International Association for Cryptologic Research

International Association
for Cryptologic Research

CryptoDB

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

Authors:
Ryuichi Harasawa
Yutaka Sueyoshi
Aichi Kudo
Download:
URL: http://eprint.iacr.org/2006/202
Search ePrint
Search Google
Abstract: 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
}