A fast scalar multiplication method with randomized projective coordinates on a Montgomery-form elliptic curve secure against side channel attacks

Katsuyuki Okeya, Kunihiko Miyazaki, Kouichi Sakurai

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

23 Citations (Scopus)

Abstract

In this paper, we propose a scalar multiplication method that does not incur a higher computational cost for randomized projective coordinates of the Montgomery form of elliptic curves. A randomized projective coordinates method is a countermeasure against side channel attacks on an elliptic curve cryptosystem in which an attacker cannot predict the appearance of a specific value because the coordinates have been randomized. However, because of this randomization, we cannot assume the Z-coordinate to be 1. Thus, the computational cost increases by multiplications of Z-coordinates, 10%. Our results clarify the advantages of cryptographic usage of Montgomery-form elliptic curves in constrained environments such as mobile devices and smart cards.

Original languageEnglish
Title of host publicationInformation Security and Cryptology - ICISC 2001 - 4th International Conference, Proceedings
PublisherSpringer Verlag
Pages428-439
Number of pages12
Volume2288
ISBN (Print)3540433198, 9783540433194
Publication statusPublished - 2002
Event4th International Conference on Information Security and Cryptology, ICISC 2001 - Seoul, Korea, Republic of
Duration: Dec 6 2001Dec 7 2001

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume2288
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other4th International Conference on Information Security and Cryptology, ICISC 2001
CountryKorea, Republic of
CitySeoul
Period12/6/0112/7/01

Fingerprint

Scalar multiplication
Side Channel Attacks
Elliptic Curves
Smart cards
Mobile devices
Cryptography
Costs
Computational Cost
Elliptic Curve Cryptosystem
Smart Card
Countermeasures
Randomisation
Mobile Devices
Multiplication
Form
Side channel attack
Predict

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

Cite this

Okeya, K., Miyazaki, K., & Sakurai, K. (2002). A fast scalar multiplication method with randomized projective coordinates on a Montgomery-form elliptic curve secure against side channel attacks. In Information Security and Cryptology - ICISC 2001 - 4th International Conference, Proceedings (Vol. 2288, pp. 428-439). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 2288). Springer Verlag.

A fast scalar multiplication method with randomized projective coordinates on a Montgomery-form elliptic curve secure against side channel attacks. / Okeya, Katsuyuki; Miyazaki, Kunihiko; Sakurai, Kouichi.

Information Security and Cryptology - ICISC 2001 - 4th International Conference, Proceedings. Vol. 2288 Springer Verlag, 2002. p. 428-439 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 2288).

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

Okeya, K, Miyazaki, K & Sakurai, K 2002, A fast scalar multiplication method with randomized projective coordinates on a Montgomery-form elliptic curve secure against side channel attacks. in Information Security and Cryptology - ICISC 2001 - 4th International Conference, Proceedings. vol. 2288, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 2288, Springer Verlag, pp. 428-439, 4th International Conference on Information Security and Cryptology, ICISC 2001, Seoul, Korea, Republic of, 12/6/01.
Okeya K, Miyazaki K, Sakurai K. A fast scalar multiplication method with randomized projective coordinates on a Montgomery-form elliptic curve secure against side channel attacks. In Information Security and Cryptology - ICISC 2001 - 4th International Conference, Proceedings. Vol. 2288. Springer Verlag. 2002. p. 428-439. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
Okeya, Katsuyuki ; Miyazaki, Kunihiko ; Sakurai, Kouichi. / A fast scalar multiplication method with randomized projective coordinates on a Montgomery-form elliptic curve secure against side channel attacks. Information Security and Cryptology - ICISC 2001 - 4th International Conference, Proceedings. Vol. 2288 Springer Verlag, 2002. pp. 428-439 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
@inproceedings{5655525af3434f13ba8e89748175758f,
title = "A fast scalar multiplication method with randomized projective coordinates on a Montgomery-form elliptic curve secure against side channel attacks",
abstract = "In this paper, we propose a scalar multiplication method that does not incur a higher computational cost for randomized projective coordinates of the Montgomery form of elliptic curves. A randomized projective coordinates method is a countermeasure against side channel attacks on an elliptic curve cryptosystem in which an attacker cannot predict the appearance of a specific value because the coordinates have been randomized. However, because of this randomization, we cannot assume the Z-coordinate to be 1. Thus, the computational cost increases by multiplications of Z-coordinates, 10{\%}. Our results clarify the advantages of cryptographic usage of Montgomery-form elliptic curves in constrained environments such as mobile devices and smart cards.",
author = "Katsuyuki Okeya and Kunihiko Miyazaki and Kouichi Sakurai",
year = "2002",
language = "English",
isbn = "3540433198",
volume = "2288",
series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",
publisher = "Springer Verlag",
pages = "428--439",
booktitle = "Information Security and Cryptology - ICISC 2001 - 4th International Conference, Proceedings",
address = "Germany",

}

TY - GEN

T1 - A fast scalar multiplication method with randomized projective coordinates on a Montgomery-form elliptic curve secure against side channel attacks

AU - Okeya, Katsuyuki

AU - Miyazaki, Kunihiko

AU - Sakurai, Kouichi

PY - 2002

Y1 - 2002

N2 - In this paper, we propose a scalar multiplication method that does not incur a higher computational cost for randomized projective coordinates of the Montgomery form of elliptic curves. A randomized projective coordinates method is a countermeasure against side channel attacks on an elliptic curve cryptosystem in which an attacker cannot predict the appearance of a specific value because the coordinates have been randomized. However, because of this randomization, we cannot assume the Z-coordinate to be 1. Thus, the computational cost increases by multiplications of Z-coordinates, 10%. Our results clarify the advantages of cryptographic usage of Montgomery-form elliptic curves in constrained environments such as mobile devices and smart cards.

AB - In this paper, we propose a scalar multiplication method that does not incur a higher computational cost for randomized projective coordinates of the Montgomery form of elliptic curves. A randomized projective coordinates method is a countermeasure against side channel attacks on an elliptic curve cryptosystem in which an attacker cannot predict the appearance of a specific value because the coordinates have been randomized. However, because of this randomization, we cannot assume the Z-coordinate to be 1. Thus, the computational cost increases by multiplications of Z-coordinates, 10%. Our results clarify the advantages of cryptographic usage of Montgomery-form elliptic curves in constrained environments such as mobile devices and smart cards.

UR - http://www.scopus.com/inward/record.url?scp=84949949652&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84949949652&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:84949949652

SN - 3540433198

SN - 9783540433194

VL - 2288

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

SP - 428

EP - 439

BT - Information Security and Cryptology - ICISC 2001 - 4th International Conference, Proceedings

PB - Springer Verlag

ER -