Tate-Pairing Implementations for Tripartite Key Agreement

We give a closed formula for the Tate-pairing on the hyperelliptic curve y 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 participants by extending Joux's pairing-based protocol to n rounds