Orders of points on elliptic curves

IE Shparlinski

Orders of points on elliptic curves

IE Shparlinski^*

^*Corresponding author for this work

School of Computing

Research output: Chapter in Book/Report/Conference proceeding › Conference proceeding contribution › peer-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 language	English
Title of host publication	Affine algebraic geometry
Subtitle of host publication	special session on affine algebraic geometry at the first joint AMS-RSME meeting
Editors	J Gutierrez, Shpilrain, JT Yu
Place of Publication	Providence
Publisher	American Mathematical Society
Pages	245-251
Number of pages	7
ISBN (Print)	0821834762
Publication status	Published - 2005
Event	1st RSME-AMS Joint Meeting - Seville, Spain Duration: 19 Jun 2003 → 21 Jun 2003

Publication series

Name	Contemporary Mathematics Series
Publisher	American Mathematical Society
Volume	369
ISSN (Print)	0271-4132

Conference

Conference	1st RSME-AMS Joint Meeting
Country/Territory	Spain
City	Seville
Period	19/06/03 → 21/06/03

Keywords

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

Cite this

@inproceedings{69284fc5766f46dcb954497eeec75e9f,

title = "Orders of points on elliptic curves",

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.",

keywords = "elliptic curves, orders of points, pseudorandom number generators, FINITE-FIELD, CYCLICITY",

author = "IE Shparlinski",

year = "2005",

language = "English",

isbn = "0821834762",

series = "Contemporary Mathematics Series",

publisher = "American Mathematical Society",

pages = "245--251",

editor = "J Gutierrez and Shpilrain and JT Yu",

booktitle = "Affine algebraic geometry",

address = "United States",

note = "1st RSME-AMS Joint Meeting ; Conference date: 19-06-2003 Through 21-06-2003",

}

Orders of points on elliptic curves. / Shparlinski, IE.
Affine algebraic geometry: special session on affine algebraic geometry at the first joint AMS-RSME meeting. ed. / J Gutierrez; Shpilrain; JT Yu. Providence: American Mathematical Society, 2005. p. 245-251 (Contemporary Mathematics Series; Vol. 369).

Research output: Chapter in Book/Report/Conference proceeding › Conference proceeding contribution › peer-review

TY - GEN

T1 - Orders of points on elliptic curves

AU - Shparlinski, IE

PY - 2005

Y1 - 2005

N2 - 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.

AB - 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.

KW - elliptic curves

KW - orders of points

KW - pseudorandom number generators

KW - FINITE-FIELD

KW - CYCLICITY

UR - http://www.ams.org/mathscinet-getitem?mr=2126665

M3 - Conference proceeding contribution

SN - 0821834762

T3 - Contemporary Mathematics Series

SP - 245

EP - 251

BT - Affine algebraic geometry

A2 - Gutierrez, J

A2 - Shpilrain, null

A2 - Yu, JT

PB - American Mathematical Society

CY - Providence

T2 - 1st RSME-AMS Joint Meeting

Y2 - 19 June 2003 through 21 June 2003

ER -

Orders of points on elliptic curves

Abstract

Publication series

Conference

Keywords

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Cite this