On the power of multidoubling in speeding up elliptic scalar multiplication

Yasuyuki Sakai; Kouichi Sakurai

doi:10.1007/3-540-45537-x_21

On the power of multidoubling in speeding up elliptic scalar multiplication

Yasuyuki Sakai, Kouichi Sakurai

Mathematical Informatics

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

1 Citation (Scopus)

Abstract

We discuss multidoubling methods for efficient elliptic scalar multiplication. The methods allows computation of 2kP directly from P without computing the intermediate points, where P denotes a randomly selected point on an elliptic curve. We introduce algorithms for elliptic curves with Montgomery form and Weierstrass form defined over finite fields with characteristic greater than 3 in terms of affine coordinates. These algorithms are faster than k repeated doublings. Moreover, we apply the algorithms to scalar multiplication on elliptic curves and analyze computational complexity. As a result of our implementation with respect to the Montgomery and Weierstrass forms in terms of affine coordinates, we achieved running time reduced by 28% and 31%, respectively, in the scalar multiplication of an elliptic curve of size 160-bit over finite fields with characteristic greater than 3.

Original language	English
Title of host publication	Selected Areas in Cryptography - 8th Annual International Workshop, SAC 2001, Revised Papers
Editors	Serge Vaudenay, Amr M. Youssef
Publisher	Springer Verlag
Pages	268-283
Number of pages	16
ISBN (Print)	9783540430667
DOIs	https://doi.org/10.1007/3-540-45537-x_21
Publication status	Published - 2001
Event	8th Annual International Workshop on Selected Areas in Cryptography, SAC 2001 - Toronto, Canada Duration: Aug 16 2001 → Aug 17 2001

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	2259
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Other

Other	8th Annual International Workshop on Selected Areas in Cryptography, SAC 2001
Country/Territory	Canada
City	Toronto
Period	8/16/01 → 8/17/01

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
Computer Science(all)

Access to Document

10.1007/3-540-45537-x_21

Cite this

Sakai, Y., & Sakurai, K. (2001). On the power of multidoubling in speeding up elliptic scalar multiplication. In S. Vaudenay, & A. M. Youssef (Eds.), Selected Areas in Cryptography - 8th Annual International Workshop, SAC 2001, Revised Papers (pp. 268-283). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 2259). Springer Verlag. https://doi.org/10.1007/3-540-45537-x_21

On the power of multidoubling in speeding up elliptic scalar multiplication. / Sakai, Yasuyuki; Sakurai, Kouichi.

Selected Areas in Cryptography - 8th Annual International Workshop, SAC 2001, Revised Papers. ed. / Serge Vaudenay; Amr M. Youssef. Springer Verlag, 2001. p. 268-283 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 2259).

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

Sakai, Y & Sakurai, K 2001, On the power of multidoubling in speeding up elliptic scalar multiplication. in S Vaudenay & AM Youssef (eds), Selected Areas in Cryptography - 8th Annual International Workshop, SAC 2001, Revised Papers. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 2259, Springer Verlag, pp. 268-283, 8th Annual International Workshop on Selected Areas in Cryptography, SAC 2001, Toronto, Canada, 8/16/01. https://doi.org/10.1007/3-540-45537-x_21

Sakai Y, Sakurai K. On the power of multidoubling in speeding up elliptic scalar multiplication. In Vaudenay S, Youssef AM, editors, Selected Areas in Cryptography - 8th Annual International Workshop, SAC 2001, Revised Papers. Springer Verlag. 2001. p. 268-283. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/3-540-45537-x_21

Sakai, Yasuyuki ; Sakurai, Kouichi. / On the power of multidoubling in speeding up elliptic scalar multiplication. Selected Areas in Cryptography - 8th Annual International Workshop, SAC 2001, Revised Papers. editor / Serge Vaudenay ; Amr M. Youssef. Springer Verlag, 2001. pp. 268-283 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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On the power of multidoubling in speeding up elliptic scalar multiplication

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