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An identity-based strong designated verifier signature scheme provides restricted verifiability only for a verifier designated by a signer and proper privacy for the signer. In this paper, the authors show that strong designated verifier signature schemes do not satisfy the self-unverifiability requirement in the sense that not only exposure of the verifier's secret key but also of the signer's secret key enables an attacker to verify signatures, which should have been the exclusive right of the verifier. They also present a generic method to construct a strong identity-based designated verifier signature scheme with self-unverifiability from identity-based key encapsulation and identity-based key sharing schemes.
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