={LXVII.3}, YEAR={1994}, PAGES={269--281} } @article {rEIC94e, author = {J. {Eichenauer-Herrmann} and H. Niederreiter}, title = {Digital Inversive Pseudorandom Numbers}, journal = {{ACM} Transactions on Modeling and Computer Simulation}, year = {1994}, volume = {4}, pages = {339--349} } @ARTICLE {rEIC95a, AUTHOR="J. {Eichenauer-Herrmann}", TITLE="Pseudorandom Number Generation by Nonlinear Methods", JOURNAL={International Statistical Reviews}, VOLUME={63}, YEAR={1995}, PAGES={247--255} } @ARTICLE {rEIC95b, AUTHOR="J. {Eichenauer-Herrmann}", TITLE="A Unified Approach to the Analysis of Compound Pseudorandom Numbers", JOURNAL={Finite Fields and their Applications}, VOLUME={1}, YEAR={1995}, PAGES={102--114} } @ARTICLE {rEIC95c, AUTHOR="J. {Eichenauer-Herrmann} and H. Niederreiter", TITLE="An Improved Upper Bound for the Discrepancy of Quadratic Congruential Pseudorandom Numbers", JOURNAL={Acta Arithmetica}, VOLUME={LXIX.2}, YEAR={1995}, PAGES={193--198} } @ARTICLE {rEIC95d, AUTHOR="J. {Eichenauer-Herrmann}", TITLE="Modified Explicit Inversive Congruential Pseudorandom Numbers with Power-of-Two Modulus", JOURNAL={Statistics and Computing}, VOLUME={6}, YEAR={1996}, PAGES={31--36} } @ARTICLE {rEIC95e, AUTHOR="J. {Eichenauer-Herrmann}", TITLE="Nonoverlapping Pairs of Explicit Inversive Congruential Pseudorandom Numbers", JOURNAL={Monatshefte f{\"ur} Mathematik}, VOLUME={119}, YEAR={1995}, PAGES={49--61} } @ARTICLE {rEIC95f, AUTHOR="J. {Eichenauer-Herrmann}", TITLE="Discrepancy Bounds for Nonoverlapping Pairs of Quadratic Congruential Pseudorandom Numbers", JOURNAL={Arch. Math.}, VOLUME={65}, YEAR={1995}, PAGES={362--368} } @ARTICLE {rEIC95g, AUTHOR="J. {Eichenauer-Herrmann}", TITLE="Quadratic Congruential Pseudorandom Numbers: Distribution of Triples", JOURNAL={Journal of Computational and Applied Mathematics}, VOLUME={62}, YEAR={1995}, PAGES={239--253} } @ARTICLE {rEIC95h, AUTHOR="J. {Eichenauer-Herrmann}", TITLE="Inversive Congruential Pseudorandom Numbers: A Tutorial", JOURNAL={International Statistical Reviews}, VOLUME={63}, YEAR={1995}, PAGES={247--255} } @inproceedings {rEIC95i, author = {Eichenauer-Herrmann, J. and Emmerich, F.}, title = {A review of compound methods for pseudorandom number generation}, booktitle = {Proceedings of the 1st Salzburg Minisymposium on Pseudorandom Number Generation and Quasi-{M}onte {C}arlo Methods, {S}alzburg, Nov 18, 1994}, year = {1995}, editor = {Hellekalek, P. and Larcher, G. and Zinterhof, P.}, publisher = {ACPC -- Austrian Center for Parallel Computation, Universit{\"a}t Wien, Austria} } @ARTICLE {rEIC96a, AUTHOR="J. {Eichenauer-Herrmann} and F. Emmerich", TITLE="Compound Inversive Congruential Pseudorandom Numbers: An Average-Case Analysis", JOURNAL="Mathematics of Computation", VOLUME={65}, NUMBER={213}, YEAR={1996}, PAGES={215--225} } @ARTICLE {rEIC96b, AUTHOR="J. {Eichenauer-Herrmann} and G. Larcher", TITLE="Average Behavior of Compound Nonlinear Congruential Pseudorandom Numbers", JOURNAL={Finite Fields and their Applications}, VOLUME={2}, YEAR={1996}, PAGES={111--123} } @ARTICLE {rEIC96c, AUTHOR="J. {Eichenauer-Herrmann}", TITLE="Modified Explicit Inversive Congruential Pseudorandom Numbers with Power-of-Two Modulus", JOURNAL={Statistics and Computing}, VOLUME={6}, YEAR={1996}, PAGES={31--36} } @article {rEIC96e, author = {J. {Eichenauer-Herrmann}}, title = {Equidistribution Properties of Inversive Congruential Pseudorandom Numbers with Power of Two Modulus}, journal = {Metrika}, year = {1996}, volume = {44}, pages = {199--205} } @article {rEIC96f, author = {J. {Eichenauer-Herrmann}}, title = {Parallel Streams of Nonlinear Congruential Pseudorandom Number}, journal = {Finite Fields Appl.}, year = {1996}, note = {to appear} } @article {rEIC96g, author = {J. {Eichenauer-Herrmann}}, title = {Average Behaviour of Compound Nonlinear Congruential Pseudorandom Numbers}, journal = {Finite Fields and their Appl.}, year = {1996}, volume = {2}, pages = {111--123} } @article {rEIC97a, author = {J. {Eichenauer-Herrmann} and E. Herrmann}, title = {Compound Cubic Congruential Pseudorandom Numbers}, journal = {Computing}, year = {1997}, volume = {59}, pages = {85--90} } @article {rEIC97b, author = {J. {Eichenauer-Herrmann}}, title = {Quadratic Congruential Pseudorandom Numbers: Distribution of Lagged Pairs}, journal = {Journal of Computational and Applied Mathematics}, year = {1997}, pages = {75--85}, volume = {79} } @article {rEIC97c, AUTHOR = {Eichenauer-Herrmann, J{\"u}rgen and Niederreiter, Harald}, TITLE = {Inversive congruential pseudorandom numbers: distribution of triples}, JOURNAL = {Mathematics of Computation}, VOLUME = {66}, YEAR = {1997}, NUMBER = {220}, PAGES = {1629--1644}, ISSN = {0025-5718}, } @incollection {rEIC97d, author = {J. {Eichenauer-Herrmann} and E. Herrmann and S. Wegenkittl}, title = {A Survey of Quadratic and Inversive Congruential Pseudorandom Numbers}, booktitle = {{M}onte {C}arlo and Quasi-{M}onte {C}arlo Methods 1996}, editor = {P. Hellekalek and G. Larcher and H. 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Math.}, year = {1997}, note = {to appear} } @article {rEIC98a, AUTHOR = {Eichenauer-Herrmann, J{\"u}rgen and Niederreiter, Harald}, TITLE = {Lower bounds for the discrepancy of triples of inversive congruential pseudorandom numbers with power of two modulus}, JOURNAL = {Monatshefte f\"ur Mathematik}, VOLUME = {125}, YEAR = {1998}, NUMBER = {3}, PAGES = {211--217}, ISSN = {0026-9255}, } @ARTICLE {rELI72a, AUTHOR="P. Elias", TITLE="The Efficient Construction of an Unbiased Random Sequence", JOURNAL={The Annals of Mathematical Statistics}, YEAR={1972}, VOLUME={43}, NUMBER={3}, PAGES={865--870}} @article {rEMM96a, author = {F. Emmerich}, title = {Pseudorandom Vector Generation by the Compound Inversive Method}, journal = {Mathematics of computation}, year = {1996}, volume = {65}, number = {214}, pages = {749--760} } @article {rEMM97a, author = {F. 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Entacher}, title = {Numerical integration with generalized Haar function systems}, booktitle = {Proceedings of the 1st Salzburg Minisymposium on Pseudorandom Number Generation and Quasi-{M}onte {C}arlo Methods, Salzburg, Nov. 1994}, volume = {ACPC/TR 95-4}, series = {Technical Report Series}, publisher = {ACPC---Austrian Center for Parallel Computation, {U}niversity of {V}ienna, {A}ustria}, year = {1995}, pages = {25--41}} @inproceedings {rENT95a, author = {K. Entacher and H. Leeb}, title = {Inversive pseudorandom number generators: empirical results}, booktitle = {Proceedings of the Conference Parallel Numerics 95, Sorrento, Italy, September 27--29, 1995}, year = {1995} } @unpublished {rENT95b, author = {K. Entacher}, title = {Selected Random Number Generators in the Run Test}, note = {Manuscript, Dept.~of Mathematics, University of Salzburg}, year = {1995} } @phdthesis {rENT95c, author = {K. Entacher}, title = {Generalized Haar function systems in the theory of uniform distributions of sequences modulo one}, year = {1995}, school = {University of Salzburg} } @techreport {rENT97a, author = {K. Entacher}, title = {A Collection of Selected Pseudorandom Number Generators with Linear Structures}, institution = {pLab Report, Institut f\"ur Mathematik, Universit\"at Salzburg}, year = {1997} } @article {rENT97b, author = {K. Entacher}, title = {Quasi-{M}onte {C}arlo methods for numerical integration of multivariate {H}aar series}, journal = {BIT}, year = {1997}, pages = {846--861}, volume = {37} } @incollection{ rENT97c, author = "K. Entacher and O. Lendl and A. Uhl and S. Wegenkittl", title = "Analyzing streams of pseudorandom numbers for parallel Monte Carlo integration", editor = {R. Wyrzykowski and H. Piech and B. Mochnacki and M. Vajtersic and P. Zinterhof}, booktitle = {Proceedings of the International Workshop on Parallel Numerics (Parnum'97)}, publisher = {Zakopane, Poland}, pages = {59--71}, month = {September}, year = {1997}, url = "citeseer.nj.nec.com/entacher97analyzing.html" } @article {rENT98a, author = {K. Entacher}, TITLE="Bad Subsequences of Well-Known Linear Congruential Pseudorandom Number Generators", JOURNAL={ACM Transactions on Modeling and Computer Simulation}, VOLUME={8}, NUMBER={1}, YEAR={1998}, PAGES={61--70} } @INPROCEEDINGS {rENT00b, old = {rHEL98e}, old = {rENT98e}, old = {rENT99e}, author = {K. Entacher and P. Hellekalek and P. L'Ecuyer}, title = {Quasi-{M}onte {C}arlo Node Sets from Linear Congruential Generators}, booktitle = {{M}onte {C}arlo and Quasi-{M}onte {C}arlo Methods 1998}, pages = {188--198}, year = {2000}, editor = {H. Niederreiter and J. Spanier}, address = {Berlin}, publisher = {Springer}, OPTannote = {} } @INPROCEEDINGS {rENT00bx, author = {K. Entacher and P. Hellekalek and P. L'Ecuyer}, title = {Quasi-{M}onte {C}arlo Node Sets from Linear Congruential Generators}, crossref = {rNIE00a}, pages = {188--198}, OPTannote = {} } @INPROCEEDINGS {rENT01a, AUTHOR = "K. Entacher and T. Schell and A. Uhl", TITLE = "Evolutionary Optimization of Random Number Generators", booktitle = {{M}onte {C}arlo Simulation}, editor = {G. I. Schu\"eller and P. D. Spanos}, xBOOKTITLE={Proceedings of the International Conference {M}onte {C}arlo 2000}, PUBLISHER = {A. A. Balkema}, address = {Rotterdam}, YEAR = {2001}, PAGES = {19--26} } @INPROCEEDINGS {rENT01b, AUTHOR = "K. Entacher and T. Schell", TITLE = "From `pseudo' to `quasi'", booktitle = {{M}onte {C}arlo Simulation}, editor = {G. I. Schu\"eller and P. D. Spanos}, xBOOKTITLE={Proceedings of the International Conference {M}onte {C}arlo 2000}, PUBLISHER = {A. A. Balkema}, address = {Rotterdam}, YEAR = {2001}, PAGES = {27--34} } @MASTERSTHESIS {rERD92a, AUTHOR="E. D. 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Etzion", TITLE="On Pseudo-Random Arrays Constructed from Patterns with Distinct Differences", booktitle={Sequences: Combinatorics, Compression Security, and Transmission}, editor={R. M. Capocelli}, publisher={Springer-Verlag}, address = {New York, NY}, YEAR={1990}, PAGES={195--207} } @INPROCEEDINGS {rFAI85a, AUTHOR = {R. C. Fairfield and R. L. Mortenson and K. B. Coulthart}, TITLE = {An {LSI} Random Number Generator (RNG)}, BOOKTITLE = {Advances in Cryptology: Proceedings of Eurocrypt 1984}, YEAR = {1985}, series = {Lecture Notes in Computer Science}, publisher = {Springer-Verlag}, address = {Berlin}, OPTvolume = {}, PAGES = {203--230} } @book {rFAN02a, title = {{M}onte {C}arlo and Quasi-{M}onte {C}arlo Methods 2000}, editor = {K.-T. Fang and F. J. Hickernell and H. Niederreiter}, publisher = {Springer-Verlag}, address = {Berlin}, year = {2002}, } @ARTICLE{rFAU82a, author ={H. 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Lagarias", TITLE="Linear Congruential Generators Do Not Produce Random Sequences", BOOKTITLE={Proceedings of the 25th {IEEE} Symposium on Foundations of Computer Science}, YEAR={1984}, PAGES={480--484} } @ARTICLE {rFRI88a, AUTHOR="A. M. Frieze and J. Hastad and R. Kannan and J. C. Lagarias and A. Shamir", TITLE="Reconstructing Truncated Integer Variables Satisfying Linear Congruences", JOURNAL={SIAM Journal on Computing}, YEAR={1988}, VOLUME={17}, NUMBER={2}, PAGES={262--280} } @INPROCEEDINGS {rFRI01a, AUTHOR="I. Friedel and A. Keller", TITLE="Fast Generation of Randomized Low-Discrepancy Point Sets", booktitle = {{M}onte {C}arlo and Quasi-{M}onte {C}arlo Methods 2000}, pages = {257--273}, year = {2001}, editor = {K.-T. Fang and F. J. Hickernell and H. Niederreiter}, address = {Berlin}, publisher = {Springer-Verlag}, } @ARTICLE {rFUS83a, AUTHOR="M. 