Efficient scalar multiplications on elliptic curves without repeated doublings and their practical performance

Yasuyuki Sakai, Kouichi Sakurai

Research output: Chapter in Book/Report/Conference proceedingConference contribution

7 Citations (Scopus)

Abstract

We introduce efficient algorithms for scalar multiplication on elliptic curves defined over 1Fp. The algorithms compute 2fc P directly from P, where P is a random point on an elliptic curve, without computing the intermediate points, which is faster than k repeated doublings. Moreover, we apply the algorithms to scalar multiplication on elliptic curves, and analyze their computational complexity. As a result of their implementation with respect to affine (resp. weighted projective) coordinates, we achieved an increased performance factor of 1.45 (45%) (resp. 1.15 (15%)) in the scalar multiplication of the elliptic curve of size 160bit.

Original languageEnglish
Title of host publicationInformation Security and Privacy - 5th Australasian Conference, ACISP 2000, Proceedings
EditorsEd Dawson, Andrew Clark, Colin Boyd
PublisherSpringer Verlag
Pages59-73
Number of pages15
ISBN (Print)3540677429
DOIs
Publication statusPublished - Jan 1 2000
Event5th Australasian Conference on Information Security and Privacy, ACISP 2000 - Brisbane, Australia
Duration: Jul 10 2000Jul 12 2000

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume1841
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other5th Australasian Conference on Information Security and Privacy, ACISP 2000
CountryAustralia
CityBrisbane
Period7/10/007/12/00

Fingerprint

Scalar multiplication
Doubling
Elliptic Curves
Computational complexity
Computational Complexity
Efficient Algorithms
Computing

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

Cite this

Sakai, Y., & Sakurai, K. (2000). Efficient scalar multiplications on elliptic curves without repeated doublings and their practical performance. In E. Dawson, A. Clark, & C. Boyd (Eds.), Information Security and Privacy - 5th Australasian Conference, ACISP 2000, Proceedings (pp. 59-73). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 1841). Springer Verlag. https://doi.org/10.1007/10718964_6

Efficient scalar multiplications on elliptic curves without repeated doublings and their practical performance. / Sakai, Yasuyuki; Sakurai, Kouichi.

Information Security and Privacy - 5th Australasian Conference, ACISP 2000, Proceedings. ed. / Ed Dawson; Andrew Clark; Colin Boyd. Springer Verlag, 2000. p. 59-73 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 1841).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Sakai, Y & Sakurai, K 2000, Efficient scalar multiplications on elliptic curves without repeated doublings and their practical performance. in E Dawson, A Clark & C Boyd (eds), Information Security and Privacy - 5th Australasian Conference, ACISP 2000, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 1841, Springer Verlag, pp. 59-73, 5th Australasian Conference on Information Security and Privacy, ACISP 2000, Brisbane, Australia, 7/10/00. https://doi.org/10.1007/10718964_6
Sakai Y, Sakurai K. Efficient scalar multiplications on elliptic curves without repeated doublings and their practical performance. In Dawson E, Clark A, Boyd C, editors, Information Security and Privacy - 5th Australasian Conference, ACISP 2000, Proceedings. Springer Verlag. 2000. p. 59-73. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/10718964_6
Sakai, Yasuyuki ; Sakurai, Kouichi. / Efficient scalar multiplications on elliptic curves without repeated doublings and their practical performance. Information Security and Privacy - 5th Australasian Conference, ACISP 2000, Proceedings. editor / Ed Dawson ; Andrew Clark ; Colin Boyd. Springer Verlag, 2000. pp. 59-73 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
@inproceedings{26947161b3904c26b52f68a5af979bc8,
title = "Efficient scalar multiplications on elliptic curves without repeated doublings and their practical performance",
abstract = "We introduce efficient algorithms for scalar multiplication on elliptic curves defined over 1Fp. The algorithms compute 2fc P directly from P, where P is a random point on an elliptic curve, without computing the intermediate points, which is faster than k repeated doublings. Moreover, we apply the algorithms to scalar multiplication on elliptic curves, and analyze their computational complexity. As a result of their implementation with respect to affine (resp. weighted projective) coordinates, we achieved an increased performance factor of 1.45 (45{\%}) (resp. 1.15 (15{\%})) in the scalar multiplication of the elliptic curve of size 160bit.",
author = "Yasuyuki Sakai and Kouichi Sakurai",
year = "2000",
month = "1",
day = "1",
doi = "10.1007/10718964_6",
language = "English",
isbn = "3540677429",
series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",
publisher = "Springer Verlag",
pages = "59--73",
editor = "Ed Dawson and Andrew Clark and Colin Boyd",
booktitle = "Information Security and Privacy - 5th Australasian Conference, ACISP 2000, Proceedings",
address = "Germany",

}

TY - GEN

T1 - Efficient scalar multiplications on elliptic curves without repeated doublings and their practical performance

AU - Sakai, Yasuyuki

AU - Sakurai, Kouichi

PY - 2000/1/1

Y1 - 2000/1/1

N2 - We introduce efficient algorithms for scalar multiplication on elliptic curves defined over 1Fp. The algorithms compute 2fc P directly from P, where P is a random point on an elliptic curve, without computing the intermediate points, which is faster than k repeated doublings. Moreover, we apply the algorithms to scalar multiplication on elliptic curves, and analyze their computational complexity. As a result of their implementation with respect to affine (resp. weighted projective) coordinates, we achieved an increased performance factor of 1.45 (45%) (resp. 1.15 (15%)) in the scalar multiplication of the elliptic curve of size 160bit.

AB - We introduce efficient algorithms for scalar multiplication on elliptic curves defined over 1Fp. The algorithms compute 2fc P directly from P, where P is a random point on an elliptic curve, without computing the intermediate points, which is faster than k repeated doublings. Moreover, we apply the algorithms to scalar multiplication on elliptic curves, and analyze their computational complexity. As a result of their implementation with respect to affine (resp. weighted projective) coordinates, we achieved an increased performance factor of 1.45 (45%) (resp. 1.15 (15%)) in the scalar multiplication of the elliptic curve of size 160bit.

UR - http://www.scopus.com/inward/record.url?scp=23044517520&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=23044517520&partnerID=8YFLogxK

U2 - 10.1007/10718964_6

DO - 10.1007/10718964_6

M3 - Conference contribution

SN - 3540677429

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 59

EP - 73

BT - Information Security and Privacy - 5th Australasian Conference, ACISP 2000, Proceedings

A2 - Dawson, Ed

A2 - Clark, Andrew

A2 - Boyd, Colin

PB - Springer Verlag

ER -