Group Signatures with Time-bound Keys Revisited: A New Model and an Efficient Construction

Chu et al. (ASIACCS 2012) proposed group signature with time-bound keys (GS-TBK) where each signing key is associated to an expiry time τ. In addition to prove the membership of the group, a signer needs to prove that the expiry time has not passed, i.e., t<τ where t is the current time. A signer whose expiry time has passed is automatically revoked, and this revocation is called natural revocation. Simultaneously, signers can be revoked before their expiry times have passed due to the compromise of the credential. This revocation is called premature revocation. A nice property of the Chu et al. proposal is that the size of revocation lists can be reduced compared to those of Verifier-Local Revocation (VLR) group signature schemes, by assuming that natural revocation accounts for most of signer revocations in practice, and prematurely revoked signers are only a small fraction. In this paper, we point out that the definition of traceability of Chu et al. did not capture unforgeability of expiry time of signing keys which guarantees that no adversary who has a signing key associated to an expiry time τ can compute a valid signature after τ has passed. We introduce a security model that captures unforgeability, and propose a GS-TBK scheme secure in the new model. Our scheme also provides the constant signing costs whereas those of the previous schemes depend on the bit-length of the time representation. Finally, we give implementation results, and show that our scheme is feasible in practical settings.