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Good", TITLE="The Serial Test for Sampling Numbers and Other Tests for Randomness", JOURNAL={Proceedings of the Cambridge Philos. Society}, VOLUME={49}, YEAR={1953}, PAGES={276--284} } @ARTICLE {rGOO57a, AUTHOR="I. J. Good", TITLE="On the Serial Test for Random Sequences", JOURNAL={Annals of Mathematical Statistics}, VOLUME={23}, YEAR={1957}, PAGES={262--264} } @ARTICLE {rGOO67a, AUTHOR="I. J. Good and T. N. Gover", TITLE="The Generalized Serial Test and the Binary Expansion of {$\sqrt{2}$}", JOURNAL={Journal of the Royal Statistical Society, Series {A}}, NOTE={Also Corrigendum in 131 (1968), 434}, VOLUME={130}, YEAR={1967}, PAGES={102--107} } @ARTICLE {rGOO69a, AUTHOR="I. J. Good", TITLE="How Random are Random Numbers?", JOURNAL={The American Statistician}, VOLUME={}, YEAR={1969}, PAGES={42--45} } @ARTICLE {rGOR03a, AUTHOR="M. Goresky and A. Klapper", TITLE="Efficient Multiply-with-Carry Random Number Generators with Maximal Period", JOURNAL={ACM Transactions on Modeling and Computer Simulation}, VOLUME={13}, NUMBER={4}, YEAR={2003}, PAGES={310--321} } @MASTERSTHESIS {rGRA01a, AUTHOR = "J. Granger-Pich\'e", TITLE = {G\'en\'erateurs pseudo-al\'eatoires combinant des r\'ecurrences lin\'eaires et non lin\'eaires}, SCHOOL={D\'epartement d'informatique et de recherche op\'eration\-nelle, Universit\'e de Montr\'eal}, language={french}, xmonth = {}, YEAR ={2001} } @ARTICLE {rGRE55a, AUTHOR="R. E. Greenwood", TITLE="Coupon collector's test for random digits", JOURNAL={Math. Tables and other Aids to Computation}, VOLUME={9}, YEAR={1955}, PAGES={1--5, 224, 229} } @INCOLLECTION {rGRO86a, AUTHOR="H. Grothe", TITLE={{M}atrixgeneratoren zur {E}rzeugung Gleichverteilter {Z}ufallsvektoren}, BOOKTITLE={Kolloquium \"uber Zufallszahlen und Simultationen}, PUBLISHER="Darmstadt, L. Afflerbach and J. Lehn eds., B. G.", ADDRESS={Teubner Stuttgart}, YEAR={1986} } @ARTICLE {rGRO87a, AUTHOR="H. Grothe", TITLE="Matrix Generators for Pseudo-Random Vectors Generation", JOURNAL={Statistische Hefte}, VOLUME={28}, YEAR={1987}, PAGES={233--238} } @PHDTHESIS {rGRO88a, AUTHOR="H. Grothe", TITLE="{M}atrixgeneratoren zur {E}rzeugung Gleichverteilter {P}seudozufallsvektoren", YEAR={1988}, LANGUAGE={German}, TYPE={Dissertation (thesis)}, SCHOOL={Tech.\ Hochschule Darmstadt}, ADDRESS={Germany} } @ARTICLE {rGRU73a, AUTHOR="A. Grube", TITLE="{M}ehrfach rekursiv-erzeugte {P}seudo-{Z}ufallszahlen", LANGUAGE={German}, JOURNAL={Zeitschrift f{\"u}r angewandte Mathematik und Mechanik}, VOLUME={53}, YEAR={1973}, PAGES={T223--T225} } @ARTICLE {rGUI89a, AUTHOR="D. Guinier", TITLE="A Fast Uniform ``Astronomical'' Random Number Generator", JOURNAL={ACM SIGSAC Review}, VOLUME={7}, NUMBER={1}, MONTH={Spring}, YEAR={1989}, PAGES={1--13} } @ARTICLE {rHAA87a, AUTHOR="A. Haas", TITLE="The Multiple Prime Random Number Generator", JOURNAL={ACM Transactions on Mathematical Software}, VOLUME={13}, NUMBER={4}, YEAR={1987}, PAGES={368--381} } @ARTICLE{rHAL60a, author = {J. H. Halton}, title = {On the efficiency of certain quasi-random sequences of points in evaluating multi-dimensional integrals}, journal = {Numerische Mathematik}, volume = 2, pages = {84--90}, year = 1960} @ARTICLE {rHAL89a, AUTHOR="J. H. Halton", TITLE="Pseudo-random Trees: Multiple Independent Sequence Generators for Parallel and Branching Computations", JOURNAL={Journal of Computational Physics}, VOLUME={84}, YEAR={1989}, PAGES={1--56} } @article{rHAM05a, author = {K. Hamano}, title = {The Distribution of the Spectrum for the Discrete {F}ourier Transform Test Included in {SP800-22}}, journal = {IEICE Transactions}, volume = {88-A}, number = {1}, year = {2005}, pages = {67-73} } @ARTICLE {rHAM60a, AUTHOR="J. M. Hammersley", TITLE="{M}onte {C}arlo Methods for Solving Multivariate Problems", JOURNAL={Annals of the {N}ew {Y}ork Academy of Science}, VOLUME={86}, YEAR={1960}, PAGES={844--874} } @ARTICLE {rHAN93a, AUTHOR="T. Hansen and G. L. Mullen and H. Niederreiter", TITLE="Good Parameters for a Class of Node Sets in Quasi-{M}onte {C}arlo Integration", JOURNAL={Mathematics of Computation}, VOLUME={61}, YEAR={1993}, PAGES={225--234} } @ARTICLE {rHAN96a, AUTHOR="W. B. Han", TITLE="The Coefficients of Primitive Polynomials over Finite Fields", JOURNAL="Mathematics of Computation", VOLUME={65}, NUMBER={213}, YEAR={1996}, PAGES={331--340} } @ARTICLE {rHAR08a, old = {rHAR07a}, AUTHOR="H. Haramoto and M. Matsumoto and T. Nishimura and F. Panneton and P. L'Ecuyer", TITLE="Efficient Jump Ahead for {${\bf F}_2$}-Linear Random Number Generators", JOURNAL="INFORMS Journal on Computing", VOLUME={20}, NUMBER={3}, YEAR={2008}, Xnote = {GERAD Report G-2006-62}, PAGES={385--390} } @ARTICLE {rHEI98a, author = {S. Heinrich}, title = {Efficient Algorithms for Computing the $L_2$ Discrepancy}, journal = {Mathematics of Computation}, volume = {??}, pages = {??}, year = {1998} } @ARTICLE {rHEL93a, author = {P. Hellekalek}, title = {General Discrepancy Estimates: the {W}alsh Function System}, journal = {Acta Arithmetica}, volume = {67}, pages = {209--218}, year = {1994} } @ARTICLE {rHEL93b, author = {P. Hellekalek}, title = {General Discrepancy Estimates {II}: The {H}aar Function System}, journal = {Acta Arithmetica}, volume = {67}, pages = {313--322}, year = {1994} } @ARTICLE {rHEL93c, author = {P. Hellekalek}, title = {General Discrepancy Estimates {III}: the {E}rd{\"o}s-{T}ur{\'a}n-{K}oksma Inequality for the {H}aar Function System}, journal = {Monatsh. Math.}, volume = {120}, pages = {25--45}, year = {1995}} @TECHREPORT {rHEL94a, author = {P. Hellekalek}, title = {Study of algorithms for primitive polynomials}, institution = {Research Institute for Software Technology, University of Salzburg, Austria}, type = {Report {D}5{H}-1, {CEI-PACT P}roject, {WP}5.1.2.1.2}, year = {1994} } @TECHREPORT {rHEL94b, author = {P. Hellekalek and M. Mayer and A. Weingartner}, title = {Implementation of algorithms for {IMP}-polynomials}, institution = {Research Institute for Software Technology, University of Salzburg, Austria}, type = {Report {D}5{H}-2, {CEI-PACT P}roject, {WP}5.1.2.1.2}, year = {1994}} @inproceedings {rHEL95a, author = {P. Hellekalek}, editor = {C. Alexopoulos and K. Kang and W. R. Lilegdon and D. Goldsman}, title = {Inversive Pseudorandom Number Generators: Concepts, Results, and Links}, booktitle = {Proceedings of the 1995 Winter Simulation Conference}, publisher = {{IEEE} Press}, year = {1995}, pages = {255--262}} @inproceedings {rHEL97a, author = {P. Hellekalek}, title = {Good Random Number Generators are (not so) Easy to Find}, booktitle = {Proc. Second {IMACS} Symposium on Mathematical Modelling, {V}ienna}, year = {1997}, editor = {I. Troch and F. Breitenecker}, publisher = {{ARGESIM}-Reports, {ISBN} 3-901608-11-7} } @ARTICLE {rHEL97b, author = {P. Hellekalek and H. Leeb}, year = {1997}, title = {Dyadic Diaphony}, journal = {Acta Arithmetica}, volume = {80}, pages = {187--196}, abstract = {dyadic diaphony; continuous version of Tezuka's Walsh spectral test}, keywords = {diaphony, Walsh spectral test} } @ARTICLE {rHEL98a, author = {P. Hellekalek and H. Niederreiter}, title = {The Weighted Spectral Test: Diaphony}, journal = {ACM Transactions on Modeling and Computer Simulation}, volume = {8}, number = {1}, pages = {43--60}, year = {1998}, abstract = {proofs of the weighted spectral test with diaphony}, keywords = {diaphony, spectral test} } @incollection {rHEL98b, ex = {rHEL99a}, author = {Hellekalek, P.}, title = {On the Assessment of Random and Quasi-random Point Sets}, booktitle = {Random and Quasi-Random Point Sets}, editor = {P. Hellekalek and G. Larcher}, publisher = {Springer}, address = {New York, NY}, volume = {138}, pages = {49--108}, year = {1998}, series = {Lecture Notes in Statistics} } @incollection {rHEL98bx, author = {Hellekalek, P.}, title = {On the Assessment of Random and Quasi-random Point Sets}, pages = {49--108}, crossref = {rHEL98s}, } @INcollection {rHEL98c, old = {1997c}, author = {Hellekalek, P.}, year = {1998}, title = {On correlation analysis of pseudorandom numbers}, editor = {Hellekalek, P. and Larcher, G. and Niederreiter, H. and Zinterhof, P.}, booktitle = {{M}onte {C}arlo and Quasi-{M}onte {C}arlo Methods 1996}, publisher = {Springer-Verlag, New York, NY}, series = {Lecture Notes in Statistics}, volume = {127}, pages = {251--265}, abstract = {weighted spectral test: the concept; examples: diaphony; continuous version of Tezuka's Walsh spectral test} } @INPROCEEDINGS {rHEL98d, author = {Hellekalek, P.}, year = {1998}, title = {Don't Trust Parallel {M}onte {C}arlo!}, booktitle = {Twelfth Workshop on Parallel and Distributed Simulation, Banff, Canada}, publisher = {{IEEE} Computer Society}, address = {Los Alamitos, California}, pages = {82--89} } @book {rHEL98e, editor = {Hellekalek, P. and Larcher, G. and Niederreiter, H. and Zinterhof, P.}, title = {{M}onte {C}arlo and Quasi-{M}onte {C}arlo Methods 1996}, publisher = {Springer}, address = {New York, NY}, volume = {127}, year = {1998}, series = {Lecture Notes in Statistics} } @Article{rHEL98f, author = {P. Hellekalek}, title = {Good Random Number Generators are (not so) Easy to Find}, journal = {Mathematics and Computers in Simulation}, year = {1998}, volume = {46}, OPTnumber = {}, pages = {485--505}, OPTannote = {survey for practitioners} } @book {rHEL98s, title = {Random and Quasi-Random Point Sets}, editor = {P. Hellekalek and G. Larcher}, publisher = {Springer}, address = {New York, NY}, volume = {138}, year = {1998}, series = {Lecture Notes in Statistics} } @ARTICLE {rHEL03a, AUTHOR="P. Hellekalek and S. Wegenkittl", TITLE="Empirical Evidence concerning {AES}", JOURNAL={ACM Transactions on Modeling and Computer Simulation}, VOLUME={13}, NUMBER={4}, YEAR={2003}, PAGES={322--333} } @MANUAL {rHEN94a, AUTHOR={M. Hennecke}, TITLE={{RANEXP}: Experimental Random Number Generator Package}, INSTITUTION={University of Karlsruhe -- Computer Center}, NOTE={Author's e-mail: {\tt hennecke@rz.uni-karlsruhe.de}}, YEAR={1994} } @Article{rHER76a, author = {T. Herzog and J. C. {Owings Jr.}}, title = {...}, journal = {Zeitschrift f\"ur Mathematische Logik und Grundlagen der Mathematik}, year = {1976}, volume = {22}, pages = {385--389} } @ARTICLE {rHER92a, AUTHOR={J. R. Heringa and H. W. J. Bl{\"o}te and A. Compagner}, TITLE="New Primitive Trinomials of {M}ersenne-Exponent Degrees for Random-Number Generation", JOURNAL={International Journal of Modern Physics C}, VOLUME={3}, NUMBER={3}, YEAR={1992}, PAGES={561--564} } @incollection {rHER97a, author = {E. Herrmann and S. Wegenkittl}, title = {Visualization of Empirical Test Results for Pseudorandom Number Generators}, booktitle = {{M}onte {C}arlo and Quasi-{M}onte {C}arlo Methods 1996}, editor = {P. Hellekalek and G. Larcher and H. Niederreiter and P. Zinterhof}, publisher = {Springer-Verlag}, address = {New York, NY}, volume = {127}, pages = {??--??}, year = {1998}, series = {Lecture Notes in Statistics} } @Article{rHIL70a, author = {G. W. Hill}, title = {Algorithm 395: {S}tudent's $t$-Distribution}, journal = {Communications of the {ACM}}, year = {1970}, volume = {13}, OPTnumber = {}, pages = {617--619}, OPTmonth = {}, } @ARTICLE {rHIL93a, AUTHOR="M. Hildebrand", TITLE="Random Processes of the Form {$X_{n+1} = a_n X_n + b_n$} (mod {$p$})", JOURNAL={The Annals of Probability}, VOLUME={21}, YEAR={1993}, PAGES={710--720} } @ARTICLE {rHOA78a, AUTHOR="D. C. Hoaglin and M. L. King", TITLE="A Remark on Algorithm {AS} 98: The Spectral Test for the Evaluation of Congruential Pseudo-random Generators", JOURNAL={Applied Statistics}, VOLUME={27}, YEAR={1978}, PAGES={375--377} } @ARTICLE {rHOL94a, AUTHOR="B. L. Holian and O. E. Percus and T. T. Warnock and P. A. Whitlock", TITLE="Pseudorandom Number Generator for Massively Parallel Molecular-Dynamics Simulations", JOURNAL={Physical Review {E}}, VOLUME={50}, NUMBER={2}, YEAR={1994}, PAGES={1607--1615} } @ARTICLE {rHOR48a, AUTHOR="H. B. Horton", TITLE="A Method for Obtaining Random Numbers", JOURNAL={Annals of Mathematical Statistics}, VOLUME={19}, YEAR={1948}, PAGES={81--85} } @ARTICLE {rHOR49a, AUTHOR="H. B. Horton and R. T. {Smith III}", TITLE="A Direct Method for Producing Random Digits in any Number System", JOURNAL={Annals of Mathematical Statistics}, VOLUME={20}, YEAR={1949}, PAGES={82--90} } @ARTICLE {rHOR90a, AUTHOR={W. H{\"o}ermann and G. Derflinger}, TITLE={The {ACR} Method for generating normal random variables}, JOURNAL={OR Spektrum}, VOLUME={12}, PAGES={181--185}, YEAR={1990}} @ARTICLE {rHOR93a, AUTHOR={W. H{\"o}rmann and G. Derflinger}, TITLE="A Portable Random Number Generator Well Suited for the Rejection Method", JOURNAL={{ACM} Transactions on Mathematical Software}, VOLUME={19}, NUMBER={4}, YEAR={1993}, PAGES={489--495} } @ARTICLE {rHOR94a, AUTHOR={W. H{\"o}rmann and G. Derflinger}, TITLE="The Transformed Rejection Method for Generating Random Variables, An Alternative to the Ratio-of-Uniforms Method", JOURNAL={Communications in Statistics: Simulation and Computation}, VOLUME={23}, NUMBER={3}, YEAR={1994}, PAGES={847--860} } @ARTICLE {rHOR96a, AUTHOR={W. H{\"o}rmann and G. Derflinger}, TITLE="Rejection-Inversion to Generate Variates from Monotone Discrete Distributions", JOURNAL={{ACM} Transactions on Modeling and Computer Simulation}, VOLUME={6}, NUMBER={3}, YEAR={1996}, PAGES={169--184} } @inproceedings {rHOR00a, AUTHOR={W. H{\"o}rmann and J. Leydold}, TITLE="Automatic Random Variate Generation for Simulation Input", BOOKTITLE={Proceedings of the 2000 Winter Simulation Conference}, editor = {J. A. Joines and R. R. Barton and K. Kang and P. A. Fishwick}, PUBLISHER="{IEEE} Press", ADDRESS= {Pistacaway, NJ}, MONTH={Dec}, YEAR={2000}, PAGES={675--682} } @ARTICLE {rHOR02a, AUTHOR={W. H{\"o}rmann and G. Derflinger}, TITLE="Fast Generation of Order