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
TateAte pairingHyperelliptic 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
Creative Commons Attribution
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},
      note = {\url{https://eprint.iacr.org/2006/202}},
      url = {https://eprint.iacr.org/2006/202}
}
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