Cryptology ePrint Archive: Report 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.

Category / Keywords: Tate/Ate pairing, Hyperelliptic curves

Publication Info: 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.

Date: received 20 Jun 2006, last revised 9 Jan 2008

Contact author: harasawa at cis nagasaki-u ac jp

Available format(s): Postscript (PS) | Compressed Postscript (PS.GZ) | PDF | BibTeX Citation

Note: We add the cost of the Ate pairing.

Version: 20080109:103057 (All versions of this report)

Short URL: ia.cr/2006/202