### 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 |
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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) |
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Volume | 1841 |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 5th Australasian Conference on Information Security and Privacy, ACISP 2000 |
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Country | Australia |

City | Brisbane |

Period | 7/10/00 → 7/12/00 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Computer Science(all)

### Cite this

*Information Security and Privacy - 5th Australasian Conference, ACISP 2000, Proceedings*(pp. 59-73). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 1841). Springer Verlag. https://doi.org/10.1007/10718964_6

**Efficient scalar multiplications on elliptic curves without repeated doublings and their practical performance.** / Sakai, Yasuyuki; Sakurai, Kouichi.

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

*Information Security and Privacy - 5th Australasian Conference, ACISP 2000, Proceedings.*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 1841, Springer Verlag, pp. 59-73, 5th Australasian Conference on Information Security and Privacy, ACISP 2000, Brisbane, Australia, 7/10/00. https://doi.org/10.1007/10718964_6

}

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 -