Eunjeong Lee

Efficient identity-based authenticated key agreement protocol from pairings

Since Boneh and Franklin [Advances in cryptology--CRYPTO LNCS 2139 (2001) 213] gave the first feasible solutions for identity-based encryption using Weil pairing on elliptic curves, many identity-based key agreement protocols and signature schemes using bilinear pairing have been suggested. As argued in [Designs, Codes and Cryptography 28 (2003) 119], secure and efficient key agreement protocols should provide certain security attributes and low communication overhead. The communication overhead depends on the number of key components transmitted by each entity. Until now, there is no secure two-pass ID-based authenticated key agreement protocol, which provides perfect secrecy and transmits only one key component. Here, we propose a few ID-based authenticated key agreement protocols based on a bilinear pairing. Our final protocol is a two-pass authenticated key agreement protocol with required security attributes and minimal communication overhead.

Implementation of Tate Pairing on Hyperelliptic Curves of Genus 2

Since Tate pairing was suggested to construct a cryptosystem, fast computation of Tate pairing has been researched recently. Barreto et. al [3] and Galbraith [8] provided efficient algorithms for Tate pairing on y 2=x 3-x+b in characteristic 3 and Duursma and Lee [6] gave a closed formula for Tate pairing on y 2=x p -x+d in characteristic p. In this paper, we present completely general and explicit formulae for computing of Tate pairing on hyperelliptic curves of genus 2. We have computed Tate parings on a supersingular hyperelliptic curve over prime fields and the detailed algorithms are explained. This is the first attempt to present the implementation results for Tate pairing on a hyperelliptic curve of genus bigger than 1.