Orders of points on elliptic curves

IE Shparlinski*

*Corresponding author for this work

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

Abstract

We show that a randomly chosen point on a randomly chosen elliptic curve modulo a prime p, with overwhelming probability generates a cyclic subgroup of size close to p. We apply this result to obtain lower bounds for periods of two recently introduced pseudorandom number generators on elliptic curves.

Original languageEnglish
Title of host publicationAffine algebraic geometry
Subtitle of host publicationspecial session on affine algebraic geometry at the first joint AMS-RSME meeting
EditorsJ Gutierrez, Shpilrain, JT Yu
Place of PublicationProvidence
PublisherAmerican Mathematical Society
Pages245-251
Number of pages7
ISBN (Print)0821834762
Publication statusPublished - 2005
Event1st RSME-AMS Joint Meeting - Seville, Spain
Duration: 19 Jun 200321 Jun 2003

Publication series

NameContemporary Mathematics Series
PublisherAmerican Mathematical Society
Volume369
ISSN (Print)0271-4132

Conference

Conference1st RSME-AMS Joint Meeting
CountrySpain
CitySeville
Period19/06/0321/06/03

Keywords

  • elliptic curves
  • orders of points
  • pseudorandom number generators
  • FINITE-FIELD
  • CYCLICITY

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