Seminar

Language English
From 2012/01/20 10:30
To 2012/01/20 12:00
PlaceRoom 152, Building No.3, Faculty of Science, Kyoto University
Seminar NameAlgebra Geometrical Seminar
Title The Tate-Lichtenbaum pairing on a hyperelliptic curve via hyperelliptic nets　
Field Algebra
Geometry
SpeakersYukihiro Uchida
AffiliationKyoto
AbstractIn 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.
Linkhttp://www.math.kyoto-u.ac.jp/~mhyo/agsem/agseminar.html