### 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 |
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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 |

Publication status | Published - Jan 1 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) |
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Volume | 2259 |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 8th Annual International Workshop on Selected Areas in Cryptography, SAC 2001 |
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Country | Canada |

City | Toronto |

Period | 8/16/01 → 8/17/01 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Computer Science(all)

### Cite this

*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.

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

*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.

}

TY - GEN

T1 - On the power of multidoubling in speeding up elliptic scalar multiplication

AU - Sakai, Yasuyuki

AU - Sakurai, Kouichi

PY - 2001/1/1

Y1 - 2001/1/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84949222913&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84949222913&partnerID=8YFLogxK

M3 - Conference contribution

SN - 9783540430667

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 268

EP - 283

BT - Selected Areas in Cryptography - 8th Annual International Workshop, SAC 2001, Revised Papers

A2 - Vaudenay, Serge

A2 - Youssef, Amr M.

PB - Springer Verlag

ER -