A relation between group order of elliptic curve and extension degree of definition field

Taichi Sumo, Yuki Mori, Yasuyuki Nogami, Tomoko Matsushima, Satoshi Uehara

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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 qri ) is divisible by r 2i and it has the torsion structure denoted by Z ri Z ri 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 languageEnglish
Title of host publication2012 World Telecommunications Congress, WTC 2012
Publication statusPublished - May 4 2012
Event2012 World Telecommunications Congress, WTC 2012 - Miyazaki, Japan
Duration: Mar 5 2012Mar 6 2012

Publication series

Name2012 World Telecommunications Congress, WTC 2012

Other

Other2012 World Telecommunications Congress, WTC 2012
CountryJapan
CityMiyazaki
Period3/5/123/6/12

ASJC Scopus subject areas

  • Computer Networks and Communications

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    Sumo, T., Mori, Y., Nogami, Y., Matsushima, T., & Uehara, S. (2012). A relation between group order of elliptic curve and extension degree of definition field. In 2012 World Telecommunications Congress, WTC 2012 [6170444] (2012 World Telecommunications Congress, WTC 2012).