Welcome to the resource topic for 2006/125
Title:
Fast computation of Tate pairing on general divisors of genus 3 hyperelliptic curves
Authors: Eunjeong Lee, Hyang-Sook Lee, Yoonjin Lee
Abstract:For the Tate pairing computation over hyperelliptic
curves, there are developments by Duursma-Lee and Barreto et al.,
and those computations are focused on {\it degenerate} divisors.
As divisors are not degenerate form in general, it is necessary to
find algorithms on {\it general} divisors for the Tate pairing
computation. In this paper, we present two efficient methods for
computing the Tate pairing over divisor class groups of the
hyperelliptic curves y^2 = x^p - x + d, ~ d = \pm 1 of genus 3.
First, we provide the {\it pointwise} method, which is a
generalization of the previous developments by Duursma-Lee and
Barreto et al. In the second method, we use the {\it resultant}
for the Tate pairing computation. According to our theoretical
analysis of the complexity, the {\it resultant} method is 48.5
\% faster than the pointwise method in the best case and 15.3
\% faster in the worst case, and our implementation result shows
that the {\it resultant} method is much faster than the pointwise
method. These two methods are completely general in the sense that
they work for general divisors with Mumford representation, and
they provide very explicit algorithms.
ePrint: https://eprint.iacr.org/2006/125
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