## CryptoDB

### Paper: Ate pairing for $y^{2}=x^{5}-\alpha x$ in characteristic five

Authors: Ryuichi Harasawa Yutaka Sueyoshi Aichi Kudo URL: http://eprint.iacr.org/2006/202 Search ePrint Search Google Recently, the authors proposed a method for computing the Tate pairing using a distortion map for $y^{2}=x^{5} -\alpha x$ ($\alpha = \pm2$) over finite fields of characteristic five. In this paper, we show the Ate pairing, an invariant of the Tate pairing, can be applied to this curve. This leads to about $50\%$ computational cost-saving over the Tate pairing.
##### BibTeX
@misc{eprint-2006-21695,
title={Ate pairing for $y^{2}=x^{5}-\alpha x$ in characteristic five},
booktitle={IACR Eprint archive},
keywords={Tate/Ate pairing, Hyperelliptic curves},
url={http://eprint.iacr.org/2006/202},
note={The full version, entitled "Tate and Ate Pairings for $y^{2} = x^{5} - \alpha x$ in Characteristic Five", is published in Japan Journal of Industrial and Applied Mathematics (JJIAM), Vol. 24, No. 3, pp. 251 - 274, 2007. harasawa@cis.nagasaki-u.ac.jp 13887},
author={Ryuichi Harasawa and Yutaka Sueyoshi and Aichi Kudo},
year=2006
}