Paper 2005/166
Tate pairing computation on the divisors of hyperelliptic curves for cryptosystems
Eunjeong Lee and 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.
Note: Minor corrections have been made.
Metadata
- Available format(s)
-
PDF
- Publication info
- Published elsewhere. Unknown where it was published
- Keywords
- Tate pairing computationhyperelliptic curve cryptosystemspairing-based cryptosystems
- Contact author(s)
- ejlee @ kias re kr
- History
- 2005-08-22: last of 2 revisions
- 2005-06-06: received
- See all versions
- Short URL
- https://ia.cr/2005/166
- License
-
CC BY
BibTeX
@misc{cryptoeprint:2005/166,
author = {Eunjeong Lee and Yoonjin Lee},
title = {Tate pairing computation on the divisors of hyperelliptic curves for cryptosystems},
howpublished = {Cryptology ePrint Archive, Paper 2005/166},
year = {2005},
note = {\url{https://eprint.iacr.org/2005/166}},
url = {https://eprint.iacr.org/2005/166}
}
