Tate and Ate pairings for y2 =x5−αx in characteristic five

DOI IR IR (HANDLE) HANDLE 1 Citations 41 References

Search this article

Description

In this paper, we consider the Tate and Ate pairings for the genus-2 supersingular hyperelliptic curves y2=x5−αx (α=±2) defined over finite fields of characteristic five. More precisely, we construct a distortion map explicitly, and show that the map indeed gives an input for which the value of the Tate pairing is not trivial. We next describe a computation of the Tate pairing by using the proposed distortion map. We also see that this type of curve is equipped with a simple quintuple operation on the Jacobian group, which leads to an improvement for computing the Tate pairing. We further show the Ate pairing, a variant of the Tate pairing for elliptic curves, can be applied to this curve. The Ate pairing yields an algorithm which is about 50% more efficient than the Tate pairing in this case.

Journal

Citations (1)*help

See more

References(41)*help

See more

Keywords

Details 詳細情報について

Report a problem

Back to top