Tate pairing computation on the divisors of hyperelliptic curves for cryptosystems

Eunjeong Lee; Yoonjin Lee

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 computation hyperelliptic curve cryptosystems pairing-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},
      url = {https://eprint.iacr.org/2005/166}
}