Statistics", JOURNAL={{ACM} Transactions on Modeling and Computer Simulation}, VOLUME={12}, NUMBER={2}, YEAR={2002}, PAGES={83--93} } @ARTICLE {rHOR03a, AUTHOR="W. H{\"o}rmann and J. Leydold", TITLE="Continuous Random Variate Generation by Fast Numerical Inversion", JOURNAL={ACM Transactions on Modeling and Computer Simulation}, VOLUME={13}, NUMBER={4}, YEAR={2003}, PAGES={347--362} } @Book{rHOR04a, author = {W. H\"ormann and J. Leydold and G. Derflinger}, title = {Automatic Nonuniform Random Variate Generation}, publisher = {Springer-Verlag}, year = {2004}, OPTseries = {}, address = {Berlin}, OPTannote = {} } @ARTICLE {rHOS86a, AUTHOR="J. M. Hosack", TITLE="The Use of {C}ebysev Mixing to Generate Pseudo-random Numbers", JOURNAL={Journal of Computational Physics}, VOLUME={67}, YEAR={1986}, PAGES={482--486} } @ARTICLE {rHUB94a, AUTHOR="K. Huber", TITLE="On the Period Length of Generalized Inversive Pseudorandom Number Generators", JOURNAL={Applied Algebra in Engineering, Communications, and Computing}, VOLUME={5}, YEAR={1994}, PAGES={255--260} } @ARTICLE {rHUL62a, AUTHOR="T. E. Hull", TITLE="Random Number Generators", JOURNAL={SIAM Review}, VOLUME={4}, YEAR={1962}, PAGES={230--254} } @INPROCEEDINGS {rIMP89a, AUTHOR="R. Impagliazzo and L. A. Levin and M. Luby", TITLE="Pseudo-random Generation From One-Way Functions (Extended Abstract)", BOOKTITLE={Proceedings of the Symposium on Theory of Computing '89}, YEAR={1989}, PAGES={12--24}, PUBLISHER="ACM Publications" } @Manual {rIBM68a, title = {System/360 Scientific Subroutine Package, Version {III}, Programmer's Manual}, OPTkey = {}, optauthor = {IBM}, organization = {IBM}, address = {White Plains, New York}, OPTedition = {}, OPTmonth = {}, year = {1968}, pages = {77}, OPTnote = {}, OPTannote = {} } @INPROCEEDINGS {rIMP89b, AUTHOR="R. Impagliazzo and D. Zuckerman", TITLE="How to Recycle Random Bits", BOOKTITLE={Proceedings of the 30th Symposium on Foundations of Computer Science}, YEAR={1989}, PAGES={248--254}, PUBLISHER="{IEEE} Press" } @ARTICLE {rINOa, AUTHOR="H. Inoue and H. Kumahora and Y. Yoshizawa and M. Ichimura and O. Miyatake", TITLE="Random Numbers Generated by a Physical Device", JOURNAL={Applied Statistics}, VOLUME={32}, NUMBER={2}, YEAR={1983}, PAGES={115--120} } @ARTICLE {rIZU88a, AUTHOR="T. Izumi", TITLE="Fast Generation of a White and Normal Random Signal", JOURNAL={{IEEE} Transactions on Instrumentation and Measurement}, VOLUME={37}, NUMBER={2}, YEAR={1988}, PAGES={316--318} } @ARTICLE {rJAM90a, AUTHOR="F. James", TITLE="A Review of Pseudorandom Number Generators", JOURNAL={Computer Physics Communications}, VOLUME={60}, YEAR={1990}, PAGES={329--344} } @ARTICLE {rJAM94a, AUTHOR="F. James", TITLE={{RANLUX}: A {F}ortran Implementation of the High-Quality Pseudorandom Number Generator of {L}{\"u}scher}, JOURNAL={Computer Physics Communications}, VOLUME={79}, YEAR={1994}, PAGES={111--114} } @INPROCEEDINGS{rJEN96a, AUTHOR = "B. Jenkins", TITLE = "{ISAAC}", editor = {Dieter Gollmann}, booktitle = {Fast Software Encryption, Proceedings of the Third International Workshop, Cambridge, UK}, publisher = {Springer-Verlag}, series = {Lecture Notes in Computer Science}, volume = {1039}, isbn = {3-540-60865-6}, note = {\url{http://burtleburtle.net/bob/rand/isaacafa.html}}, pages = {41--49}, year = {1996} } @ARTICLE {rJEN00a, AUTHOR="T. Jennewein and U. Achleitner and G. Weihs and H. Weinfurter and A. Zeilinger", TITLE="A Fast and Compact Quantum Random Number Generator", JOURNAL={Review of Scientific Instruments}, YEAR={2000}, VOLUME={71}, PAGES={1675--1680} } @ARTICLE {rJEN83a, AUTHOR="L. P. Jennergren", TITLE="Another Method for Random Number Generation on Microcomputers", JOURNAL={Simulation}, VOLUME={41}, YEAR={1983}, PAGES={79} } @article{rJOE03a, author = {S. Joe and F. Y. Kuo}, title = {Remark on Algorithm 659: Implementing {S}obol's quasirandom sequence generator}, journal = {{ACM} Transactions on Mathematical Software}, volume = {29}, number = {1}, year = {2003}, pages = {49--57}, } @inproceedings{rJOE06a, author = {S. Joe}, title = {Construction of Good Rank-1 Lattice Rules Based on the Weighted Star Discrepancy}, booktitle = {{M}onte {C}arlo and Quasi-{M}onte {C}arlo Methods 2004}, pages = {181--196}, year = {2006}, editor = {H. Niederreiter and D. Talay}, OPTaddress = {Berlin}, OPTpublisher = {Springer-Verlag}, } @article{rJOE08a, author = {S. Joe and F. Y. Kuo}, title = {Constructing {S}obol Sequences with Better Two-Dimensional Projections}, journal = {{SIAM} Journal on Scientific Computing}, volume = {30}, number = {5}, year = {2008}, pages = {2635--2654}, } @ARTICLE {rJOH96a, AUTHOR="B. C. Johnson", TITLE="Radix-{$b$} Extensions to Some Common Tests for Randomness", JOURNAL={ACM Transactions on Modeling and Computer Simulation}, xVOLUME={79}, YEAR={1996}, xPAGES={111--114}, NOTE={Submitted} } @ARTICLE {rJON96a, AUTHOR={M. C. Jones and A. D. Lunn}, TITLE="Transformations and Random Variate Generation: Generalised Ratio-of-Uniforms Methods", JOURNAL={Journal of Statistical Computation and Simulation}, VOLUME={55}, NUMBER={1--2}, YEAR={1996}, PAGES={49--55} } @article {rKAC83a, author = {M. Kac}, title = {What is Random~?}, journal = {American Scientist}, volume = {71}, pages = {405--406}, year = {1983} } @INPROCEEDINGS {rKAI94a, AUTHOR="W. D. Kaigh and E. F. Schuster", TITLE="{SRS} Runs and Spacings Tests to Assess Randomness", BOOKTITLE={Proceedings of Computational Statistics ........ QA 276}, YEAR={1994}, PAGES={272--277}, PUBLISHER="??" } @ARTICLE {rKAN88a, AUTHOR="R. Kannan and A. K. Lenstra and L. Lov{\'a}sz", TITLE="Polynomial Factorization and Nonrandomness of Bits of Algebraic and Some Transcendental Numbers", JOURNAL={Mathematics of Computation}, VOLUME={50}, NUMBER={181}, YEAR={1988}, PAGES={235--250} } @BOOK {rKAR91a, AUTHOR="Z. A. Karian and E. J. Dudewicz", TITLE={Modern Statistical, Systems, and {GPSS} Simulation: The First Course}, PUBLISHER="Computer Science Press", ADDRESS={Freeman, New York, NY}, YEAR={1991} } @techreport {rKEL05a, author = {S. S. Keller}, title = {{NIST}-Recommended Random Number Generator based on {ANSI X9.31} {A}ppendix {A.2.4} using the 3-Key Triple {DES} and {AES} Algorithms}, institution = {U.S. DoC/National Institute of Standards and Technology}, year = {2005}, note = {See \url{http://csrc.nist.gov/cryptval/rng/931rngext.pdf}}, pages = {1--4} } @Article{rKEM81a, author = {A. W. Kemp}, title = {Efficient Generation of Logarithmically Distributed Pseudo-random Variables}, journal = {Applied Statistics}, year = {1981}, volume = {30}, OPTnumber = {}, pages = {249--253}, OPTannote = {} } @ARTICLE {rKEN38a, AUTHOR="M. G. Kendall and B. Babington-Smith", TITLE="Randomness and other random sampling numbers", JOURNAL={Journal of the Royal Statistical Society}, VOLUME={101}, YEAR={1938}, PAGES={147--166} } @ARTICLE {rKEN39a, AUTHOR="M. G. Kendall and B. Babington-Smith", TITLE="Second paper on random sampling numbers", JOURNAL={Journal of the Royal Statistical Society Supplement}, VOLUME={6}, YEAR={1939}, PAGES={51--61} } @ARTICLE {rKER37a, AUTHOR="W. O. Kermack and A. G. Kendrick", TITLE="Tests for randomness in a series of numerical observations", JOURNAL={Proc. of the Royal Society of Edinburgh}, VOLUME={57}, YEAR={1937}, PAGES={228--240} } @ARTICLE {rKER37b, AUTHOR="W. O. Kermack and A. G. Kendrick", TITLE="Some distributions associated with a randomly arranged set of numbers", JOURNAL={Proc. of the Royal Society of Edinburgh}, VOLUME={57}, YEAR={1937}, PAGES={332--376} } @misc{rKim04a, author = {S. Kim and K. Umeno and A. Hasegawa}, title = {Corrections of the {NIST} Statistical Test Suite for Randomness}, year = {2004}, note = {Cryptology ePrint Archive: Report 2004/018. Available at \url{http://eprint.iacr.org/2004/018.pdf}} } @ARTICLE {rKIN76a, AUTHOR="A. J. Kinderman and J. G. Ramage", TITLE="Computer Generation of Normal Random Variables", JOURNAL={Journal of the American Statistical Association}, VOLUME={71}, PAGES={893--898}, YEAR={1976}} @ARTICLE {rKIN77a, AUTHOR="A. J. Kinderman and J. F. Monahan", TITLE="Computer Generation of Random Variables Using the Ratio of Uniform Deviates", JOURNAL={{ACM} Transactions on Mathematical Software}, VOLUME={3}, PAGES={257--260}, YEAR={1977}} @ARTICLE {rKIN80a, AUTHOR="A. J. Kinderman and J. F. Monahan", TITLE="New Methods for Generating {S}tudent's t and Gamma Variables", JOURNAL={Computing}, VOLUME={25}, PAGES={369--377}, YEAR={1980}} @article{rKIR81a, author = {S. Kirkpatrick and E. Stoll}, title = {A Very Fast Shift-Register Sequence Random Number Generator}, journal = {Journal of Computational Physics}, volume = {40}, pages = {517--526}, year = {1981} } @BOOK {rKNU69a, AUTHOR="D. E. Knuth", TITLE={The Art of Computer Programming, Volume 2: Seminumerical Algorithms}, EDITION={First}, PUBLISHER="Addison-Wesley", ADDRESS={Reading, MA}, YEAR={1969} } @TECHREPORT {rKNU80a, AUTHOR="D. E. Knuth", TITLE="Deciphering a Linear Congruential Encryption", NUMBER={024800}, INSTITUTION={Dept. of Computer Science}, ADDRESS={Stanford University}, YEAR={1980} } @BOOK {rKNU81a, AUTHOR="D. E. Knuth", TITLE={The Art of Computer Programming, Volume 2: Seminumerical Algorithms}, EDITION={Second}, PUBLISHER="Addison-Wesley", ADDRESS={Reading, MA}, YEAR={1981} } @BOOK {rKNU97a, AUTHOR="D. E. Knuth", TITLE={The Art of Computer Programming, Volume 2: Seminumerical Algorithms}, EDITION={Third}, PUBLISHER="Addison-Wesley", ADDRESS={Reading, MA}, YEAR={1998} } @BOOK {rKNU98a, old = {rKNU97a}, AUTHOR="D. E. Knuth", TITLE={The Art of Computer Programming, Volume 2: Seminumerical Algorithms}, EDITION={Third}, PUBLISHER="Addison-Wesley", ADDRESS={Reading, MA}, YEAR={1998} } @ARTICLE {rKOC95a, AUTHOR="C. Ko{\c{c}}", TITLE="Recurring-with-Carry Sequences", JOURNAL={Journal of Applied Probability}, VOLUME={32}, YEAR={1995}, PAGES={966--971} } @Article{rKOL63a, author = {A. N. Kolmogorov}, title = {On Tables of Random Numbers}, journal = {Sankhya, Series A}, year = {1963}, volume = {25}, pages = {369--376} } @ARTICLE {rKON89a, AUTHOR="A. E. Koniges and C. E. Leith", TITLE="Parallel Processing of Random Number Generation for {M}onte {C}arlo Turbulence Simulation", JOURNAL={Journal of Computational Physics}, VOLUME={81}, YEAR={1989}, PAGES={230--235} } @INPROCEEDINGS {rKRA90a, AUTHOR="H. Krawczyk", TITLE="How to Predict Congruential Generators", SERIES={Lecture Notes in Computer Science}, BOOKTITLE={Advances in Cryptology: Proceedings of CRYPTO'89}, EDITOR={G. Brassard}, PUBLISHER="Springer-Verlag, Berlin", YEAR={1990}, VOLUME={435}, PAGES={138--153} } @Article{rKRO79a, author = {R. A. Kronmal and A. V. Peterson}, title = {On the Alias Method for Generating Random Variables from Discrete a Distribution}, journal = {The American Statistician}, year = {1979}, volume = {33}, number = {4}, pages = {214--218}, OPTannote = {} } @Article{rKRO84a, author = {R. A. Kronmal and A. V. Peterson}, title = {An Acceptance-Complement Analogue of the Mixture-Plus-Acceptance-Rejection Method for Generating Random Variables}, journal = {{ACM} Transactions on Mathematical Software}, year = {1984}, volume = {10}, OPTnumber = {}, pages = {271--281}, OPTannote = {} } @book {rKUI74a, author = {L. Kuipers and H. Niederreiter}, title = {Uniform Distribution of Sequences}, publisher = {John Wiley}, year = {1974}, address = {New York, NY}} @article{rKUO02a, author = {F. Y. Kuo and S. Joe}, title = {Component-by-Component Construction of Good Lattice Rules with a Composite Number of Points}, journal = {Journal of Complexity}, volume = {18}, number = {4}, year = {2002}, pages = {943--976}, } @article{rKUO03a, author = {F. Y. Kuo}, title = {Component-by-component constructions achieve the optimal rate of convergence for multivariate integration in weighted {K}orobov and {S}obolev spaces}, journal = {Journal of Complexity}, volume = {19}, number = {3}, year = {2003}, pages = {301--320}, } @article{rKUO05a, author = {F. Y. Kuo and I. H. Sloan}, title = {Quasi-{M}onte {C}arlo methods can be efficient for integration over products of spheres}, journal = {Journal of Complexity}, volume = {21}, number = {2}, year = {2005}, pages = {196--210}, } @ARTICLE {rKUR91a, AUTHOR="Y. Kurita and M. Matsumoto", TITLE="Primitive $t$-nomials $(t=3,5)$ over $GF(2)$ whose Degree is a {M}ersenne Exponent $\le 44497$", JOURNAL={Mathematics of Computation}, VOLUME={56}, NUMBER={194}, YEAR={1991}, PAGES={817--821} } @ARTICLE {rLAG88a, AUTHOR="J. C. Lagarias and J. Reeds", TITLE="Unique Extrapolation of Polynomial Recurrences", JOURNAL={SIAM Journal on Computing}, VOLUME={17}, NUMBER={2}, YEAR={1988}, PAGES={342--362} } @ARTICLE {rLAG93a, AUTHOR="J. C. Lagarias", TITLE="Pseudorandom Numbers", JOURNAL={Statistical Science}, VOLUME={8}, NUMBER={1}, YEAR={1993}, PAGES={31--39} } @ARTICLE {rLAR94a, AUTHOR = {G. Larcher and C. Traunfellner}, TITLE = {The Numerical Integration of {W}alsh Series}, JOURNAL = {Mathematics of Computation}, VOLUME = {63}, PAGES = {277--291}, YEAR = { 1994}} @INPROCEEDINGS {rLAR95b, AUTHOR = {G. Larcher and W. C. Schmid}, TITLE = {Multivariate {W}alsh Series, Digital Nets and Quasi-{M}onte {C}arlo Integration}, BOOKTITLE = {{M}onte {C}arlo and Quasi-{M}onte {C}arlo Methods in Scientific Computing}, YEAR = {1995}, EDITOR = {H. Niederreiter and P. J.