Integer Variable chi-Based Ate Pairing. - Yasuyuki Nogami; Masataka Akane; Yumi Sakemi; Hidehiro Katou; Yoshitaka Morikawa (Pairing, 2008)

Fast Ate Pairing Computation of Embedding Degree 12 Using Subfield-Twisted Elliptic Curve. - Masataka Akane; Yasuyuki Nogami; Yoshitaka Morikawa (IEICE Trans. Fundam. Electron. Commun. Comput. Sci., 2009)

Integer Variable chi-Based Cross Twisted Ate Pairing and Its Optimization for Barreto-Naehrig Curve. - Yasuyuki Nogami; Yumi Sakemi; Hidehiro Kato; Masataka Akane; Yoshitaka Morikawa (IEICE Trans. Fundam. Electron. Commun. Comput. Sci., 2009)

Scalar Multiplication Using Frobenius Expansion over Twisted Elliptic Curve for Ate Pairing Based Cryptography. - Yasuyuki Nogami; Yumi Sakemi; Takumi Okimoto; Kenta Nekado; Masataka Akane; Yoshitaka Morikawa (IEICE Trans. Fundam. Electron. Commun. Comput. Sci., 2009)