Abstract
Since Tate pairing was suggested to construct a cryptosystem, fast computation of Tate pairing has been researched recently. Barreto et. al [3] and Galbraith [8] provided efficient algorithms for Tate pairing on y 2=x 3-x+b in characteristic 3 and Duursma and Lee [6] gave a closed formula for Tate pairing on y 2=x p -x+d in characteristic p. In this paper, we present completely general and explicit formulae for computing of Tate pairing on hyperelliptic curves of genus 2. We have computed Tate parings on a supersingular hyperelliptic curve over prime fields and the detailed algorithms are explained. This is the first attempt to present the implementation results for Tate pairing on a hyperelliptic curve of genus bigger than 1.
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