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 et.al. and by Galbraith et.al. 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

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

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