Group undeniable signatures with convertibility

We introduce a new type of signature for a group of persons called a group undeniable signature, which satisfies the following requirements: (1) only group members can anonymously sign on behalf of the group; (2) a verifier must interact with the group manager to verify the signature; (3) the group manager can identify the signer of a valid signature. Convertible group undeniable signatures allow the group manager to turn select group undeniable signatures into universally verifiable group signatures. They are more suitable than group signatures in applications where signatures are generated for sensitive, nonpublic data. We propose the first convertible group undeniable signature scheme. Furthermore, our scheme is unforgeable, exculpable, unlinkable, and coalition-resistant. The proposed scheme allows the group manager to delegate the ability to confirm and deny signatures to trusted parties. The sizes of the public key and signatures are independent of the group size.