Efficient Tate Pairing Computation for Elliptic Curves over Binary Fields

In this paper, we present a closed formula for the Tate pairing computation for supersingular elliptic curves defined over the binary field \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathbb F_{2^m}$\end{document} of odd dimension. There are exactly three isomorphism classes of supersingular elliptic curves over \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathbb F_{2^m}$\end{document} for odd m and our result is applicable to all these curves.