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Mathematics of Computation

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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.

References [Enhancements On Off] (What's this?)

  • [1] J. Buchmann, M.J. Jacobson, Jr., and E. Teske, ``On Some Computational Problems in Finite Abelian Groups", Math. Comp. 66 (1997), pp. 1663-1687. MR 98a:11185
  • [2] D. E. Knuth, ``The Art of Computer Programming", vol. 3 (1973), pp. 1-99 (prob. 17). MR 56:4281
  • [3] ``Dave's Cool Java Home Page", /LaunchPad/5318 (1998).

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Additional Information

David C. Terr
Affiliation: 2614 Warring St. #7, Berkeley, CA 94704

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

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