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Average normalisations of elliptic curves

Published online by Cambridge University Press:  17 April 2009

William D. Banks  and
Igor E. Shparlinski
William D. Banks
Affiliation:
Department of Mathematics, University of Missouri, Columbia, MO 65211, United States of America e-mail: bbanks@math.missouri.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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Ciet, Quisquater, and Sica have recently shown that every elliptic curve E over a finite field 𝔽p is isomorphic to a curve y2 = x3 + ax + b with a and b of size O (p¾). In this paper, we show that almost all elliptic curves satisfy the stronger bound O (p⅔). The problem is motivated by cryptographic considerations.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 66 , Issue 3 , December 2002 , pp. 353 - 358
Copyright
Copyright © Australian Mathematical Society 2002

References

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