Exponential sums over points of elliptic curves

Omran Ahmadi; Igor E. Shparlinski

doi:10.1016/j.jnt.2014.01.016

Exponential sums over points of elliptic curves

Omran Ahmadi, Igor E. Shparlinski^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

4 Citations (Scopus)

Abstract

We derive a new bound for some bilinear sums over points of an elliptic curve over a finite field. We use this bound to improve a series of previous results on various exponential sums and some arithmetic problems involving points on elliptic curves.

Original language	English
Pages (from-to)	299-313
Number of pages	15
Journal	Journal of Number Theory
Volume	140
DOIs	https://doi.org/10.1016/j.jnt.2014.01.016
Publication status	Published - Jul 2014
Externally published	Yes

Keywords

Elliptic curves
Exponential sums
Finite fields

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10.1016/j.jnt.2014.01.016

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title = "Exponential sums over points of elliptic curves",

abstract = "We derive a new bound for some bilinear sums over points of an elliptic curve over a finite field. We use this bound to improve a series of previous results on various exponential sums and some arithmetic problems involving points on elliptic curves.",

keywords = "Elliptic curves, Exponential sums, Finite fields",

author = "Omran Ahmadi and Shparlinski, {Igor E.}",

year = "2014",

month = jul,

doi = "10.1016/j.jnt.2014.01.016",

language = "English",

volume = "140",

pages = "299--313",

journal = "Journal of Number Theory",

issn = "0022-314X",

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TY - JOUR

T1 - Exponential sums over points of elliptic curves

AU - Ahmadi, Omran

AU - Shparlinski, Igor E.

PY - 2014/7

Y1 - 2014/7

N2 - We derive a new bound for some bilinear sums over points of an elliptic curve over a finite field. We use this bound to improve a series of previous results on various exponential sums and some arithmetic problems involving points on elliptic curves.

AB - We derive a new bound for some bilinear sums over points of an elliptic curve over a finite field. We use this bound to improve a series of previous results on various exponential sums and some arithmetic problems involving points on elliptic curves.

KW - Elliptic curves

KW - Exponential sums

KW - Finite fields

UR - http://www.scopus.com/inward/record.url?scp=84896310722&partnerID=8YFLogxK

UR - http://purl.org/au-research/grants/arc/DP130100237

U2 - 10.1016/j.jnt.2014.01.016

DO - 10.1016/j.jnt.2014.01.016

M3 - Article

AN - SCOPUS:84896310722

SN - 0022-314X

VL - 140

SP - 299

EP - 313

JO - Journal of Number Theory

JF - Journal of Number Theory

ER -

Exponential sums over points of elliptic curves

Abstract

Keywords

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