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 y2 = x3 - x + b in characteristic 3 and Duursma and Lee[6] gave a closed formula for Tate pairing on y2 = xP - 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. © Springer-Verlag 2004.
CITATION STYLE
Choie, Y., & Lee, E. (2004). Implementation of tate pairing on hyperelliptic curves of genus 2. Lecture Notes in Computer Science (Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 2971, 97–111. https://doi.org/10.1007/978-3-540-24691-6_9
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