Provably secure identity-based undeniable signatures with selective and universal convertibility

In this paper, we present the first concrete example of identity-based undeniable signature with selective and universal convertibility, where the signer can release a selective proof to make a single undeniable signature publicly verifiable, or publish a universal proof to convert all his undeniable signatures, into ordinary digital signatures. Furthermore, we also formalized the security models of identity-based convertible undeniable signatures. The new models capture more essence of the, property "convertibility" of identity-based undeniable signatures, compared with other known security models. Our scheme call be regarded as an improvement of Libert and Quisquater's identity-based undeniable signature scheme published in CT-RSA 2004. The security of our scheme is formally proven in the random oracle model under some well-known complexity assumptions. Its uuforgeability relies on the hardness of the Computational Diffie-Hellman problem, while the invisibility (and anonymity) is based on the hardness of Decisional Bilinear Diffie-Hellman problem.