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Monte-Carlo Integration Using Cryptographically Secure Pseudo-random Generator

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Numerical Methods and Applications (NMA 2002)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2542))

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Abstract

The drastic reduction of randomness by random Weyl sampling enables us to use cryptographically secure pseudo-random generators for Monte-Carlo integration as well as for parallel Monte-Carlo integration.

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References

  1. Luby, M.: Pseudorandomness and Cryptographic Applications. Princeton Univ. Press (1996)

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  2. Stinton, D.R.: Cryptography — Theory and Practice. CRC Press (1995)

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  3. Sugita, H.: Pseudo-random number generator by means of irrational rotation. Monte Carlo Methods and Applications, VSP, 1-1 (1995) 35–57.

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  4. Sugita, H.: The Random sampler. C and C++ libraries for pseudo-random generation and dynamic random Weyl sampling, available at http://idisk.mac.com/hiroshi sugita/Public/imath/mathematics.html.

  5. Sugita, H.: Robust numerical integration and pairwise independent random variables. Jour. Comput. Appl. Math., 139 (2001) 1–8.

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  6. Sugita, H.: Dynamic random Weyl sampling for drastic reduction of randomness in Monte-Carlo integration. (a special issue for IMACS Seminar on Monte Carlo Methods MCM2001, Salzburg) Mathematics and Computers in Simulation, to appear.

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  7. Sugita, H. and Takanobu, S.: Random Weyl sampling for robust numerical integration of complicated functions. Monte Carlo Methods and Appl., 6-1 (1999) 27–48.

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Author information

Authors and Affiliations

  1. Faculty of Mathematics, Kyushu University, 812-0851, Fukuoka, Japan

    Hiroshi Sugita

Authors
  1. Hiroshi Sugita
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Editor information

Editors and Affiliations

  1. Central Laboratory for Parallel Processing, Bulgarian Academy of Sciences, Acad. G. Bonchev, bl. 25A, 1113, Sofia, Bulgaria

    Ivan Dimov , Ivan Lirkov  & Svetozar Margenov ,  & 

  2. National Environmental Research Institute, Frederiksborgvej 399, P.O. Box 358, 4000, Roskilde, Denmark

    Zahari Zlatev

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© 2003 Springer-Verlag Berlin Heidelberg

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Sugita, H. (2003). Monte-Carlo Integration Using Cryptographically Secure Pseudo-random Generator. In: Dimov, I., Lirkov, I., Margenov, S., Zlatev, Z. (eds) Numerical Methods and Applications. NMA 2002. Lecture Notes in Computer Science, vol 2542. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-36487-0_15

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  • DOI: https://doi.org/10.1007/3-540-36487-0_15

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-00608-4

  • Online ISBN: 978-3-540-36487-0

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