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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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Square form factorization
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by Jason E. Gower and Samuel S. Wagstaff Jr. PDF
Math. Comp. 77 (2008), 551-588 Request permission

Abstract:

We present a detailed analysis of SQUFOF, Daniel Shanks’ Square Form Factorization algorithm. We give the average time and space requirements for SQUFOF. We analyze the effect of multipliers, either used for a single factorization or when racing the algorithm in parallel.
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Additional Information
  • Jason E. Gower
  • Affiliation: Institute for Mathematics and its Applications, University of Minnesota, 424 Lind Hall, 207 Church St. S.E., Minneapolis, Minnesota 55455-0436
  • Email: gower@ima.umn.edu
  • Samuel S. Wagstaff Jr.
  • Affiliation: Center for Education and Research in Information Assurance and Security, and Department of Computer Science, Purdue University, West Lafayette, Indiana 47907
  • Email: ssw@cerias.purdue.edu
  • Received by editor(s): March 13, 2005
  • Received by editor(s) in revised form: November 9, 2006
  • Published electronically: May 14, 2007
  • Additional Notes: This paper is based on the Ph.D. thesis of the first author, supervised by the second author. Both authors are grateful for the support of the CERIAS Center at Purdue University and by the Lilly Endowment Inc.

  • Dedicated: This paper is dedicated to the memory of Daniel Shanks
  • © Copyright 2007 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Math. Comp. 77 (2008), 551-588
  • MSC (2000): Primary 11A51, 11E16, 11R11, 11Y05
  • DOI: https://doi.org/10.1090/S0025-5718-07-02010-8
  • MathSciNet review: 2353967