TY - GEN

T1 - A relation between group order of elliptic curve and extension degree of definition field

AU - Sumo, Taichi

AU - Mori, Yuki

AU - Nogami, Yasuyuki

AU - Matsushima, Tomoko

AU - Uehara, Satoshi

PY - 2012/5/4

Y1 - 2012/5/4

N2 - 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.

AB - 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.

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M3 - Conference contribution

AN - SCOPUS:84860365569

SN - 9784885522574

T3 - 2012 World Telecommunications Congress, WTC 2012

BT - 2012 World Telecommunications Congress, WTC 2012

T2 - 2012 World Telecommunications Congress, WTC 2012

Y2 - 5 March 2012 through 6 March 2012

ER -