On security proof of McCullagh Barreto's key agreement protocol and its variants

McCullagh and Barreto presented an identity-based key agreement protocol in CT-RSA 2005. Later McCullagh-Barreto and Xie proposed two variants of the protocol respectively. Due to using the Sakai-Kasahara key construction, these protocols achieve the best performance among this type of protocols. However, the security of the schemes was in doubt. In this paper, the errors in the existing security analyses of the schemes were first point out and then the McCullagh-Barreto's second protocol was slightly tweaked and formally proved based on a reasonable assumption. The formal analyse builds strong confidence in the security of the new scheme particularly for standardisation.