A multi-signer convertible limited multi-verifier signature scheme in the standard model

In a multi-signer convertible limited multi-verifier signature (MSCLMVS) scheme, a set of multi signers (co-signers) cooperatively creates a signature that can only be verified by limited verifiers. In this scheme, the conflicts between the authenticity and the privacy of the co-signers can be solved by controlling the verifiability. Moreover, the limited verifiers can designate the signature to a trusted third party such as a judge to convince him about the validity of the signature. Furthermore, both the co-signers and the limited verifiers can convert the signature to a traditional publicly verifiable signature if necessary. In this paper we present a multi-signer convertible limited multi-verifier signature scheme based on Waters' signature which is constructed by bilinear pairings. The proposed scheme is proved to be secure in the standard model by the assumption of the hardness of the Weak Gap Bilinear Diffie-Hellman problem. To the best of our knowledge, this is the first multi-signer convertible limited multi-verifier signature scheme with provable security without random oracles.