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 language | English |
|---|---|
| Title of host publication | Information Security and Privacy - 5th Australasian Conference, ACISP 2000, Proceedings |
| Editors | Ed Dawson, Andrew Clark, Colin Boyd |
| Publisher | Springer Verlag |
| Pages | 59-73 |
| Number of pages | 15 |
| ISBN (Print) | 3540677429 |
| DOIs | |
| Publication status | Published - Jan 1 2000 |
| Event | 5th Australasian Conference on Information Security and Privacy, ACISP 2000 - Brisbane, Australia Duration: Jul 10 2000 → Jul 12 2000 |
Publication series
| Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
|---|---|
| Volume | 1841 |
| ISSN (Print) | 0302-9743 |
| ISSN (Electronic) | 1611-3349 |
Other
| Other | 5th Australasian Conference on Information Security and Privacy, ACISP 2000 |
|---|---|
| Country | Australia |
| City | Brisbane |
| Period | 7/10/00 → 7/12/00 |
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All Science Journal Classification (ASJC) codes
- Theoretical Computer Science
- Computer Science(all)
Cite this
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 proceeding › Conference contribution
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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 -