Abstract
Undeniable signatures, introduced by Chaumand van Antwerpen, require a verifier to interact with thesigner to verify a signature, and hence allow the signerto control the verifiability of his signatures. Convertibleundeniable signatures allow the signer to convert undeniablesignatures into ordinary signatures. In this paperwe propose some extended variants of the famous Diffie-Hellman assumption on bilinear group system, then designa new convertible undeniable signature scheme and provideproofs for all relevant security properties based on the newassumption in the random oracle model. The advantages ofour scheme are the short length of the signatures, the lowcomputational cost of the signature, the receipt generationand the provable security.
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