On the distribution of the elliptic curve power generator

Edwin EI-Mahassni*, Igor E. Shparlinski

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference proceeding contributionpeer-review

Abstract

For a given elliptic curve E over a finite field, we obtain an upper bound on incomplete character sums with power generator on E, that is, for the sequence of points

W-n = e(n)W(0),

where W-0 is an IFq rational point on E and e is an integer, relatively prime to the order of W-0.

These results complement those obtained by T. Lange and I. E. Shparlinski, where a similar bound has been established for sums over the entire period. We propose two different approaches. One of them leads to stronger results for very short sums, while the other one is stronger for almost complete sums.

Combining these bounds with some standard arguments we also derive results about the uniformity of distribution of such sequences.

Original languageEnglish
Title of host publicationFinite fields and applications
EditorsGary L. Mullen, Daniel Panario, Igor E. Shparlinski
Place of PublicationProvidence, RI
PublisherAmerican Mathematical Society
Pages111-118
Number of pages8
ISBN (Print)9780821843093
Publication statusPublished - 2008
Event8th International Conference on Finite Fields and Applications - Melbourne, Australia
Duration: 9 Jul 200713 Jul 2007

Publication series

NameContemporary mathematics series
PublisherAmerican Mathematical Society
Volume461
ISSN (Print)0271-4132

Conference

Conference8th International Conference on Finite Fields and Applications
CountryAustralia
CityMelbourne
Period9/07/0713/07/07

Keywords

  • REINGOLD PSEUDORANDOM FUNCTION
  • EXPONENTIAL-SUMS
  • CHARACTER SUMS
  • FINITE-FIELDS

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