Elliptic curves with a pre-determined embedding degree

Authors:
Shoujirou Hirasawa;Atsuko Miyaji
Affiliations:
Japan Advanced Institute of Science and Technology, Nomi, Ishikawa, Japan;Japan Advanced Institute of Science and Technology, Nomi, Ishikawa, Japan
Venue:
ISIT'09 Proceedings of the 2009 IEEE international conference on Symposium on Information Theory - Volume 4
Year:
2009

Citing 4
Cited 0

Identity-Based Encryption from the Weil Pairing

SIAM Journal on Computing
Constructing pairing-friendly elliptic curves with embedding degree 10

ANTS'06 Proceedings of the 7th international conference on Algorithmic Number Theory
Pairing-Friendly elliptic curves of prime order

SAC'05 Proceedings of the 12th international conference on Selected Areas in Cryptography
On the minimal embedding field

Pairing'07 Proceedings of the First international conference on Pairing-Based Cryptography

Quantified Score

Hi-index	0.00

Visualization

Abstract

A pairing over an elliptic curve E(Fpm) to an extension field of Fpmk has begun to be attractive in cryptosystems, where k is called the embedding degree. The cryptosystems using a pairing are called the pairing-based cryptosystems. The embedding degree k is also an indicator of the relationship between the elliptic curve Discrete Logarithm Problem (ECDLP) and the Discrete Logarithm Problem (DLP), where ECDLP over E(Fpm) is reduced to DLP over Fpmk. An elliptic curve is determined by j-invariant or order, however the explicit condition between these parameters and an embedding degree has been described only in some degrees. In this paper, we investigate a new condition of the existence of elliptic curves with pre-determined embedding degrees, and present some examples of the elliptic curves over 160-bit, 192-bit and 224-bit Fpm.