Attack on an Identification Scheme Based on Gap Diffie-Hellman Problem

In [KK], a new identification scheme based on the Gap Diffie-Hellman problem was proposed at SCIS 2002, and it is shown that the scheme is secure against active attacks under the Gap Diffie-Hellman Intractability Assumption. Paradoxically, this identification scheme is totally breakable under passive attacks. In this paper, we show that any adversary holding only public parameters of the scheme can convince a verifier with probability 1.