-S. Shiue}, VOLUME = {106}, SERIES = {Lecture Note in Statistics}, PAGES = {252--262}, PUBLISHER = {Springer-Verlag}, ADDRESS = {New York, NY} } @article {rLAR96a, AUTHOR = {Larcher, G. and Niederreiter, H. and Schmid, W. Ch.}, TITLE = {Digital nets and sequences constructed over finite rings and their application to quasi-{M}onte {C}arlo integration}, JOURNAL = {Monatshefte f\"ur Mathematik}, VOLUME = {121}, YEAR = {1996}, NUMBER = {3}, PAGES = {231--253}, ISSN = {0026-9255}, CODEN = {MNMTA2}, } @ARTICLE {rLAR96b, ex = {rLAR95a}, AUTHOR = {Larcher, G. and Lauss, A. and Niederreiter, H. and Schmid, W. Ch.}, TITLE = {Optimal polynomials for $(t,m,s)$-nets and numerical integration of multivariate {W}alsh series}, JOURNAL = {SIAM Journal on Numerical Analysis}, VOLUME = {33}, YEAR = {1996}, NUMBER = {6}, PAGES = {2239--2253}, ISSN = {0036-1429}, } @incollection {rLAR98a, AUTHOR ="G. Larcher", TITLE ="Digital Point Sets: Analysis and Applications", booktitle = {Random and Quasi-Random Point Sets}, editor = {P. Hellekalek and G. Larcher}, publisher = {Springer}, address = {New York, NY}, volume = {138}, pages = {167--222}, year = {1998}, ISBN = {ISBN is 0-387-98554-9}, series = {Lecture Notes in Statistics} } @incollection {rLAR98ax, AUTHOR ="G. Larcher", TITLE ="Digital Point Sets: Analysis and Applications", pages = {167--222}, crossref = {rHEL98s}, } @article{rLAR99a, AUTHOR = "G. Larcher and G. Pirsic", TITLE = "Base change Problems for Generalized {W}alsh series and Multivariate Numerical Integration", JOURNAL = "Pacific Journal of Mathematics", VOLUME = "189", PAGES = "75--105", YEAR = "1999"} @INPROCEEDINGS {rLEC86a, AUTHOR="P. L'Ecuyer", TITLE="Efficient and Portable 32-Bit Random Variate Generators", BOOKTITLE={Proceedings of the 1986 Winter Simulation Conference}, YEAR={1986}, PAGES={275--277} } @INPROCEEDINGS {rLEC87a, AUTHOR="P. L'Ecuyer", TITLE="A Portable Random Number Generator for 16-Bit Computers", BOOKTITLE={Modeling and Simulation on Microcomputers 1987}, ORGANIZATION={The Society for Computer Simulation}, YEAR={1987}, PAGES={45--49} } @ARTICLE {rLEC88a, AUTHOR="P. L'Ecuyer", TITLE="Efficient and Portable Combined Random Number Generators", JOURNAL={Communications of the ACM}, VOLUME={31}, NUMBER={6}, YEAR={1988}, NOTE={See also the correspondence in the same journal, 32, 8 (1989) 1019--1024}, PAGES={742--749 and 774} } @INPROCEEDINGS {rLEC88b, AUTHOR="P. L'Ecuyer and F. Blouin", TITLE="Linear Congruential Generators of Order $k>1$", BOOKTITLE={Proceedings of the 1988 Winter Simulation Conference}, PUBLISHER="{IEEE} Press", YEAR={1988}, PAGES={432--439} } @TECHREPORT {rLEC88c, AUTHOR="P. L'Ecuyer and F. Blouin", TITLE="Generalized Linear Congruential Generators", NUMBER={DIUL-RT-8814}, INSTITUTION={Compter Science Department, Laval University}, ADDRESS={Ste-Foy (Que.), Canada}, YEAR={1988}, NOTE={Also presented at ORSA/TIMS St-Louis, 1987} } @TECHREPORT {rLEC88e, AUTHOR="P. L'Ecuyer and F. Blouin", TITLE="BonGCL, un Lociciel pour la Recherche de Bons G\'{e}n\'{e}rateurs {\`a} Congruence Lin{\'e}aire", LANGUAGE={French}, NUMBER={DIUL-RT-8803}, INSTITUTION={Compter Science Department, Laval University}, ADDRESS={Ste-Foy (Que.), Canada}, YEAR={1988} } @INPROCEEDINGS {rLEC89a, AUTHOR="P. L'Ecuyer", TITLE="A Tutorial on Uniform Variate Generation", BOOKTITLE={Proceedings of the 1989 Winter Simulation Conference}, PUBLISHER="{IEEE} Press", MONTH={Dec}, YEAR={1989}, PAGES={40--49} } @INPROCEEDINGS {rLEC89b, AUTHOR="P. L'Ecuyer and R. Proulx", TITLE="About Polynomial-Time ``Unpredictable'' Generators", BOOKTITLE={Proceedings of the 1989 Winter Simulation Conference}, PUBLISHER="{IEEE} Press", MONTH={Dec}, YEAR={1989}, PAGES={467--476} } @ARTICLE {rLEC90a, AUTHOR="P. L'Ecuyer", TITLE="Random Numbers for Simulation", JOURNAL={Communications of the ACM}, VOLUME={33}, NUMBER={10}, YEAR={1990}, PAGES={85--97} } @ARTICLE {rLEC91a, AUTHOR="P. L'Ecuyer and S. C{\^o}t{\'e}", TITLE="Implementing a Random Number Package with Splitting Facilities", JOURNAL={ACM Transactions on Mathematical Software}, VOLUME={17}, NUMBER={1}, YEAR={1991}, PAGES={98--111} } @ARTICLE {rLEC91b, AUTHOR="P. L'Ecuyer and S. Tezuka", TITLE="Structural Properties for Two Classes of Combined Random Number Generators", JOURNAL={Mathematics of Computation}, VOLUME={57}, NUMBER={196}, YEAR={1991}, PAGES={735--746} } @INPROCEEDINGS {rLEC92a, AUTHOR="P. L'Ecuyer", TITLE="Testing Random Number Generators", BOOKTITLE={Proceedings of the 1992 Winter Simulation Conference}, PUBLISHER="{IEEE} Press", YEAR={1992}, MONTH={Dec}, PAGES={305--313} } @ARTICLE {rLEC93a, AUTHOR="P. L'Ecuyer and F. Blouin and R. Couture", TITLE="A Search for Good Multiple Recursive Random Number Generators", JOURNAL={ACM Transactions on Modeling and Computer Simulation}, VOLUME={3}, NUMBER={2}, PAGES={87--98}, YEAR={1993} } @ARTICLE {rLEC94a, AUTHOR="P. L'Ecuyer", TITLE="Uniform Random Number Generation", JOURNAL={Annals of Operations Research}, VOLUME={53}, PAGES={77--120}, YEAR={1994} } @INCOLLECTION {rLEC94b, AUTHOR="P. L'Ecuyer", TITLE={Random Number Generators}, BOOKTITLE={The Encyclopedia of Operations Research and Management Science}, EDITOR={S. I. Gass et C. M. Harris eds.}, PUBLISHER="Kluwer Academic Publishers", ADDRESS={New York, NY}, YEAR={1996}, PAGES = {571--578} } @ARTICLE {rLEC94c, AUTHOR="P. L'Ecuyer", TITLE="Combined Multiple Recursive Generators", JOURNAL={Operations Research}, VOLUME={44}, NUMBER ={5}, PAGES={816--822}, YEAR={1996} } @ARTICLE {rLEC94d, new = "rLEC97b", AUTHOR="P. L'Ecuyer", TITLE="Bad Lattice Structures for Vectors of Non-Successive Values Produced by Some Linear Recurrences", JOURNAL={INFORMS Journal on Computing}, VOLUME={9}, NUMBER ={1}, PAGES={57--60}, YEAR={1997} } @ARTICLE {rLEC94e, AUTHOR="P. L'Ecuyer and R. Couture", TITLE="An Implementation of the Lattice and Spectral Tests for Multiple Recursive Linear Random Number Generators", JOURNAL={INFORMS Journal on Computing}, VOLUME={9}, NUMBER={2}, PAGES={206--217}, YEAR={1997} } @TECHREPORT {rLEC94f, AUTHOR="P. L'Ecuyer and R. Couture", TITLE="Lat{MRG} User's Guide, a Toolkit for Theoretical Testing of Linear Congruential and Multiple Recursive Generators", NOTE={In preparation}, xNUMBER={}, xINSTITUTION={GERAD, University of Montreal}, ADDRESS={Montreal, Canada}, YEAR={1996} } @UNPUBLISHED {rLEC95d, AUTHOR="P. L'Ecuyer", TITLE="Evaluation Report of AECL-10983/COG-93-423: Algorithms for Pseudorandom Numbers Generators", YEAR={1995}, MONTH={March} } @ARTICLE {rLEC96a, old="rLEC94g", AUTHOR="P. L'Ecuyer", TITLE="Maximally Equidistributed Combined {T}ausworthe Generators", JOURNAL="Mathematics of Computation", VOLUME={65}, NUMBER={213}, YEAR={1996}, PAGES={203--213} } @ARTICLE {rLEC96b, old="rLEC94c", AUTHOR="P. L'Ecuyer", TITLE="Combined Multiple Recursive Random Number Generators", JOURNAL={Operations Research}, VOLUME={44}, NUMBER ={5}, PAGES={816--822}, YEAR={1996} } @ARTICLE {rLEC96c, AUTHOR="C. L{\'e}cot", TITLE="Error Bounds for Quasi-{M}onte {C}arlo Integration with Nets", JOURNAL="Mathematics of Computation", VOLUME={65}, NUMBER={213}, YEAR={1996}, PAGES={179--187} } @UNPUBLISHED {rLEC96e, AUTHOR="P. L'Ecuyer and A. Compagner and J.-F. Cordeau", TITLE="Entropy Tests for Random Number Generators", JOURNALx={}, VOLUMEx={}, PAGESx={}, NOTE={Manuscript}, YEAR={1996} } @article {rLEC96f, AUTHOR="P. L'Ecuyer", TITLE="Tests Based on Sum-Functions of Spacings for Uniform Random Numbers", JOURNAL={Journal of Statistical Computation and Simulation}, VOLUME={59}, PAGES={251--269}, YEAR={1997} } @INPROCEEDINGS {rLEC96g, AUTHOR="P. L'Ecuyer and J.-F. Cordeau", TITLE="Tests sur les Points Rapproch\'es pour les G\'en\'erateurs de Valeurs Al\'eatoires", BOOKTITLE={Compte-Rendus de ASU'96: Les XXVIII-i\`emes Journ\'ees de Statistique}, LANGUAGE={French}, YEAR={1996}, PAGES={479--482}, ADDRESS={D\'epartement de Math\'ematiques, Universit\'e Laval} } @INCOLLECTION {rLEC96h, AUTHOR="P. L'Ecuyer", TITLE={Random Number Generators}, BOOKTITLE={The Encyclopedia of Operations Research and Management Science}, EDITOR={S. I. Gass et C. M. Harris eds.}, PUBLISHER="Kluwer Academic Publishers", ADDRESS={New York, NY}, YEAR={1996}, PAGES = {571--578} } @article {rLEC96i, new = "rLEC97d", AUTHOR="P. L'Ecuyer and T. H. Andres", TITLE="A Random Number Generator Based on the Combination of Four {LCGs}", JOURNAL={Mathematics and Computers in Simulation}, VOLUME={44}, PAGES={99--107}, YEAR={1997} } @UNPUBLISHED {rLEC96s, AUTHOR="P. L'Ecuyer", TITLE="Test{U}01: Un logiciel pour appliquer des tests statistiques \`a des g\'en\'erateurs de valeurs al\'eatoires", LANGUAGE={French}, JOURNALx={}, VOLUMEx={}, PAGESx={}, YEAR={Circa 2000}, NOTE={In preparation} } @ARTICLE {rLEC97b, old = {rLEC94d}, AUTHOR="P. L'Ecuyer", TITLE="Bad Lattice Structures for Vectors of Non-Successive Values Produced by Some Linear Recurrences", JOURNAL={INFORMS Journal on Computing}, VOLUME={9}, NUMBER ={1}, PAGES={57--60}, YEAR={1997} } @ARTICLE {rLEC97c, old="rLEC94e", AUTHOR="P. L'Ecuyer and R. Couture", TITLE="An Implementation of the Lattice and Spectral Tests for Multiple Recursive Linear Random Number Generators", JOURNAL={INFORMS Journal on Computing}, VOLUME={9}, NUMBER={2}, PAGES={206--217}, YEAR={1997} } @article {rLEC97d, old = "rLEC96i", AUTHOR="P. L'Ecuyer and T. H. Andres", TITLE="A Random Number Generator Based on the Combination of Four {LCG}s", JOURNAL={Mathematics and Computers in Simulation}, VOLUME={44}, PAGES={99--107}, YEAR={1997}, NOTExx={Manuscript (A longer version of the present paper)} } @INCOLLECTION {rLEC97e, AUTHOR="P. L'Ecuyer", TITLE={Uniform Random Number Generation}, BOOKTITLE={Encyclopedia of Computer Science and Technology}, volume = {39}, EDITOR={A. Kent and J. G. Williams}, PUBLISHER="Marcel Dekker", address = {New York, NY}, pages = {323--339}, YEAR={1998} } @article {rLEC97h, ex = {rLEC96f}, AUTHOR="P. L'Ecuyer", TITLE="Tests Based on Sum-Functions of Spacings for Uniform Random Numbers", JOURNAL={Journal of Statistical Computation and Simulation}, VOLUME={59}, PAGES={251--269}, YEAR={1997} } @INPROCEEDINGS {rLEC97i, AUTHOR="P. L'Ecuyer", TITLE="Uniform Random Number Generators: A Review", BOOKTITLE={Proceedings of the 1997 Winter Simulation Conference}, PUBLISHER="{IEEE} Press", MONTH={Dec}, YEAR={1997}, PAGES={127--134} } @INCOLLECTION {rLEC98a, ex = {rLEC97a}, AUTHOR="P. L'Ecuyer", TITLE={Random Number Generation}, BOOKTITLE={Handbook of Simulation}, EDITOR={Jerry Banks}, PUBLISHER="Wiley", PAGES = {93--137}, NOTE={chapter 4}, ISBN = {0-471-13403-1}, Price = {\$125. US}, YEAR={1998} } @UNPUBLISHED {rLEC98b, paper = {rLEC97f}, AUTHOR="P. L'Ecuyer", TITLE="Good Parameters and Implementations for Combined Multiple Recursive Random Number Generators", YEAR={1999}, NOTE={Available as file {\tt combmrg2.ps} at URL {\tt www.iro.umontreal.ca/$\sim$lecuyer}. The C code is in file {\tt combmrg2.c}} } @INPROCEEDINGS {rLEC98c, AUTHOR="P. L'Ecuyer", TITLE="Uniform Random Number Generators", BOOKTITLE={Proceedings of the 1998 Winter Simulation Conference}, PUBLISHER="{IEEE} Press", YEAR={1998}, xNOTE={good short survey}, PAGES={97--104} } @incollection {rLEC98h, old = "rLEC99h", AUTHOR ="P. L'Ecuyer and P. Hellekalek", TITLE ="Random Number Generators: Selection Criteria and Testing", booktitle = {Random and Quasi-Random Point Sets}, editor = {P. Hellekalek and G. Larcher}, publisher = {Springer-Verlag}, address = {New York, NY}, volume = {138}, pages = {223--265}, year = {1998}, ISBN = {ISBN is 0-387-98554-9}, series = {Lecture Notes in Statistics} } @INCOLLECTION {rLEC98t, old = "rLEC97s", AUTHOR ="P. L'Ecuyer", TITLE ="Random Number Generators and Empirical Tests", booktitle = {{M}onte {C}arlo and Quasi-{M}onte {C}arlo Methods 1996}, editor = {P. Hellekalek and G. Larcher and H. Niederreiter and P. Zinterhof}, publisher = {Springer-Verlag}, address = {New York, NY}, volume = {127}, pages = {124--138}, year = {1998}, series = {Lecture Notes in Statistics} } @article {rLEC99a, old = "rLEC97g", AUTHOR="P. L'Ecuyer", TITLE="Tables of Maximally Equidistributed