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International Conference on Computational Science and Its Applications

ICCSA 2014: Computational Science and Its Applications – ICCSA 2014 pp 592–606Cite as

Distributed Prime Sieve in Heterogeneous Computer Clusters

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8582))

Abstract

Prime numbers play a pivotal role in current encryption algorithms and given the rise of cloud computing, the need for larger primes has never been so high. This increase in available computation power can be used to either try to break the encryption or to strength it by finding larger prime numbers. With this in mind, this paper provides an analysis of different sieve implementations that can be used to generate primes to near 264. It starts by analyzing cache friendly sequential sieves with wheel factorization, then expands to multi-core architectures and ends with a cache friendly segmented hybrid implementation of a distributed prime sieve, designed to efficiently use all the available computation resources of heterogeneous computer clusters with variable workload and to scale very well in both the shared and distributed memory versions.

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References

  1. Standard, RSA Cryptography: RSA Public Key Cryptography Standard# 1 v. 2.2. RSA Laboratories (2012)

    Google Scholar 

  2. Lenstra Jr., H.W.: Primality testing algorithms (after Adleman, Rumely and Williams). In: Sminaire Bourbaki, vol. 1980/81 Exposs 561578, pp. 243–257. Springer, Heidelberg (1981)

    Google Scholar 

  3. O’Neill, M.E.: The genuine sieve of Eratosthenes. Journal of Functional Programming 19(1), 95 (2009)

    Article  MATH  Google Scholar 

  4. Atkin, A., Bernstein, D.: Prime sieves using binary quadratic forms. Mathematics of Computation 73(246), 1023–1030 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  5. Aiyar, V.R.: Sundaram’s Sieve for Prime Numbers. The Mathematics Student 2(2), 73 (1934)

    Google Scholar 

  6. Joye, M., Paillier, P., Vaudenay, S.: Efficient generation of prime numbers. In: Paar, C., Koç, Ç.K. (eds.) CHES 2000. LNCS, vol. 1965, pp. 340–354. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  7. Distributed prime sieve C++ implementation (git repository), https://github.com/carlosmccosta/Distributed-Prime-Sieve

  8. Dagum, L., Menon, R.: OpenMP: an industry standard API for shared-memory programming. Computational Science & Engineering 5(1), 46–55 (1998)

    Article  Google Scholar 

  9. Pritchard, P.: Explaining the wheel sieve. Acta Informatica 17(4), 477–485 (1982)

    Article  MATH  MathSciNet  Google Scholar 

  10. Primesieve, http://primesieve.org/

  11. Pritchard, P.: Fast compact prime number sieves (among others). Journal of Algorithms 4(4), 332–344 (1983)

    Article  MATH  MathSciNet  Google Scholar 

  12. Járai, A., Vatai, E.: Cache optimized linear sieve. arXiv preprint arXiv:1111.3297 (2011)

    Google Scholar 

  13. Singleton, R.C.: An efficient prime number generator. Communications of the ACM 12, 563–564 (1969)

    Article  Google Scholar 

  14. Paillard, G. A. L.: A Fully Distributed Prime Numbers Generation using the Wheel Sieve. In: Parallel and Distributed Computing and Networks, pp. 651–656 (2005)

    Google Scholar 

  15. Sorenson, J.: An analysis of two prime number sieves. In: Computer Sciences Department. University of Wisconsin-Madison (1991)

    Google Scholar 

  16. David, J.W.: Parallel Prime Sieve: Finding Prime Numbers. In.: Parallel Computing Seminar Report, Institute of Information & Mathematical Sciences, Massey University at Albany, Auckland, New Zealand (2009)

    Google Scholar 

  17. Cordeiro, M.: Parallelization of the Sieve of Eratosthenes. In: Parallel Programming, Doctoral Program in Informatics Engineering, Engineering Faculty. University of Porto (2012)

    Google Scholar 

  18. Sorenson, J., Parberry, I.: Two Fast Parallel Prime Number Sieves. Information and Computation 114(1), 115–130 (1994)

    Article  MATH  MathSciNet  Google Scholar 

  19. Bokhari, S.H.: Multiprocessing the Sieve of Eratosthenes. Computer Journal 20(4), 50–58 (1987)

    Article  Google Scholar 

  20. Anderson, G.: An Ada Multitasking Solution for the Sieve of Eratosthenes. Ada Lett. 8(5), 71–74 (1988)

    Article  Google Scholar 

  21. Shapiro, E.: The family of concurrent logic programming languages. ACM Computing Surveys (CSUR) 21(3), 413–510 (1989)

    Article  Google Scholar 

  22. Gropp, W., Lusk, E., Skjellum, A.: Using MPI: portable parallel programming with the message-passing interface, vol. 1. MIT press (1999)

    Google Scholar 

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Author information

Authors and Affiliations

  1. Faculdade de Engenharia da Universidade do Porto, Rua Dr. Roberto Frias, s/n, 4200-465, Porto, Portugal

    Carlos M. Costa, Altino M. Sampaio & Jorge G. Barbosa

Authors
  1. Carlos M. Costa
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  2. Altino M. Sampaio
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  3. Jorge G. Barbosa
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Editor information

Editors and Affiliations

  1. School of Engineering, University of Basilicata, 85100, Potenza, Italy

    Beniamino Murgante

  2. Department of Computer and Information Sciences, Covenant University, Ota, Nigeria

    Sanjay Misra

  3. Department of Production and Systems, University of Minho, 4710-057, Braga, Portugal

    Ana Maria A. C. Rocha

  4. DICAR, Polytecnico di Bari, 70125, Bari, Italy

    Carmelo Torre

  5. University of Minho, Braga, Portugal

    Jorge Gustavo Rocha  & Maria Irene Falcão  & 

  6. Monash University, 3800, Clayton, VIC, Australia

    David Taniar

  7. Department of Intelligent Informatics, Kyushu Sangyo University, 2-3-1 Matsukadai, 813-8503, Higashi-ku, Fukuoka, Japan

    Bernady O. Apduhan

  8. Department of Mathematics and Computer Science, University of Perugia, Via Vanvitelli, 1, 06123, Perugia, Italy

    Osvaldo Gervasi

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© 2014 Springer International Publishing Switzerland

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Cite this paper

Costa, C.M., Sampaio, A.M., Barbosa, J.G. (2014). Distributed Prime Sieve in Heterogeneous Computer Clusters. In: Murgante, B., et al. Computational Science and Its Applications – ICCSA 2014. ICCSA 2014. Lecture Notes in Computer Science, vol 8582. Springer, Cham. https://doi.org/10.1007/978-3-319-09147-1_43

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  • DOI: https://doi.org/10.1007/978-3-319-09147-1_43

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-09146-4

  • Online ISBN: 978-3-319-09147-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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