Timed signatures are cryptographic primitives that enable senders to predefine the validity period of a signature. Currently, two primary types of timed signatures have been developed. The first type, known as Verifiable Timed Signatures (CCS'2020), implements a delay before a signature becomes effective. The second type is Short-Lived Signatures (ASIACRYPT'2022), which allows for the setting of an expiration time for signatures upon creation. However, certain applications requiring time-sensitive authorization demand both activation and expiration times to be set, a requirement not fulfilled by the existing timed signature schemes. To overcome this limitation, we propose a novel flexible timed signature scheme called Time Interval Signatures (TIS). TIS combines Verifiable Delay Functions and Short-Lived Signatures with our Zero-Knowledge Proof of Product, facilitating the flexible setting of both activation and expiration times for the signature. Building on TIS, we present TimeGuardian, a time-bound NFT rights protocol that enables presetting authorization and revocation periods for NFT usage rights. Experimental results show that TIS achieves signature size reductions of 98.67% and 57.14% compared to existing verifiable timed signature solutions.

Ring signatures enable a user to sign a message on behalf of a group while preserving both anonymity and unforgeability. Despite these strong privacy guarantees, they present regulatory challenges. To address these issues, we introduce a novel cryptographic primitive:timed anonymous ring signatures(TARS). Unlike group signatures, which rely on a trusted third party, TARS maintains the decentralization and unforgeability of traditional ring signatures while incorporatingtimed anonymity, allowing the signer’s identity to be disclosed by any user after a predetermined time period, denoted asT. To realize this, we propose a new CCA-securetimed public key encryption(TPKE) scheme that ensures correct decryption without the secret key after the timeT. Building upon TPKE, we present two concrete TARS constructions that guarantee anonymity until timeTand unforgeability at all times. To demonstrate its applicability, we apply TARS to a decentralized bidding system that is anticollusion between the auctioneer and the bidders. The system ensures anonymous bidding while disclosing the winner’s identity after the bid announcement, maintaining a transparent, fair, and decentralized bidding process. Finally, experimental evaluations confirm the practicality and efficiency of the proposed schemes. Crucially, the TARS scheme extends conventional ring signature schemes with timed anonymity by introducing only a moderate computational overhead (experimentally measured at ≈1.37 seconds under our configuration) while preserving their cryptographic robustness.