At ISW’99, Nishioka, Hanaoka and Imai proposed a digital signature scheme on ID-based key-sharing infrastructures. That signature scheme is claimed to be secure if the discrete logarithm problem is hard to solve. Two schemes (the ID-type and the random-type schemes) based on the linear scheme for the Key Predistribution Systems (KPS) and the discrete logarithm problem (DLP) were given. In this paper we show that those two schemes fail to meet the nonrepudiation requirement: with negligible amount of computation, a signature could be forged. For the ID-type signature scheme, any verifier could forge a signature to raise repudiation between that verifier and the signer. The random type signature scheme has the same weakness. Furthermore, for the random-type signature scheme, once a signer issued a signature, anyone (not only the user in the scheme) could forge that signer\u27s signature for a n arbitrary message.
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