[Resource Topic] 2006/114: Tate pairing for $y^{2}=x^{5}-\alpha x$ in Characteristic Five

Welcome to the resource topic for 2006/114

Tate pairing for y^{2}=x^{5}-\alpha x in Characteristic Five

Authors: Ryuichi Harasawa, Yutaka Sueyoshi, Aichi Kudo


In this paper, for the genus-2 hyperelliptic curve
y^{2}=x^{5} -\alpha x (\alpha = \pm2) defined over finite fields of characteristic five,
we construct a distortion map explicitly, and show the map indeed
gives an input for which the value of the Tate pairing is not trivial.
Next we describe a computation of the Tate pairing
by using the proposed distortion map.
Furthermore, we also see that this type of curve
is equipped with a simple quintuple operation on the Jacobian group,
which leads to giving an improvement for computing the Tate pairing.
We indeed show that, for the computation of the Tate pairing
for genus-2 hyperelliptic curves,
our method is about twice as efficient as a previous work.

ePrint: https://eprint.iacr.org/2006/114

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