Combined {LFSR} Generators", JOURNAL={Mathematics of Computation}, VOLUME={68}, NUMBER={225}, PAGES={261--269}, YEAR={1999} } @article {rLEC99b, old = "rLEC97f", AUTHOR="P. L'Ecuyer", TITLE="Good Parameters and Implementations for Combined Multiple Recursive Random Number Generators", JOURNAL={Operations Research}, VOLUME={47}, NUMBER={1}, PAGES={159--164}, YEAR={1999} } @ARTICLE {rLEC99c, old = "rLEC97l", AUTHOR="P. L'Ecuyer", TITLE="Tables of Linear Congruential Generators of Different Sizes and Good Lattice Structure", JOURNAL="Mathematics of Computation", VOLUME={68}, NUMBER={225}, PAGES={249--260}, YEAR={1999} } @article {rLEC99e, AUTHOR="P. L'Ecuyer and R. Simard", TITLE="Beware of Linear Congruential Generators with Multipliers of the Form $a = \pm 2^q\pm 2^r$", JOURNAL={{ACM} Transactions on Mathematical Software}, VOLUME={25}, NUMBER={3}, PAGES={367--374}, YEAR={1999}, } @InProceedings{rLEC99w, author = {P. L'Ecuyer}, title = {Some Recommendable Uniform Random Number Generators}, booktitle = {Proceedings of the 1999 European Simulation Multiconference}, pages = {185--190}, year = {1999}, volume = {1}, organization = {The Society for Computer Simulation}, address = {Ghent, Belgium}, OPTannote = {} } @INPROCEEDINGS {rLEC00a, AUTHOR="P. L'Ecuyer and F. Panneton", TITLE={A New Class of Linear Feedback Shift Register Generators}, BOOKTITLE={Proceedings of the 2000 Winter Simulation Conference}, editor = {J. A. Joines and R. R. Barton and K. Kang and P. A. Fishwick}, PUBLISHER="{IEEE} Press", ADDRESS= {Pistacaway, NJ}, YEAR={2000}, PAGES={690--696} } @INPROCEEDINGS {rLEC00b, AUTHOR="P. L'Ecuyer and R. Touzin", TITLE={Fast Combined Multiple Recursive Generators with Multipliers of the Form $a = \pm 2^q \pm 2^r$}, BOOKTITLE={Proceedings of the 2000 Winter Simulation Conference}, editor = {J. A. Joines and R. R. Barton and K. Kang and P. A. Fishwick}, PUBLISHER="{IEEE} Press", ADDRESS= {Pistacaway, NJ}, YEAR={2000}, PAGES={683--689} } @ARTICLE {rLEC00c, old = {rLEC96d}, AUTHOR="P. L'Ecuyer and J.-F. Cordeau and R. Simard", TITLE="Close-Point Spatial Tests and their Application to Random Number Generators", JOURNAL={Operations Research}, VOLUME={48}, number={2}, PAGES={308--317}, YEAR={2000} } @article {rLEC01a, old = {rLEC99d}, old = {rLEC00d}, AUTHOR="P. L'Ecuyer and R. Simard", TITLE="On the Performance of Birthday Spacings Tests for Certain Families of Random Number Generators", JOURNAL={Mathematics and Computers in Simulation}, VOLUME={55}, number ={1--3}, PAGES={131--137}, YEAR={2001} } @INPROCEEDINGS {rLEC01d, AUTHOR="P. L'Ecuyer", TITLE={Software for Uniform Random Number Generation: Distinguishing the Good and the Bad}, BOOKTITLE={Proceedings of the 2001 Winter Simulation Conference}, OPTeditor = {}, PUBLISHER="{IEEE} Press", ADDRESS= {Pistacaway, NJ}, YEAR={2001}, PAGES={95--105} } @article {rLEC01s, AUTHOR="P. L'Ecuyer and R. Simard and E. J. Chen and W. D. Kelton", TITLE="An Object-Oriented Random-Number Package with Many Long Streams and Substreams", JOURNAL={Operations Research}, VOLUME={50}, NUMBER={6}, PAGES={1073--1075}, YEAR={2002} } @Misc{rLEC01t, author = {P. L'Ecuyer and R. Simard}, title = {TestU01: Un logiciel pour appliquer des tests statistiques \`a des g\'en\'erateurs de valeurs al\'eatoires}, year = {2001}, note = {Unpublished software user's guide}, language = {french}, OPTannote = {} } @article {rLEC02a, old = {rLEC01s}, AUTHOR="P. L'Ecuyer and R. Simard and E. J. Chen and W. D. Kelton", TITLE="An Object-Oriented Random-Number Package with Many Long Streams and Substreams", JOURNAL={Operations Research}, VOLUME={50}, NUMBER={6}, PAGES={1073--1075}, YEAR={2002} } @incollection {rLEC02b, old = {rLEC01b}, AUTHOR="P. L'Ecuyer and F. Panneton", TITLE={Construction of Equidistributed Generators Based on Linear Recurrences Modulo 2}, booktitle = {{M}onte {C}arlo and Quasi-{M}onte {C}arlo Methods 2000}, editor = {K.-T. Fang and F. J. Hickernell and H. Niederreiter}, address = {Berlin}, publisher = {Springer-Verlag}, pages = {318--330}, year = {2002}, } @article {rLEC02c, old = {rLEC98s}, AUTHOR="P. L'Ecuyer and R. Simard and S. Wegenkittl", TITLE="Sparse Serial Tests of Uniformity for Random Number Generators", JOURNAL={{SIAM} Journal on Scientific Computing}, VOLUME={24}, NUMBER = {2}, PAGES={652--668}, YEAR={2002} } @INCOLLECTION {rLEC03a, AUTHOR="P. L'Ecuyer", TITLE={Random Number Generation and Quasi-{M}onte {C}arlo}, BOOKTITLE={Encyclopedia of Actuarial Science}, EDITOR={J. Teugels and B. Sundt}, PUBLISHER={John Wiley}, ADDRESS={Chichester, UK}, YEAR={2003}, note = {to appear}, xPAGES = {} } @article{rLEC03b, new = {rLEC04a}, author = {P. L'Ecuyer and R. Touzin}, title = {On the {D}eng-{L}in Random Number Generators and Related Methods}, journal = {Statistics and Computing}, volume = {14}, pages = {5--9}, year = {2004}, } @article {rLEC03c, old = {rLEC01c}, AUTHOR="P. L'Ecuyer and J. Granger-Pich\'e", TITLE="Combined Generators with Components from Different Families", JOURNAL={Mathematics and Computers in Simulation}, VOLUME={62}, PAGES={395--404}, YEAR={2003}, } @UNPUBLISHED {rLEC03d, AUTHOR="P. L'Ecuyer and R. Simard", TITLE="Test{U}01: A Software Library in {ANSI C} for Empirical Testing of Random Number Generators", JOURNALx={}, VOLUMEx={}, PAGESx={}, YEAR={2003}, NOTE={See \url{http://www.iro.umontreal.ca/~lecuyer}} } @article{rLEC04a, author = {P. L'Ecuyer and R. Touzin}, title = {On the {D}eng-{L}in Random Number Generators and Related Methods}, journal = {Statistics and Computing}, volume = {14}, pages = {5--9}, year = {2004}, OPTannote = {} } @INCOLLECTION {rLEC04b, AUTHOR="P. L'Ecuyer", TITLE={Random Number Generation}, BOOKTITLE={Handbook of Computational Statistics}, EDITOR={J. E. Gentle and W. Haerdle and Y. Mori}, PUBLISHER={Springer-Verlag}, ADDRESS={Berlin}, YEAR={2004}, note = {Chapter II.2}, PAGES = {35--70} } @INCOLLECTION {rLEC04d, AUTHOR="P. L'Ecuyer", TITLE={Random Number Generation and Quasi-{M}onte {C}arlo}, BOOKTITLE={Encyclopedia of Actuarial Science}, EDITOR={J. L. Teugels and B. Sundt}, PUBLISHER={Wiley}, ADDRESS={Chichester}, YEAR={2004}, volume={3}, OPTnote = {}, PAGES = {1363--1369}, ISBN = {0-470-84676-3}, } @InProceedings{rLEC05a, author = {P. L'Ecuyer and F. Panneton}, title = {Fast Random Number Generators Based on Linear Recurrences Modulo 2: Overview and Comparison}, BOOKTITLE = "Proceedings of the 2005 Winter Simulation Conference", publisher = {{IEEE} Press}, YEAR = {2005}, PAGES = {110--119}, } @article{rLEC06a, old = {rLEC04c}, author = {P. L'Ecuyer and R. Simard}, title = {Inverting the Symmetrical Beta Distribution}, journal = {{ACM} Transactions on Mathematical Software}, volume = {32}, number = {4}, pages = {509--520}, year = {2006}, } @INCOLLECTION {rLEC06h, old = {rLEC04h}, AUTHOR = {P. L'Ecuyer}, TITLE={Uniform Random Number Generation}, BOOKTITLE={Simulation}, series={Handbooks in Operations Research and Management Science}, EDITOR={S. G. Henderson and B. L. Nelson}, PUBLISHER={Elsevier}, ADDRESS={Amsterdam, The Netherlands}, YEAR={2006}, note = {Chapter 3}, PAGES = {55--81} } @incollection{rLEC07a, author = {P. L'Ecuyer and F. Panneton}, title = {${{\bf F}}_2$-Linear Random Number Generators}, booktitle={Advancing the Frontiers of Simulation: A Festschrift in Honor of George Samuel Fishman}, EDITOR={C. Alexopoulos and D. Goldsman and J. R. Wilson}, PUBLISHER={Springer-Verlag}, ADDRESS={New York}, YEAR={2009}, OPTnote = {To appear}, PAGES = {169--193} } @article{rLEC07b, OLD = {rLEC06b}, author = {P. L'Ecuyer and R. Simard}, title = {{TestU01}: A {C} Library for Empirical Testing of Random Number Generators}, journal = {{ACM} Transactions on Mathematical Software}, volume = {33}, number = {4}, pages = {Article 22}, month = {August}, year = {2007}, OPTdoi = {http://doi.acm.org/10.1145/1268776.1268777}, publisher = {ACM Press}, address = {New York, NY, USA}, OPTnote = {available at \url{http://www.iro.umontreal.ca/~simardr/testu01/tu01.html}}, } @INCOLLECTION {rLEC08a, AUTHOR = {P. L'Ecuyer}, TITLE={Pseudorandom Number Generators}, BOOKTITLE={Simulation Methods in Financial Engineering}, series={Encyclopedia of Quantitative Finance}, EDITOR={Eckhart Platen and Peter Jaeckel}, PUBLISHER={Wiley}, xADDRESS={}, YEAR={2009}, note = {Forthcoming}, xPAGES = {} } @incollection{rLEC09a, old = {rLEC07a}, author = {P. L'Ecuyer and F. Panneton}, title = {${{\bf F}}_2$-Linear Random Number Generators}, booktitle={Advancing the Frontiers of Simulation: A Festschrift in Honor of George Samuel Fishman}, EDITOR={C. Alexopoulos and D. Goldsman and J. R. Wilson}, PUBLISHER={Springer-Verlag}, ADDRESS={New York}, YEAR={2009}, PAGES = {169--193} } @book{rLEC09m, editor = {P. L'Ecuyer and A. B. Owen}, title = {{M}onte {C}arlo and Quasi-{M}onte {C}arlo Methods 2008}, publisher = {Springer-Verlag}, address = {Berlin}, year = {2009} } @inproceedings{rLEE94a, author = {H. Leeb}, editor = {Vajter\v{s}ic, M. and Zinterhof, P.}, title = {{\sc pLab} -- a system for testing random numbers}, booktitle = {Proceedings of the International Workshop Parallel Numerics'94, Smolenice, Sept. 19--21}, publisher = {Slovak Academy of Sciences, Institute for Informatics}, address = {Slovakia}, year = {1994}, pages = {89--99}} @inproceedings{rLEE94b, author = {H. Leeb}, editor = {Hellekalek, P. and Larcher, G. and Zinterhof, P.}, title = {On the digit test}, booktitle = {Proceedings of the 1st Salzburg Minisymposium on Pseudorandom Number Generation and Quasi-{M}onte {C}arlo Methods, Salzburg, Nov. 1994}, volume = {ACPC/TR 95-4}, series = {Technical Report Series}, publisher = {ACPC -- Austrian Center for Parallel Computation, University of Vienna, Austria}, year = {1995}, pages = {109--121}} @mastersthesis{rLEE95a, author = {H. Leeb}, title = {Random Numbers for Computer Simulation}, school = {University of Salzburg}, year = {1995} } @unpublished {rLEE95b, author = {Leeb, H.}, title = {Selected random number generators in the digit test}, note = {Preprint, Mathematics Institute, University of Salzburg}, year = {1995} } @ARTICLE {rLEE97a, AUTHOR="H. Leeb and S. Wegenkittl", TITLE="Inversive and Linear Congruential Pseudorandom Number Generators in Empirical Tests", JOURNAL={ACM Transactions on Modeling and Computer Simulation}, VOLUME={7}, NUMBER={2}, PAGES={272--286}, YEAR={1997} } @phdthesis {rLEE97b, author = {H. Leeb}, title = {Stochastic Properties of Diaphony}, year = {1997}, school = {Department of Mathematics, University of Salzburg}, address = {Austria}, month = {November}, abstract = {} } @INcollection {rLEE98c, old = {rLEE97c}, author = {H. Leeb}, title = {Weak Limits for Diaphony}, booktitle = {{M}onte {C}arlo and Quasi-{M}onte {C}arlo Methods 1996}, editor = {P. Hellekalek and G. Larcher and H. Niederreiter and P. Zinterhof}, publisher = {Springer-Verlag}, address = {New York, NY}, volume = {127}, pages = {330--339}, year = {1998}, series = {Lecture Notes in Statistics} } @UNPUBLISHED {rLEE98a, author = {Leeb, H. and Hellekalek, P.}, year = {1998}, title = {Strong and Weak Laws for the Spectral Test and Related Quantities}, note = {Submitted}, keywords = {spectral test extension, diaphony, asymptotic distribution}, abstract = {asymptotic distribution of diaphony and the spectral test} } @ARTICLE {rLEH51a, AUTHOR="D. H. Lehmer", TITLE="Mathematical Methods in Large Scale Computing Units", JOURNAL={Annals Comp. Laboratory Harvard University}, YEAR={1951}, VOLUME={26}, PAGES={141--146} } @INPROCEEDINGS {rLEH51b, AUTHOR="D. H. Lehmer", TITLE=" ", BOOKTITLE={Second Harvard Symposium on Large Scale Automatic Computing Machinery}, YEAR={1951}, PAGES={45} } @UNPUBLISHED {rLEM01a, author = {C. Lemieux and M. Cieslak and K. Luttmer}, title = {Rand{QMC} User's Guide}, institution = {University of Calgary}, note = {In preparation}, year = {2001}} @ARTICLE {rLEV44a, AUTHOR="H. Levene and J. Wolfowitz", TITLE="The covariance matrix of runs up and down", JOURNAL={The Annals of mathematical statistics}, VOLUME={15}, YEAR={1944}, PAGES={58--69} } @ARTICLE {rLEV87a, AUTHOR="L. A. Levin", TITLE="One-Way Functions and Pseudorandom Generators", JOURNAL={Combinarica}, VOLUME={7}, NUMBER={4}, YEAR={1987}, PAGES={357--363} } @article {rLEV95a, author = {V. F. Lev}, title = {On two versions of $L^2$-discrepancy and geometrical interpretation of diaphony}, journal = {Acta Math. Hungar.