| 概要 | In the area of cryptography, it is an important problem to find a fast
algorithm to compute pairings on curves such as the Weil and
Tate-Lichtenbaum pairings. Recently, Stange proposed a new algorithm to
compute the Tate(-Lichtenbaum) pairing on an elliptic curve. This
algorithm
is based on elliptic nets, which are also defined by Stange as a
generalization of elliptic divisibility sequences. In this talk, we define
hyperelliptic nets as a generalization of elliptic nets to hyperelliptic
curves. We also give an expression for the Tate-Lichtenbaum pairing on a
hyperelliptic curve in terms of hyperelliptic nets. Using this expression,
we give an algorithm to compute the Tate-Lichtenbaum pairing on a curve of
genus 2. |