In this paper, we show that the ID-based tripartite authenticated multiple-key agreement protocol by Liu et al. [ID-based tripartite key agreement protocol with pairing, 2003 IEEE International Symposium on Information Theory, 2003, pp. 136-143, or available at Cryptology ePrint Archive, Report 2002/1221 is insecure against an unknown key-share attack. And then we propose a more efficient ID-based tripartite authenticated multiple-key agreement protocol to overcome the attack. (c) 2004 Elsevier Inc. All rights reserved.
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