}, year = {1995}, volume = {69}, number = {4}, pages = {281--300} } @ARTICLE {rLEW69a, AUTHOR="P. A. W. Lewis and A. S. Goodman and J. M. Miller", TITLE="A Pseudo-random Number Generator for the System/360", JOURNAL={{IBM} System's Journal}, VOLUME={8}, YEAR={1969}, PAGES={136--143}, annote = {The 16807 multiplier} } @ARTICLE {rLEW73a, AUTHOR="T. G. Lewis and W. H. Payne", TITLE="Generalized Feedback Shift Register Pseudorandom Number Algorithm", JOURNAL={Journal of the ACM}, VOLUME={20}, NUMBER={3}, YEAR={1973}, PAGES={456--468} } @ARTICLE {rLEY00a, AUTHOR="J. Leydold", TITLE="Automatic Sampling with the Ratio-of-Uniform Method", JOURNAL={ACM Transactions on Mathematical Software}, VOLUME={26}, NUMBER={1}, PAGES={78--98}, YEAR={2000} } @inproceedings {rLEY02a, AUTHOR={J. Leydold and E. Janka and W. H\"ormann}, TITLE={Variants of Transformed Density Rejection and Correlation Induction}, booktitle = {{M}onte {C}arlo and Quasi-{M}onte {C}arlo Methods 2000}, pages = {345--356}, year = {2002}, editor = {K.-T. Fang and F. J. Hickernell and H. Niederreiter}, address = {Berlin}, publisher = {Springer-Verlag}, annote = {non-uniform, acceptance/rejection, hat function, squeeze}, } @Book{rLI93a, author = {M. Li and P. M. B. Vit\'anyi}, title = {An Introduction to {K}olmogorov Complexity and its Applications}, publisher = {Springer-Verlag}, year = {1993} } @Book{rLI97a, author = {M. Li and P. M. B. Vit\'anyi}, title = {An Introduction to {K}olmogorov Complexity and its Applications}, publisher = {Springer-Verlag}, edition = {Second}, year = {1997} } @article{rLIA00a, AUTHOR="J. J. Liang and K. T. Fang and F. J. Hickernell and R. Li", TITLE="Testing multivariate uniformity and its applications", JOURNAL={Mathematics of Computation}, VOLUME={70}, number ={233}, PAGES={337--355}, YEAR={2000} } @article {rLIA01a, AUTHOR="Y. Liang and P. A. Whitlock", TITLE="A new empirical test for parallel Pseudo-Random Number Generators", JOURNAL={Mathematics and Computers in Simulation}, VOLUME={55}, number ={1--3}, PAGES={149--158}, YEAR={2001} } @ARTICLE {rLIN68a, AUTHOR="J. H. Lindholm", TITLE="An Analysis of the Pseudo-Randomness Properties of Subsequences of Long $m$-Sequences", JOURNAL={{IEEE} Transactions on Information Theory}, VOLUME={IT-14}, NUMBER={4}, YEAR={1968}, PAGES={569--576} } @Article{rLOV66a, author = {D. Loveland}, title = {A New Interpretation of the {V}on {M}ises Concept of Random Sequence}, journal = {Zeitschrift f\"ur Mathematische Logik und Grundlagen der Mathematik}, year = {1966}, volume = {12}, pages = {279--294} } @ARTICLE {rLUB88a, AUTHOR="M. Luby and C. Rackoff", TITLE="How to Construct Pseudorandom Permutations From Pseudorandom Functions", JOURNAL={SIAM J. Computing}, VOLUME={17}, NUMBER={2}, YEAR={1988}, PAGES={373--386} } @BOOK {rLUB96a, old={rLUB93a}, AUTHOR="M. Luby", TITLE={Pseudorandomness and Cryptographic Applications}, PUBLISHER="Princeton University Press", ADDRESS = "Princeton", YEAR={1996} } @ARTICLE {rLUS94a, AUTHOR={M. L{\"u}scher}, TITLE="A Portable High-Quality Random Number Generator for Lattice Field Theory Simulations", INSTITUTIONxx={Deutsches Elektronen-Synchrotron DESY, Hamburg}, JOURNAL={Computer Physics Communications}, VOLUME={79}, YEAR={1994}, PAGES={100--110} } @ARTICLE {rMAC65a, AUTHOR="N. M. MacLaren and G. Marsaglia", TITLE="Uniform Random Number Generators", JOURNAL={Journal of the ACM}, VOLUME={12}, YEAR={1965}, PAGES={83--89} } @ARTICLE{rMAC89a, author = {N. M. MacLaren}, title = {The Generation of Multiple Independent Sequences of Pseudorandom Numbers}, journal = {Applied Statistics}, volume = {38}, pages = {351--359}, year = {1989} } @ARTICLE {rMAC92a, AUTHOR="N. M. MacLaren", TITLE="A Limit on the Usable Length of a Pseudorandom Sequence", JOURNAL={Journal of Statistical Computing and Simulation}, VOLUME={42}, YEAR={1992}, PAGES={47--54} } @ARTICLE {rMAD72a, AUTHOR="R. S. Maddocks and S. Matthews and C. H. Vincent and E. W. Walker", TITLE="A Compact and Accurate Generator for Truly Random Binary Digits", JOURNAL={Journal of Physics E}, YEAR={1972}, VOLUME={5}, NUMBER={6}, PAGES={542--544} } @TECHREPORT {rMAH93a, author = "W. E. Mahoney and P. D. Coddington", title = "Evaluating Parallel Random Number Generators", journal="Journal of Undergraduate Research in High-Performance Computing", volume = "3", year = "1993", editor = {E. A. Bogucz and V. E. Weinman}, note={Available at \url{http://www.npac.syr.edu/REU/reu93/abs93.html#mahoney}}, institution={Northeast Parallel Architectures Center at Syracuse University} } @InCollection{rMAI72a, author = {D. Maisonneuve}, title = {Recherche et Utilisation des ``Bons Treillis'', Programmation et R\'esultats Num\'eriques}, booktitle = {Applications of Number Theory to Numerical Analysis}, pages = {121--201}, publisher = {Academic Press}, year = {1972}, editor = {S. K. Zaremba}, address = {New York, NY}, OPTannote = {} } @techreport{rMAR62a, AUTHOR="G. Marsaglia", TITLE="Improving the Polar Method for Generating a Pair of Random Variables", institution="Boeing Scientific Research Laboratory", YEAR={1962}, ADDRESS={Seattle, Washington} } @Article{rMAR66a, author = {P. Martin-L\"of}, title = {The Definition of Random Sequences}, journal = {Information and Control}, year = {1966}, volume = {9}, pages = {602--619}, } @Article{rMAR66b, author = {P. Martin-L\"of}, title = {On the Concept of a Random Sequence}, journal = {Theory of Probability and its Applications}, year = {1966}, volume = {11}, pages = {177--179}, } @ARTICLE {rMAR68a, AUTHOR="G. Marsaglia", TITLE="Random Numbers Fall Mainly in the Planes", JOURNAL={Proceedings of the National Academy of Sciences of the United States of America}, VOLUME={60}, YEAR={1968}, PAGES={25--28} } @Article{rMAR69a, author = {P. Martin-L\"of}, title = {Algorithms and Randomness}, journal = {Rev. Int. Statist. Inst.}, year = {1969}, volume = {37}, pages = {265--272}, } @Article{rMAR71a, author = {P. Martin-L\"of}, title = {Complexity Oscillations in Infinite Binary Sequences}, journal = {Zeitschrift f\"ur Wahrscheinlichkeitstheorie verw. Gebiete}, year = {1971}, volume = {19}, pages = {225--230} } @INPROCEEDINGS{rMAR72a, AUTHOR="G. Marsaglia", TITLE="The structure of linear congruential sequences", editor = {S. K. Zaremba}, publisher = {Academic Press}, BOOKTITLE={Applications of Number Theory to Numerical Analysis}, PAGES={249--285}, ADDRESS={London}, YEAR={1972} } @TECHREPORT {rMAR73a, AUTHOR="G. Marsaglia and K. Ananthanarayanan and N. Paul", TITLE="How to use the {M}c{G}ill {R}andom {N}umber {P}ackage ``{SUPER-DUPER}''", INSTITUTION="School of Computer Science, McGill University", ADDRESS={Montreal, Canada}, YEAR={1973} } @Article{rMAR75a, author = {Per Martin-L\"of}, title = {Reply to {S}verdrup's Polemical Article ``Tests Without Power''}, journal = {Scandinavian Journal of Statistics}, year = {1975}, volume = {2}, pages = {161--165} } @ARTICLE {rMAR83a, AUTHOR="K. Marse and S. D. Roberts", TITLE="Implementing a Portable {FORTRAN} Uniform (0,1) Generator", JOURNAL={Simulation}, VOLUME={41}, NUMBER={4}, YEAR={1983}, PAGES={135--139} } @INPROCEEDINGS {rMAR85a, AUTHOR="G. Marsaglia", TITLE="A Current View of Random Number Generators", BOOKTITLE={Computer Science and Statistics, Sixteenth Symposium on the Interface}, PUBLISHER={Elsevier Science Publishers}, YEAR={1985}, PAGES={3--10}, ADDRESS={North-Holland, Amsterdam} } @ARTICLE {rMAR85b, AUTHOR="G. Marsaglia and L.-H. Tsay", TITLE="Matrices and the Structure of Random Number Sequences", JOURNAL={Linear Algebra and its Applications}, VOLUME={67}, YEAR={1985}, PAGES={147--156} } @ARTICLE {rMAR85c, AUTHOR="G. Marsaglia", TITLE="Note on a Proposed Test for Random Number Generators", JOURNAL={{IEEE} Transactions on Computers}, VOLUME={C-34}, NUMBER={8}, YEAR={1985}, PAGES={756--758} } @ARTICLE {rMAR90a, AUTHOR="G. Marsaglia and B. Narasimhan and A. Zaman", TITLE="A Random Number Generator for {PC}'s", JOURNAL={Computer Physics Communications}, VOLUME={60}, YEAR={1990}, PAGES={345--349} } @ARTICLE {rMAR90b, AUTHOR="G. Marsaglia and A. Zaman and W. W. Tsang", TITLE="Towards a Universal Random Number Generator", JOURNAL={Statistics and Probability Letters}, VOLUME={8}, YEAR={1990}, PAGES={35--39} } @ARTICLE {rMAR91a, AUTHOR="G. Marsaglia and A. Zaman", TITLE="A New Class of Random Number Generators", JOURNAL={The Annals of Applied Probability}, VOLUME={1}, YEAR={1991}, PAGES={462--480} } @ARTICLE {rMAR93a, AUTHOR="G. Marsaglia", TITLE="Remarks on Choosing and Implementing Random Number Generators", JOURNAL={Communications of the ACM}, VOLUME={36}, NUMBER={7}, YEAR={1993}, PAGES={105--110} } @ARTICLE {rMAR93b, AUTHOR="G. Marsaglia and A. Zaman", TITLE="Monkey Tests for Random Number Generators", JOURNAL={Computers Math. Applic.}, VOLUME={26}, NUMBER={9}, YEAR={1993}, PAGES={1--10} } @TECHREPORT {rMAR93c, AUTHOR="G. Marsaglia and A. Zaman", TITLE="The {KISS} Generator", INSTITUTION="Department of Statistics, University of Florida", xNUMBER={}, xDATE={FEB-28}, YEAR={1993} } @UNPUBLISHED {rMAR94a, AUTHOR="G. Marsaglia", TITLE="Yet Another RNG", YEAR={1994}, NOTE={Posted to the electronic billboard {\tt sci.stat.math}, August~1} } @ARTICLE {rMAR94b, AUTHOR="G. Marsaglia and A. Zaman and J. C. W. Marsaglia", TITLE="Rapid Evaluation of the Inverse Normal Distribution Function", JOURNAL={Statistics and Probability Letters}, VOLUME={19}, YEAR={1994}, PAGES={259--266} } @UNPUBLISHED {rMAR96a, AUTHOR="G. Marsaglia", TITLE="The {M}arsaglia Random Number {CDROM} including the {DIEHARD} Battery of Tests of Randomness", YEAR={1996}, NOTE={See \url{http://www.stat.fsu.edu/pub/diehard}} } @UNPUBLISHED {rMAR96b, AUTHOR="G. Marsaglia", TITLE="{DIEHARD:} A Battery of Tests of Randomness", YEAR={1996}, NOTE={See \url{http://www.stat.fsu.edu/pub/diehard}} } @UNPUBLISHED {rMAR97a, AUTHOR="G. Marsaglia", TITLE="A Random Number Generator for {C}", YEAR={1997}, MONTH={September 30}, NOTE={Posted to the electronic billboard \url{sci.math.num-analysis}} } @ARTICLE {rMAR98a, AUTHOR="G. Marsaglia and W. W. Tsang", TITLE="The {M}onty {P}ython Method for Generating Random Variables", JOURNAL={{ACM} Transactions on Mathematical Software}, VOLUME={24}, YEAR={1998}, PAGES={341--350} } @UNPUBLISHED {rMAR99a, AUTHOR="G. Marsaglia", TITLE="Random Numbers for {C}: The {END}?", YEAR={1999}, MONTH={January 20}, NOTE={Posted to the electronic billboard \url{sci.crypt.random-numbers}} } @UNPUBLISHED {rMAR02a, AUTHOR="G. Marsaglia", TITLE="Good 64-bit {RNG}'s", YEAR={2002}, MONTH={August 25}, NOTE={Posted to the electronic billboard \url{sci.crypt.random-numbers}} } @ARTICLE {rMAR02b, AUTHOR="G. Marsaglia and W. W. Tsang", TITLE="Some Difficult-to-pass Tests of Randomness", JOURNAL={Journal of Statistical Software}, VOLUME={7}, NUMBER={3}, xNOTE={See \url{http://www.jstatsoft.org/v07/i03/tuftests.pdf}}, YEAR={2002}, PAGES={1--9} } @ARTICLE {rMAR03a, AUTHOR="G. Marsaglia", TITLE="Xorshift {RNG}s", JOURNAL={Journal of Statistical Software}, VOLUME={8}, NUMBER={14}, xNOTE={See \url{http://www.jstatsoft.org/v08/i14/xorshift.pdf}}, YEAR={2003}, PAGES={1--6} } @ARTICLE {rMAR09a, AUTHOR="A. H. Marshall and M. Zenga", TITLE="Simulating {C}oxian Phase-Type Distributions for Patient Survival", JOURNAL={International Transactions in Operations Research}, VOLUME={16}, NUMBER={2}, YEAR={2009}, PAGES={213--226} } @INCOLLECTION {rMAS95a, AUTHOR="M. Mascagni and M. L. Robinson and D. V. Pryor and S. A. Cuccaro", TITLE="Parallel Pseudorandom Number Generation Using Additive Lagged-{F}ibonacci Recursions", BOOKTITLE={{M}onte {C}arlo and Quasi-{M}onte {C}arlo Methods in Scientific Computing}, PUBLISHER={Springer-Verlag}, EDITOR={H. Niederreiter and P. J.-S. Shiue}, SERIES={Lecture Notes in Statistics}, volume={106}, YEAR={1995}, PAGES={263--277} } @Article {rMAS95b, AUTHOR="M. Mascagni and S. A. Cuccaro and and D. V. Pryor and M. L. Robinson", TITLE= "A Fast, High Quality, and Reproducible Parallel Lagged-{F}ibonacci Pseudorandom Number Generator", journal = {Journal of Computational Physics}, year = {1995}, volume = {119}, OPTnumber = {}, pages = {211--219}, OPTannote = {} } @techreport {rMAS96a, author = {N. Masuda and F. Zimmerman}, title = {{PRNG}lib: A Parallel Random Number Generator Library}, institution = {Swiss Center for Scientific Computing}, year = {1996}, type = {Technical Report}, volume = {TR-96-08}, pages = {1--48} } @Article{rMAS98a, author = {M. Mascagni}, title = {Parallel Linear Congruential Generators with Prime Moduli}, journal = {Parallel Computing}, year = {1998}, volume = {24}, OPTnumber = {}, pages = {923--936}, OPTannote = {} } @Article{rMAS00a, author = {M. Mascagni and A. Srinivasan}, title = {Algorithm 806: {SPRNG}: A Scalable Library for Pseudorandom Number Generation}, journal = {{ACM} Transactions on Mathematical Software}, year = {2000}, volume = {26}, OPTnumber = {}, pages = {436--461}, OPTannote = {} } @INPROCEEDINGS {rMAS01a, AUTHOR = "M. Mascagni and S. Rahimi", TITLE = "Parallel Inversive Congruential Generators: Software and Field-Programmable Gate Array Implementation", booktitle = {{M}onte {C}arlo Simulation}, editors = {G. I. Schu\"eller and P. D. Spanos}, xBOOKTITLE={Proceedings of the International Conference {M}onte {C}arlo 2000}, PUBLISHER = {A. A. Balkema}, address = {Rotterdam}, YEAR = {2001}, PAGES = {35--39} } @ARTICLE {rMAT73a, AUTHOR = {G. Matheron}, TITLE = {The Intrinsic Random Functions and their Applications}, YEAR = {1973}, JOURNAL = {Adv. Appl. Prob.