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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

A modification of Shanks'
baby-step giant-step algorithm


Author: David C. Terr
Journal: Math. Comp. 69 (2000), 767-773
MSC (1991): Primary 68P10, 20C40
Published electronically: March 4, 1999
MathSciNet review: 1653994
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Abstract | References | Similar Articles | Additional Information

Abstract: I describe a modification to Shanks' baby-step giant-step algorithm for computing the order $n$ of an element $g$ of a group $G$, assuming $n$ is finite. My method has the advantage of being able to compute $n$ quickly, which Shanks' method fails to do when the order of $G$ is infinite, unknown, or much larger than $n$. I describe the algorithm in detail. I also present the results of implementations of my algorithm, as well as those of a similar algorithm developed by Buchmann, Jacobson, and Teske, for calculating the order of various ideal classes of imaginary quadratic orders.


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Additional Information

David C. Terr
Affiliation: 2614 Warring St. #7, Berkeley, CA 94704
Email: davidcterr@aol.com

DOI: http://dx.doi.org/10.1090/S0025-5718-99-01141-2
PII: S 0025-5718(99)01141-2
Received by editor(s): September 4, 1996
Received by editor(s) in revised form: May 30, 1998
Published electronically: March 4, 1999
Article copyright: © Copyright 2000 American Mathematical Society