Square form factorization

Authors:
Jason E. Gower and Samuel S. Wagstaff Jr.

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

Published electronically:
May 14, 2007

MathSciNet review:
2353967

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Abstract | References | Similar Articles | Additional Information

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

DOI:
https://doi.org/10.1090/S0025-5718-07-02010-8

Keywords:
Integer factorization,
binary quadratic form

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

Article copyright:
© Copyright 2007
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.