}, VOLUME = {5}, PAGES = {439--468} } @TECHREPORT {rMAT88a, xxbecame = {rMAT96a}, AUTHOR="M. Matsumoto and Y. Kurita", TITLE="The Fixed Point of an $m$-sequence and Local Non-Randomness", NUMBER={88-027}, INSTITUTION={Department of Information Science, University of Tokyo}, YEAR={1988} } @UNPUBLISHED {rMAT91a, xxbecame = {rMAT98b}, AUTHOR="M. Matsumoto", TITLE="Cellular Automata as $m$-Sequence Generators", YEAR={1991}, NOTE={Manuscript} } @ARTICLE {rMAT92a, AUTHOR="M. Matsumoto and Y. Kurita", TITLE="Twisted {GFSR} Generators", JOURNAL={ACM Transactions on Modeling and Computer Simulation}, VOLUME={2}, NUMBER={3}, YEAR={1992}, PAGES={179--194} } @INPROCEEDINGS {rMAT93a, AUTHOR = {Y. Matias and J. S. Vitter and W.-C. Ni}, TITLE = {Dynamic Generation of Discrete Random Variates}, BOOKTITLE = {Proceedings Fourth Annual {ACM-SIAM} Symposium on Discrete Algorithms}, YEAR = {1993}, PAGES = {361--370} } @INPROCEEDINGS {rMAT93b, AUTHOR="Y. Matias and J. S. Vitter and W.-C. Ni", TITLE="Dynamic Generation of Discrete Random Variates", BOOKTITLE={Proceedings of the Fourth {ACM-SIAM} Symposium on Discrete Algorithms}, xPUBLISHER={xxx}, xEDITOR={xxx}, YEAR={1993}, PAGES={361--370} } @ARTICLE {rMAT94a, AUTHOR="M. Matsumoto and Y. Kurita", TITLE="Twisted {GFSR} Generators {II}", JOURNAL={ACM Transactions on Modeling and Computer Simulation}, VOLUME={4}, NUMBER={3}, YEAR={1994}, PAGES={254--266} } @INPROCEEDINGS {rMAT94b, AUTHOR = {M. Matsui}, TITLE = {Linear Cryptanalysis Method for {DES} Cypher}, BOOKTITLE = {Advances in Cryptology: Proceedings of Eurocrypt 1993}, YEAR = {1994}, series = {Lecture Notes in Computer Science}, volume = {765}, PAGES = {386--397} } @ARTICLE {rMAT96a, AUTHOR="M. Matsumoto and Y. Kurita", TITLE="Strong Deviations from Randomness in $m$-Sequences Based on Trinomials", JOURNAL={ACM Transactions on Modeling and Computer Simulation}, VOLUME={6}, NUMBER={2}, YEAR={1996}, PAGES={99--106} } @article {rMAT98a, AUTHOR="M. Matsumoto and T. Nishimura", TITLE="Mersenne Twister: A 623-Dimensionally Equidistributed Uniform Pseudo-Random Number Generator", JOURNAL={ACM Transactions on Modeling and Computer Simulation}, VOLUME={8}, NUMBER={1}, YEAR={1998}, PAGES={3--30} } @article {rMAT98b, AUTHOR="M. Matsumoto", TITLE="Simple Cellular Automata as Pseudo-Random $m$-sequence Generators for Built-In Self Test", JOURNAL={ACM Transactions on Modeling and Computer Simulation}, VOLUME={8}, NUMBER={1}, YEAR={1998}, PAGES={31--42} } @ARTICLE{rMAT98c, author = {J. Matous\v{e}k}, title = {On the {$L_2$}-discrepancy for Anchored Boxes}, journal = {Journal of Complexity}, volume = {14}, pages = {527--556}, year = {1998}} @InProceedings{rMAT00a, AUTHOR = {M. Matsumoto and T. Nishimura}, title = {Dynamic {C}reation of {P}seudorandom {N}umber {G}enerators}, booktitle = {{M}onte {C}arlo and Quasi-{M}onte {C}arlo Methods 1998}, pages = {56--69}, year = {2000}, editor = {H. Niederreiter and J. Spanier}, address = {Berlin}, publisher = {Springer}, OPTannote = {} } @inproceedings {rMAT02a, AUTHOR="M. Matsumoto and T. Nishimura", TITLE={A Nonempirical Test on the Weight of Pseudorandom Number Generators}, booktitle = {{M}onte {C}arlo and Quasi-{M}onte {C}arlo Methods 2000}, pages = {381--395}, year = {2002}, editor = {K.-T. Fang and F. J. Hickernell and H. Niederreiter}, address = {Berlin}, publisher = {Springer-Verlag}, } @article {rMAT03a, AUTHOR="M. Matsumoto and T. Nishimura", TITLE="Sum-Discrepancy Test on Pseudorandom Number Generators", JOURNAL={Mathematics and Computers in Simulation}, VOLUME={62}, xNUMBER={}, YEAR={2003}, PAGES={431--442} } @article {rMAT07a, AUTHOR="M. Matsumoto and I. Wada and A. Kuramoto and H. Ashihara", TITLE="Common Defects in Initialization of Pseudorandom Number Generators", JOURNAL={ACM Transactions on Modeling and Computer Simulation}, VOLUME={17}, NUMBER={4}, YEAR={2007}, PAGES={Article 15} } @ARTICLE {rMAU92a, AUTHOR="U. M. Maurer", TITLE="A Universal Statistical Test for Random Bit Generators", JOURNAL={Journal of Cryptology}, VOLUME={5}, NUMBER={2}, YEAR={1992}, PAGES={89--105} } @InProceedings{rMAU02a, author = {U. M. Maurer}, title = {Indistinguishability of Random Systems}, booktitle = {Advances in Cryptology: Eurocrypt 2002}, pages = {110--132}, year = {2002}, editor = {G. Goos and J. Hartmanis and J. van Leeuwen}, number = {2332}, series = {Lecture Notes in Computer Science}, address = {Berlin}, publisher = {Springer-Verlag}, biblio-um = {QA76.9 A25 E87}, OPTannote = {} } @ARTICLE {rMCI89a, AUTHOR="D. McIntosh", TITLE="Random Atari: Enhancing the Number Generator", JOURNAL={{ANTIC}}, VOLUME={7}, NUMBER={11}, YEAR={1989}, PAGES={12} } @INPROCEEDINGS {rMCI91a, AUTHOR="J. L. McInnes and B. Pinkas", TITLE="On the Impossibility of Private Key Cryptography with Weakly Random keys", BOOKTITLE={Advances in Cryptology: {CRYPTO'90}}, series = {Lecture Notes in Computer Science}, number = {537}, address = {Berlin}, publisher = {Springer-Verlag}, pages = {421--435}, YEAR={1991} } @Unpublished{rMER03a, author = {S. Mertens and H. Bauke}, title = {Entropy of Pseudorandom Number Generators}, note = {Manuscript}, institution = {Institut f\"ur Theoretische Physik, Otto-von-Guericke Universit\"at, Germany}, OPTkey = {}, OPTmonth = {}, year = {2003}, OPTannote = {}, } @article{rMIC76a, author = {J. R. Michael and W. R. Schuchany and R. W. Haas}, title = {Generating Random Variates Using Transformations with Multiple Roots}, journal = {The American Statistician}, volume = {30}, pages = {88--90}, year = {1976} } @INPROCEEDINGS {rMIC88a, AUTHOR="S. Micali and C. P. Schnorr", TITLE="Super-Efficient Perfect Random Number Generators", YEAR={1988}, SERIES={Lecture Notes in Computer Science}, BOOKTITLE={Advances in Cryptology: Proceedings of CRYPTO'88}, PUBLISHER="Springer-Verlag, Berlin", VOLUME={403}, PAGES={??--??} } @ARTICLE {rMIC91a, AUTHOR="S. Micali and C. P. Schnorr", TITLE="Efficient, Perfect Polynomial Random Number Generators", JOURNAL={Journal of Cryptology}, YEAR={1991}, VOLUME={4}, NUMBER={3}, PAGES={157--172} } @ARTICLE {rMOD84a, AUTHOR="D. T. Modianos and R. C. Scott and L. W. Corwell", TITLE="Random Number Generation on Microcomputers", JOURNAL={Iterfaces}, VOLUME={14}, NUMBER={2}, YEAR={1984}, PAGES={81--87} } @ARTICLE {rMOD87a, AUTHOR="D. T. Modianos and R. C. Scott and L. W. Cornwell", TITLE="Testing Intrinsic Random Number Generators", JOURNAL={Byte}, VOLUME={12}, NUMBER={1}, YEAR={1987}, PAGES={175--178} } @BOOK {rMOL04a, AUTHOR="C. Moler", TITLE={Numerical Computing with {MATLAB}}, PUBLISHER="SIAM", ADDRESS={Philadelphia, PA}, YEAR={2004} } @ARTICLE {rMON85a, AUTHOR="J. F. Monahan", TITLE="Accuracy in Random Number Generation", JOURNAL={Mathematics of Computation}, VOLUME={45}, NUMBER={172}, YEAR={1985}, PAGES={559--568} } @UNPUBLISHED {rMOR96a, AUTHOR="T. Moreau", TITLE="A Practical ``Perfect'' Pseudo-Random Number Generator", NOTE={Manuscript}, ADDRESS={Connotech Experts-Conseils, Montr{\'}eal}, YEAR={1996} } @TECHREPORT {rMOR98a, AUTHOR="H. Morohosi and M. Fushimi", YEAR={1998}, TITLE="Designing Asymptotically Random {GFSR} Sequences", INSTITUTION={The University of Tokyo}, ADDRESS={Dept.\ of Math.\ Engineering and Information Physics}, NUMBER={METR 98-11} } @ARTICLE {rMUL68a, AUTHOR="M. E. Muller", TITLE="Random Numbers", JOURNAL={Inter. Enc. Social Science}, VOLUME={13}, YEAR={1968}, PAGES={307--313} } @ARTICLE {rMUL87a, AUTHOR="G.L Mullen and H. Niederreiter", TITLE="Optimal Characteristic Polynomials for Digital Multistep Pseudorandom Numbers", JOURNAL={Computing}, VOLUME={39}, YEAR={1987}, PAGES={155--163} } @INCOLLECTION {rMUL95a, AUTHOR = {Mullen, Gary L. and Mahalanabis, Arijit and Niederreiter, Harald}, TITLE = {Tables of $(t,m,s)$-net and $(t,s)$-sequence parameters}, BOOKTITLE = {{M}onte {C}arlo and quasi-{M}onte {C}arlo methods in scientific computing (Las Vegas, NV, 1994)}, PAGES = {58--86}, SERIES = {Lecture Notes in Statistics}, VOLUME = {106}, PUBLISHER = {Springer}, ADDRESS = {New York, NY}, YEAR = {1995}, } @ARTICLE {rMUR08a, AUTHOR = "T. E. Murphy and R. Roy", TITLE = "Chaotic Lasers: The World's Fastest Dice", JOURNAL = {Nature Photonics}, VOLUME = {2}, YEAR = {2008}, PAGES = {714--715} } @ARTICLE {rMUR70a, AUTHOR="H. F. Murry", TITLE="A Natural Approach for Generating Natural Random Variables", JOURNAL={{IEEE} Transactions on Computers}, VOLUME={C-19}, YEAR={1970}, PAGES={1210--1213} } @manual{rNAG02a, author = {NAG}, title = {The {NAG C} Library Manual, Mark 7}, note = {\url{http://www.nag.co.uk/numeric/cl/manual/pdf/G05/g05cac.pdf} and \url{http://www.nag.co.uk/numeric/fl/manual/pdf/G05/g05kaf.pdf}}, organization = {The Numerical Algorithms Group}, year = {2002} } @ARTICLE {rNAN78a, AUTHOR="R. E. Nance and Overstreet, Jr, C.", TITLE="Some Experimental Observations on the Behavior of Composite Random Number Generators", JOURNAL={Operations Research}, VOLUME={26}, NUMBER={5}, YEAR={1978}, PAGES={915--935} } @InCollection{rNEU51a, author = {J. {von Neumann}}, title = {Various techniques used in connection with random digits}, booktitle = {The {M}onte {C}arlo Method}, editor = {A. S. Householder et al.}, publisher = {National Bureau of Standards, Applied Mathematics Series}, volume = 12, year = 1951, pages = {36--38}, } @ARTICLE {rNEU76a, AUTHOR="F. Neuman and R. B. Merrick", TITLE="Autocorrelation Peaks in Congruential Pseudorandom Number Generators", JOURNAL={{IEEE} Transactions of Computers}, VOLUME={C-25}, YEAR={1976}, PAGES={457--460} } @ARTICLE {rNEU76b, AUTHOR="F. Neuman and C. F. Martin", TITLE="The Autocorrelation Structure of Tausworthe Pseudorandom Number Generators", JOURNAL={{IEEE} Transactions of Computers}, VOLUME={C-25}, YEAR={1976}, PAGES={460--464} } @manual{rNEW89a, author = {Newbridge Microsystems}, title = {{CALMOS NM810RNG} Random Number Generator}, note = {Document 600810.MD500.01}, organization = {Newbridge Microsystems}, address = {603 March Road, Kanata, Canada}, month = {November}, year = {1989} } @ARTICLE {rNIE78a, AUTHOR="H. Niederreiter", TITLE="Quasi-{M}onte {C}arlo Methods and Pseudorandom Numbers", JOURNAL={Bulletin of the American Mathematical Society}, VOLUME={84}, NUMBER={6}, YEAR={1978}, PAGES={957--1041} } @ARTICLE {rNIE85a, AUTHOR="H. Niederreiter", TITLE="The Serial Test for Pseudorandom Numbers Generated by the Linear Congruential Method", JOURNAL={Numerische Mathematik}, VOLUME={46}, YEAR={1985}, PAGES={51--68} } @ARTICLE {rNIE86a, AUTHOR="H. Niederreiter", TITLE="A Pseudorandom Vector Generator Based on Finite Field Arithmetic", JOURNAL={Mathematica Japonica}, VOLUME={31}, YEAR={1986}, PAGES={759--774} } @ARTICLE {rNIE86b, AUTHOR="H. Niederreiter", TITLE="Multidimensional Numerical Integration Using Pseudorandom Numbers", JOURNAL={Mathematical Programming Study}, VOLUME={27}, YEAR={1986}, PAGES={17--38} } @ARTICLE {rNIE86c, AUTHOR = "H. Niederreiter", TITLE = "Low Discrepancy Point Sets", JOURNAL = "Monatshefte f{\"u}r Mathematik", VOLUME = "102", PAGES = "155--167", Year = "1986"} @ARTICLE {rNIE87a, AUTHOR="H. Niederreiter", TITLE="A Statistical Analysis of Generalized Feedback Shift Register Pseudorandom Number Generators", JOURNAL={SIAM Journal on Scientific and Statistical Computing}, VOLUME={8}, NUMBER={6}, YEAR={1987}, PAGES={1035--1051} } @ARTICLE {rNIE87b, AUTHOR = "H. Niederreiter", TITLE = "Point Sets and Sequences with Small Discrepancy", JOURNAL = "Monatshefte f{\"u}r Mathematik", VOLUME = "104", PAGES = "273--337", Year = "1987"} @ARTICLE {rNIE88a, AUTHOR="H. Niederreiter", TITLE="Remarks on Nonlinear Congruential Pseudorandom Numbers", JOURNAL={Metrika}, VOLUME={35}, YEAR={1988}, PAGES={321--328} } @ARTICLE {rNIE88b, AUTHOR="H. Niederreiter", TITLE="Statistical Independence of Nonlinear Congruential Pseudorandom Numbers", JOURNAL={Monatshefte f{\"u}r Mathematik}, VOLUME={106}, YEAR={1988}, PAGES={149--159} } @ARTICLE {rNIE88c, AUTHOR="H. Niederreiter", TITLE="The Serial Test for Digital $k$-Step Pseudorandom Numbers", JOURNAL={Mathematical Journal of Okayama University}, VOLUME={30}, YEAR={1988}, PAGES={93--119} } @ARTICLE {rNIE88d, AUTHOR="H. Niederreiter", TITLE="Low-Discrepancy and Low-Dispersion Sequences", JOURNAL={Journal of Number Theory}, VOLUME={30}, YEAR={1988}, PAGES={51--70} } @ARTICLE {rNIE89a, AUTHOR="H. Niederreiter", TITLE="The Serial Test for Congruential Pseudorandom Numbers Generated by Inversions", JOURNAL={Mathematics of Computation}, VOLUME={52}, NUMBER={185}, YEAR={1989}, PAGES={135--144} } @ARTICLE {rNIE90b, AUTHOR="H. Niederreiter", TITLE="Lower Bounds for the Discrepancy of Inversive Congruential Pseudorandom Numbers", JOURNAL={Mathematics of Computation}, VOLUME={55}, YEAR={1990}, PAGES={277--287} } @ARTICLE {rNIE90c, AUTHOR="H. Niederreiter", TITLE="Statistical Independance Properties of Pseudorandom Vectors Produced by Matrix Generators", JOURNAL={Journal of Computational and Applied Mathematics}, YEAR={1990}, VOLUME={31}, PAGES={139--151} } @ARTICLE {rNIE91a, AUTHOR="H. Niederreiter", TITLE="Recent Trends in Random Number and Random Vector Generation", JOURNAL={Annals of Operations Research}, VOLUME={31}, YEAR={1991}, PAGES={323--345} } @INPROCEEDINGS {rNIE91b, AUTHOR="H. Niederreiter", TITLE="The Linear Complexity Profile and the Jump Complexity of Keystream Sequences", BOOKTITLE={Advances in Cryptology: Proceedings of {EUROCRYPT'90}}, PUBLISHER="Springer-Verlag", ADDRESS={Berlin}, YEAR={1991}, PAGES={174--188} } @INPROCEEDINGS {rNIE92a, AUTHOR="H. Niederreiter", TITLE="New Methods for Pseudorandom Number and Pseudorandom Vector Generation", BOOKTITLE={Proceedings of the 1992 Winter Simulation Conference}, PUBLISHER="{IEEE} Press", YEAR={1992}, PAGES={264--269} } @BOOK {rNIE92b, AUTHOR="H. Niederreiter", TITLE={Random Number Generation and Quasi-{M}onte {C}arlo Methods}, SERIES={SIAM CBMS-NSF Regional Conference Series in Applied Mathematics}, VOLUME={63}, PUBLISHER="SIAM", ADDRESS={Philadelphia, PA}, YEAR={1992} } @ARTICLE{rNIE92c, author = {H. Niederreiter}, title = {Low-discrepancy point sets obtained by digital constructions over finite fields}, journal = {Czechoslovak Math.