Cryptology ePrint Archive: Report 2003/053

Tate-pairing implementations for tripartite key agreement

Iwan Duursma and Hyang-Sook Lee

Abstract: We give a closed formula for the Tate-pairing on the hyperelliptic curve $y^2 = x^p - x + d$ in characteristic $p$. This improves recent implementations by Barreto and by Galbraith for the special case $p=3$. As an application, we propose a $n$-round key agreement protocol for up to $3^n$ participants by extending Joux's pairing-based protocol to $n$ rounds.

Category / Keywords: public-key cryptography / elliptic curve cryptosystem, Tate-pairing implementation, bilinear Diffie-Hellman problem, group key

Date: received 16 Mar 2003

Contact author: duursma at math uiuc edu

Available format(s): Postscript (PS) | Compressed Postscript (PS.GZ) | BibTeX Citation

Version: 20030318:060637 (All versions of this report)

Short URL:

[ Cryptology ePrint archive ]