On the Number of the Pairing-friendly Curves

MI: Global COE Program Education-and-Research Hub for Mathematics-for-IndustryグローバルCOEプログラム「マス･フォア･インダストリ教育研究拠点」In pairing-based cryptography, it is necessary to choose an elliptic curve with a small embedding degree and a large prime-order subgroup, which is called a “pairing-friendly curve”. In this paper, we study the number of the pairing-friendly curves with a given large prime-order subgroup