On the power of multidoubling in speeding up elliptic scalar multiplication

Yasuyuki Sakai, Kouichi Sakurai

Research output: Chapter in Book/Report/Conference proceedingConference 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 languageEnglish
Title of host publicationSelected Areas in Cryptography - 8th Annual International Workshop, SAC 2001, Revised Papers
EditorsSerge Vaudenay, Amr M. Youssef
PublisherSpringer Verlag
Pages268-283
Number of pages16
ISBN (Print)9783540430667
Publication statusPublished - Jan 1 2001
Event8th Annual International Workshop on Selected Areas in Cryptography, SAC 2001 - Toronto, Canada
Duration: Aug 16 2001Aug 17 2001

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume2259
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other8th Annual International Workshop on Selected Areas in Cryptography, SAC 2001
CountryCanada
CityToronto
Period8/16/018/17/01

Fingerprint

Scalar multiplication
Elliptic Curves
Galois field
Computational complexity
Doubling
Computational Complexity
Denote
Computing
Form

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

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.

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 proceedingConference 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.
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)).
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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