Welcome to the resource topic for 2005/166
Title:
Tate pairing computation on the divisors of hyperelliptic curves for cryptosystems
Authors: Eunjeong Lee, Yoonjin Lee
Abstract:In recent papers \cite{Bar05} and \cite{CKL}, Barreto et al and Choie et al worked on hyperelliptic curves H_b defined by y^2+y = x^5 + x^3 + b over a finite field \Ftn with b=0 or 1 for a secure and efficient pairing-based cryptosystems. We find a completely general method for computing the Tate-pairing over divisor class groups of the curves H_b in a very explicit way. In fact, the Tate-pairing is defined over the entire divisor class group of a curve, not only over the points on a curve. So far only pointwise approach has been made in ~\cite{Bar05} and ~\cite{CKL} for the Tate-pairing computation on the hyperelliptic curves H_b over \Ftn. Furthermore, we obtain a very efficient algorithm for the Tate pairing computation over divisors by reducing the cost of computing. We also find a crucial condition for divisor class group of hyperelliptic curve to have a significant reduction of the loop cost in the Tate pairing computation.
ePrint: https://eprint.iacr.org/2005/166
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