ASS-CC proposed by Komano et al. the first signature scheme that is based on hardness of a section finding problem (SFP) on algebraic surface. It is claimed that ASS-CC is existentially unforgeable against the adaptive chosen-message attack, on the assumption of the hardness of SFP. In this paper, we give a counterexample to the security claim. In particular, a forger can generate a signature on any message under the key-only attack, without solving SFP. The cost of the forgery is almost the same to the legitimate signing algorithm.
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