On exponential sums and group generators for elliptic curves over finite fields

David R. Kohel, Igor E. Shparlinski

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

48 Citations (Scopus)

Abstract

In the paper an upper bound is established for certain exponential sums, analogous to Gaussian sums, defined on the points of an elliptic curve over a prime finite field. The bound is applied to prove the existence of group generators for the set of points on an elliptic curve over Fq among certain sets of bounded size. We apply this estimate to obtain a deterministic O(q1/2+ε) algorithm for finding generators of the group in echelon form, and in particular to determine its group structure.

Original languageEnglish
Title of host publicationAlgorithmic Number Theory
Subtitle of host publication4th International Symposium, ANTS-IV Leiden, The Netherlands, July 2-7, 2000 Proccedings
EditorsWieb Bosma
Place of PublicationBerlin
PublisherSpringer, Springer Nature
Pages395-404
Number of pages10
Volume1838
ISBN (Electronic)9783540449942
ISBN (Print)3540676953
Publication statusPublished - 2000
Event4th International Symposium on Algorithmic Number Theory, ANTS 2000 - Leiden, Netherlands
Duration: 2 Jul 20007 Jul 2000

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume1838
ISSN (Print)03029743
ISSN (Electronic)16113349

Other

Other4th International Symposium on Algorithmic Number Theory, ANTS 2000
CountryNetherlands
CityLeiden
Period2/07/007/07/00

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