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

Ryuichi Harasawa; Yutaka Sueyoshi; Aichi Kudo

Paper 2006/202

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

Ryuichi Harasawa, Yutaka Sueyoshi, and Aichi Kudo

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.

Note: We add the cost of the Ate pairing.

Metadata

Available format(s): PDF PS
Publication info: Published elsewhere. 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.
Keywords: Tate Ate pairing Hyperelliptic curves
Contact author(s): harasawa @ cis nagasaki-u ac jp
History: 2008-01-09: last of 2 revisions; 2006-06-20: received; See all versions
Short URL: https://ia.cr/2006/202
License: CC BY

BibTeX

@misc{cryptoeprint:2006/202,
      author = {Ryuichi Harasawa and Yutaka Sueyoshi and Aichi Kudo},
      title = {Ate pairing for $y^{2}=x^{5}-\alpha x$ in characteristic five},
      howpublished = {Cryptology {ePrint} Archive, Paper 2006/202},
      year = {2006},
      url = {https://eprint.iacr.org/2006/202}
}