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