On the security of the Okamoto-Tanaka ID-based key exchange scheme against active attacks

As far as the knowledge of authors, the rigorous security of Okamoto-Tanaka identity-based key exchange scheme was shown in [4] for the first time since its invention. However, the analysis deals with only the passive attack. In this paper, we give several models of active attacks against the scheme and show the rigorous security of the scheme in these models. We prove several relationships among attack models, including that (1) breaking the scheme in one attack model is equivalent to breaking the RSA public-key cryptosystem and (2) breaking the scheme in another attack model is equivalent to breaking the Diffie-Hellman key exchange scheme over Z_n. The difference of the complexity stems from the difference of the timing of dishonest party's sending out and receiving messages.