Foundations of Dynamic Group Signatures: The Case of Malicious Openers and Issuers

Dynamic group signatures are commonly formalized in the model of Bellare, Shi, and Zhang (BSZ, CT-RSA 2005), whose security notions are defined relative to specific trust assumptions and registration state. We revisit these assumptions and systematically study which guarantees continue to hold when the trust assumptions on the issuer and opener are considered independently and no trusted registration structure is shared between them. In particular, we show that the meaning of traceability changes substantially in such settings. With a malicious issuer and an honest opener, the natural analogue of traceability only ensures that every valid signature admits an accepted opening; it does not ensure that the resulting identity obtained its membership through a valid join. With a malicious opener, classical accountability guarantees likewise fail to enforce this connection to group membership. We demonstrate this by constructing a scheme satisfying the BSZ-style security notions in which a malicious opener can produce valid signatures that are not associated with any membership established through the join algorithm, even though the issuer is honest. To capture the missing relations between joining, signing, and opening, we introduce three unforgeability-type properties. Certificate-unforgeability binds valid signatures to issued membership certificates. Key-unforgeability requires signature generation to rely on a corresponding member signing key. Opening-unforgeability prevents accepted openings to identities for which no membership was issued. We prove that these properties are logically independent and give a construction satisfying the classical and additional guarantees under mild assumptions. Our results identify precisely which aspects of accountability follow from trusted issuers, trusted openers, or shared registration state, and which must be required explicitly once these assumptions are removed.