### Abstract

Recent innovative public key cryptographic applications such as ID-based cryptography are based on pairing cryptography. They efficiently use some torsion group structures constructed on certain elliptic curves defined over finite fields. For this purpose, this paper shows that a relation between group order of elliptic curve and extension degree of definition field especially from the viewpoint of torsion structure for pairing- based cryptographic use. In detail, it is shown that the order of elliptic curve over r ^{i}-th extension field denoted by #E(F _{q}ri ) is divisible by r ^{2i} and it has the torsion structure denoted by Z _{r}i Z _{r}i when the base order of elliptic curve denoted by #E(Fq) is divisible by r^i and the order of the multiplicative group of the definition field is also divisible by r^i, where r denotes the order of one cyclic group in the torsion structure.

Original language | English |
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Title of host publication | 2012 World Telecommunications Congress, WTC 2012 |

Publication status | Published - May 4 2012 |

Event | 2012 World Telecommunications Congress, WTC 2012 - Miyazaki, Japan Duration: Mar 5 2012 → Mar 6 2012 |

### Publication series

Name | 2012 World Telecommunications Congress, WTC 2012 |
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### Other

Other | 2012 World Telecommunications Congress, WTC 2012 |
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Country | Japan |

City | Miyazaki |

Period | 3/5/12 → 3/6/12 |

### ASJC Scopus subject areas

- Computer Networks and Communications

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## Cite this

*2012 World Telecommunications Congress, WTC 2012*[6170444] (2012 World Telecommunications Congress, WTC 2012).