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Finding the group structure of elliptic curves over finite fields

Published online by Cambridge University Press:  17 April 2009

John B. Friedlander ,
Carl Pomerance  and
Igor E. Shparlinski
John B. Friedlander
Affiliation:
Department of Mathematics, University of Toronto, Toronto, Ontario M5S 3G3, Canada e-mail: frdlndr@math.toronto.edu
Carl Pomerance
Affiliation:
Department of Mathematics, Dartmouth College, Hanover, NH 03755–355, United States of America e-mail: carlp@gauss.dartmouth.edu
Igor E. Shparlinski
Affiliation:
Department of Computing, Macquarie University, Sydney, NSW 2109, Australia e-mail: igor@ics.mq.edu.au
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We show that an algorithm of V. Miller to compute the group structure of an elliptic curve over a prime finite field runs in probabilistic polynomial time for almost all curves over the field. Important to our proof are estimates for some divisor sums.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 72 , Issue 2 , October 2005 , pp. 251 - 263
Copyright
Copyright © Australian Mathematical Society 2005

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