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Fast parallel GCD algorithm of many integers

Published: 28 January 2014 Publication History

Abstract

We present a new parallel algorithm which computes the GCD of n integers of O(n) bits in O(n / log n) time with O(n2+ε) processors, for any ε > 0 on CRCW PRAM model.

References

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A. Borodin, J. von zur Gathen and J. Hopcroft, Fast parallel matrix and GCD computations, Information and Control, 52, 3, 1982, 241--256
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B. Chor and O. Goldreich, An improved parallel algorithm for integer GCD, Algorithmica, 5, 1990, 1--10
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G. Cooperman, S. Feisel, J. von zur Gathen and G. Havas, GCD of many integers, Lect. Notes in Comp. Sci., Springer-Verlag, Berlin, 1627 (1999), 310--317
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G. Havas, S. Majewski, Extended gcd calculation, Congressus Numerantium, 111, 1627 (1998), 104--114
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S.M. Sedjelmaci, On A Parallel Lehmer-Euclid GCD Algorithm, in Proc. of the International Symposium on Symbolic and Algebraic Computation (ISSAC'2001), 2001, 303--308
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S.M. Sedjelmaci, Fast Parallel GCD algorithm of many integers, lipn.univ-paris13.fr/~sedjelmaci, Rapport interne, LIPN, April, 2013
[7]
J. Sorenson, Two Fast GCD Algorithms, J. of Algorithms, 16, 1994, 110--144

Cited By

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  • (2017)Two Fast Parallel GCD Algorithms of Many IntegersProceedings of the 2017 ACM International Symposium on Symbolic and Algebraic Computation10.1145/3087604.3087610(397-404)Online publication date: 23-Jul-2017
  • (2016)Reversible circuit design for GCD computation in cryptography algorithmsInternational Journal of Circuit Theory and Applications10.1002/cta.229345:2(242-259)Online publication date: Dec-2016

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Published In

cover image ACM Communications in Computer Algebra
ACM Communications in Computer Algebra  Volume 47, Issue 3/4
September/December 2013
116 pages
ISSN:1932-2232
EISSN:1932-2240
DOI:10.1145/2576802
Issue’s Table of Contents

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 28 January 2014
Published in SIGSAM-CCA Volume 47, Issue 3/4

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Cited By

View all
  • (2017)Two Fast Parallel GCD Algorithms of Many IntegersProceedings of the 2017 ACM International Symposium on Symbolic and Algebraic Computation10.1145/3087604.3087610(397-404)Online publication date: 23-Jul-2017
  • (2016)Reversible circuit design for GCD computation in cryptography algorithmsInternational Journal of Circuit Theory and Applications10.1002/cta.229345:2(242-259)Online publication date: Dec-2016

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