\ Journal}, volume = {42}, pages = {143--166}, year = {1992}} @ARTICLE {rNIE93a, AUTHOR="H. Niederreiter", TITLE="On a New Class of Pseudorandom Numbers for Simulation Methods", JOURNAL={Journal of Computational and Applied Mathematics}, YEAR={1994}, VOLUME={56}, PAGES={159--167} } @ARTICLE {rNIE93b, AUTHOR="H. Niederreiter", TITLE="Factorization of polynomials and some linear-algebra problems over finite fields", JOURNAL={Linear Algebra and its Applications}, YEAR={1993}, VOLUME={192}, PAGES={301--328} } @ARTICLE {rNIE94a, AUTHOR="H. Niederreiter", TITLE="Pseudorandom Vector Generation by the Inversive Method", JOURNAL={ACM Transactions on Modeling and Computer Simulation}, YEAR={1994}, VOLUME={4}, NUMBER={2}, PAGES={191--212} } @ARTICLE {rNIE94b, AUTHOR="H. Niederreiter", TITLE="On a New Class of Pseudorandom Numbers for Simulation Methods", JOURNAL={Journal of Computational and Applied Mathematics}, YEAR={1994}, VOLUME={56}, PAGES={159--167} } @INCOLLECTION {rNIE95a, AUTHOR="H. Niederreiter", TITLE="New Developments in Uniform Pseudorandom Number and Vector Generation", BOOKTITLE={{M}onte {C}arlo and Quasi-{M}onte {C}arlo Methods in Scientific Computing}, PUBLISHER={Springer-Verlag}, ADDRESS = {New York, NY}, EDITOR={H. Niederreiter and P. J.-S. Shiue}, SERIES={Lecture Notes in Statistics}, volume={106}, YEAR={1995}, PAGES={87--120} } @ARTICLE {rNIE95b, AUTHOR="H. Niederreiter", TITLE="The Multiple-Recursive Matrix Method for Pseudorandom Number Generation", JOURNAL={Finite Fields and their Applications}, YEAR={1995}, VOLUME={1}, PAGES={3--30} } @ARTICLE {rNIE95c, AUTHOR="H. Niederreiter", TITLE="Pseudorandom Vector Generation by the Multiple-Recursive Matrix Method", JOURNAL={Mathematics of Computation}, YEAR={1995}, VOLUME={64}, NUMBER={209}, PAGES={279--294} } @book {rNIE95m, author = {H. Niederreiter and P. J.-S. Shiue}, TITLE={{M}onte {C}arlo and Quasi-{M}onte {C}arlo Methods in Scientific Computing}, PUBLISHER={Springer-Verlag}, ADDRESS = {New York, NY}, SERIES={Lecture Notes in Statistics}, volume={106}, YEAR={1995}, } @ARTICLE {rNIE96a, AUTHOR = {H. Niederreiter and C. Xing}, TITLE = {Low-Discrepancy Sequences and Global Function Fields with Many Rational Places}, YEAR = {1996}, JOURNAL= {Finite Fields and Their Applications}, VOLUME = {2}, PAGES = {241--273} } @ARTICLE {rNIE96b, AUTHOR="H. Niederreiter", TITLE="Improved Bounds in the Multiple-Recursive Matrix Method for Pseudorandom Number and Vector Generation", JOURNAL={Finite Fields and their Applications}, YEAR={1996}, VOLUME={2}, PAGES={225--240} } @incollection {rNIE96c, AUTHOR = {Niederreiter, H. and Xing, C.}, TITLE = {Quasirandom points and global function fields}, BOOKTITLE = {Finite fields and applications (Glasgow, 1995)}, PAGES = {269--296}, SERIES = {London Math. Soc. Lecture Note Ser.}, VOLUME = {233}, PUBLISHER = {Cambridge Univ. Press}, ADDRESS = {Cambridge}, YEAR = {1996}, } @INPROCEEDINGS {rNIE97a, author = {H. Niederreiter and C. Xing }, title = {The Algebraic-Geometry Approach to Low-Discrepancy Sequences}, booktitle = {{M}onte {C}arlo and Quasi-{M}onte {C}arlo Methods 1996}, editor = {P. Hellekalek and G. Larcher and H. Niederreiter and P. Zinterhof}, publisher = {Springer-Verlag}, address = {New York, NY}, volume = {127}, pages = {139--160}, year = {1998}, series = {Lecture Notes in Statistics} } @incollection {rNIE98a, AUTHOR ="H. Niederreiter and C. Xing", TITLE ="Nets, $(t,s)$-Sequences, and Algebraic Geometry", booktitle = {Random and Quasi-Random Point Sets}, editor = {P. Hellekalek and G. Larcher}, publisher = {Springer}, address = {New York, NY}, volume = {138}, pages = {267--302}, year = {1998}, ISBN = {ISBN is 0-387-98554-9}, series = {Lecture Notes in Statistics} } @incollection {rNIE98ax, AUTHOR ="H. Niederreiter and C. Xing", TITLE ="Nets, $(t,s)$-Sequences, and Algebraic Geometry", crossref = {rHEL98s}, pages = {267--302}, } @book {rNIE00a, old = {rNIE99a}, editor = {H. Niederreiter and J. Spanier}, title = {{M}onte {C}arlo and Quasi-{M}onte {C}arlo Methods 1998}, publisher = {Springer-Verlag}, address = {Berlin}, year = {2000} } @INPROCEEDINGS {rNIE01a, AUTHOR = "H. Niederreiter", TITLE = "Design and Analysis of Nonlinear Pseudorandom Number Generators", booktitle = {{M}onte {C}arlo Simulation}, editors = {G. I. Schu\"eller and P. D. Spanos}, xBOOKTITLE={Proceedings of the International Conference {M}onte {C}arlo 2000}, PUBLISHER = {A. A. Balkema}, address = {Rotterdam}, YEAR = {2001}, PAGES = {3--9} } @Article{rNIE01b, author = {H. Niederreiter}, title = {On the Distribution of Compound Inversive Congruential Pseudorandom Numbers}, journal = {Monatshefte f\"ur Mathematik}, year = {2001}, volume = {132}, OPTnumber = {}, pages = {35--48}, OPTannote = {} } @article{rNIE01c, author = {H. Niederreiter and G. Pirsic}, title = {Duality for Digital Nets and its Applications}, journal = {Acta Arithmetica}, volume = {97}, pages = {173--182}, year = {2001}} @article{rNIE01d, author = {H. Niederreiter and A. Winterhof}, title = {On a New Class of Inversive Pseudorandom Numbers for Parallelized Simulation Methods}, journal = {Periodica Mathematica Hungarica}, volume = {42}, number = {1--2}, pages = {77--87}, year = {2001}} @inproceedings {rNIE02a, AUTHOR = "H. Niederreiter and I. E. Shparlinski", TITLE = {Recent Advances in the Theory of Nonlinear Pseudorandom Number Generators}, booktitle = {{M}onte {C}arlo and Quasi-{M}onte {C}arlo Methods 2000}, pages = {86--102}, year = {2002}, editor = {K.-T. Fang and F. J. Hickernell and H. Niederreiter}, address = {Berlin}, publisher = {Springer-Verlag}, } @article{rNIE03a, author = {H. Niederreiter}, title = {The Existence of Good Extensible Polynomial Lattice Rules}, journal = {Monatshefte f\"ur Mathematik}, year = {2003}, volume = {139}, pages = {297--307}, OPTannote = {} } @incollection{rNIE04a, author = {H. Niederreiter}, title = {Digital Nets and Coding Theory}, booktitle = {Coding, Cryptography and Combinatorics}, editor = {K. Q. Feng and H. Niederreiter and C. P. Xing}, series = {Progress in Computer Science and Applied Logic}, volume = {23}, publisher = {Birkh\"auser}, address = {Basel}, year = {2004}, pages = {247--257}, OPTannote = {cyclic nets} } @book {rNIE04m, editor = {H. Niederreiter}, title = {{M}onte {C}arlo and Quasi-{M}onte {C}arlo Methods 2002}, publisher = {Springer-Verlag}, address = {Berlin}, year = {2004} } @article{rNIE05a, author = {H. Niederreiter}, title = {Constructions of $(t,m,s)$-Nets and $(t,s)$-Sequences}, journal = {Finite Fields and Their Applications}, year = {2005}, volume = {11}, pages = {578--600}, OPTannote = {} } @book {rNIE06m, editor = {H. Niederreiter and D. Talay}, title = {{M}onte {C}arlo and Quasi-{M}onte {C}arlo Methods 2004}, publisher = {Springer-Verlag}, address = {Berlin}, year = {2006} } @Book{rNIS92a, author = "N. Nisan", title = "Using Hard Problems to Create Pseudorandom Generators", publisher = "The {MIT} Press", year = "1992", OPTkey = "complexity, cryptology", series = "{ACM} Distinguished Dissertations", address = "Cambridge, MA" } @InProceedings{rNIS96a, author = {N. Nisan}, title = {Extracting Randomness: How and Why, A Survey}, booktitle = {11th Annual {IEEE} Conference on Computational Complexity}, editor = {S. Homer and J.-Y. Cai}, year = {1996}, publisher = {{IEEE} Compter Society Press}, address = {Los Alamitos, CA}, pages = {44--58} } @Article {rNIS00a, author = {T. Nishimura}, title = {Tables of 64-bit {M}ersenne Twisters}, journal = {{ACM} Transactions on Modeling and Computer Simulation}, year = {2000}, volume = {10}, number = {4}, pages = {348--357}, OPTannote = {} } @techreport {rNIS00b, key = {NIST}, author = {NIST}, title = {Digital Signature Standards ({DSS})}, institution = {U.S. DoC/National Institute of Standards and Technology}, year = {2000}, type = {{FIPS}-186-2}, note = {See \url{http://csrc.nist.gov/csrc/fedstandards.html}} } @techreport {rNIS01a, key = {NIST}, author = {NIST}, title = {ADVANCED ENCRYPTION STANDARD ({AES})}, institution = {U.S. DoC/National Institute of Standards and Technology}, year = {2001}, type = {{FIPS}-197}, note = {See \url{http://csrc.nist.gov/CryptoToolkit/tkencryption.html}} } Xpages = {1--47} } @techreport {rNIS02a, key = {NIST}, author = {{NIST}}, title = {SECURE HASH STANDARD ({SHS})}, institution = {U.S. DoC/National Institute of Standards and Technology}, year = {2002}, type = {{FIPS}-186-2, with change notice added in February 2004}, note = {See \url{http://csrc.nist.gov/CryptoToolkit/tkhash.html}}, pages = {1--79} } @inproceedings{rNUY06a, author = {D. Nuyens and R. Cools}, title = {Fast Component-by-Component Construction, a Reprise for Different Kernels}, booktitle = {{M}onte {C}arlo and Quasi-{M}onte {C}arlo Methods 2004}, pages = {373--387}, year = {2006}, editor = {H. Niederreiter and D. Talay}, OPTaddress = {Berlin}, OPTpublisher = {Springer-Verlag}, } @article{rNUY06b, author = {D. Nuyens and R. Cools}, title = {Fast algorithms for component-by-component construction of rank-1 lattice rules in shift-invariant reproducing kernel {H}ilbert spaces}, journal = {Mathematics of Computation}, pages = {903--920}, volume = {75}, year = {2006} } @article{rNUY06c, author = {D. Nuyens and R. Cools}, title = {Fast component-by-component construction of rank-1 lattice rules with a non-prime number of points}, journal = {Journal of Complexity}, pages = {4--28}, volume = {22}, year = {2006}, } @article{rOKT09a, author = {G. \"Okten}, title = {Generalized {von Neumann-Kakutani} Transformation and Random-Start Scrambled {H}alton Sequences}, journal = {Journal of Complexity}, pages = {318--331}, volume = {25}, number = {4}, year = {2009}, } @INCOLLECTION {rOWE95a, AUTHOR="A. B. Owen", TITLE="Randomly Permuted $(t,m,s)$-Nets and $(t,s)$-Sequences", BOOKTITLE={{M}onte {C}arlo and Quasi-{M}onte {C}arlo Methods in Scientific Computing}, PUBLISHER={Springer-Verlag}, EDITOR={H. Niederreiter and P. J.-S. 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L'Ecuyer}, title = {Infinite-Dimensional Point Sets Based on Linear Recurrences over {GF($2^w$)}}, booktitle = {{M}onte {C}arlo and Quasi-{M}onte {C}arlo Methods 2004}, OPTvolume = {}, OPTnumber = {}, OPTpages = {}, year = {2005}, editor = {H. Niederreiter and D. Talay}, address = {Berlin}, publisher = {Springer-Verlag}, note = {to appear}, } @phdthesis {rPAN04t, author = {F. Panneton}, title = {Construction d'ensembles de points bas\'ee sur des r\'ecurrences lin\'eaires dans un corps fini de caract\'eristique 2 pour la simulation {M}onte {C}arlo et l'int\'egration quasi-{M}onte {C}arlo}, school = {D\'epartement d'informatique et de recherche op\'erationnelle, Universit\'e de Montr\'eal}, address = {Canada}, month = {August}, year = {2004}, } @article{rPAN05a, old = {rPAN04c}, author = {F. Panneton and P. 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