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

doi:10.1007/3-540-45861-1_32

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

Mathematical Informatics

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

27 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 language	English
Title of host publication	Information Security and Cryptology - ICISC 2001 - 4th International Conference, Proceedings
Editors	Kwangjo Kim
Publisher	Springer Verlag
Pages	428-439
Number of pages	12
ISBN (Print)	3540433198, 9783540433194
DOIs	https://doi.org/10.1007/3-540-45861-1_32
Publication status	Published - 2002
Event	4th International Conference on Information Security and Cryptology, ICISC 2001 - Seoul, Korea, Republic of Duration: Dec 6 2001 → Dec 7 2001

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	2288
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Other

Other	4th International Conference on Information Security and Cryptology, ICISC 2001
Country/Territory	Korea, Republic of
City	Seoul
Period	12/6/01 → 12/7/01

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
Computer Science(all)

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10.1007/3-540-45861-1_32

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 K. Kim (Ed.), Information Security and Cryptology - ICISC 2001 - 4th International Conference, Proceedings (pp. 428-439). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 2288). Springer Verlag. https://doi.org/10.1007/3-540-45861-1_32

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. ed. / Kwangjo Kim. 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 proceeding › Conference 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 K Kim (ed.), Information Security and Cryptology - ICISC 2001 - 4th International Conference, Proceedings. 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. https://doi.org/10.1007/3-540-45861-1_32

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 Kim K, editor, Information Security and Cryptology - ICISC 2001 - 4th International Conference, Proceedings. Springer Verlag. 2002. p. 428-439. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/3-540-45861-1_32

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. editor / Kwangjo Kim. Springer Verlag, 2002. pp. 428-439 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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

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