Briefing
The core research problem in timed cryptography is the linear scaling of proof size and computational cost in Verifiable Timed Signatures (VTS), which severely limits their practical application in decentralized systems. This paper introduces a novel VTS construction based on the RSA group, utilizing a commitment to a valid RSA signature alongside a Trapdoor Verifiable Delay Function (TVDF) and a specialized Zero-Knowledge Proof of Knowledge (ZKPoK). The foundational breakthrough is achieving a constant-size signature and verification overhead, regardless of the specified time delay. This new asymptotic efficiency fundamentally re-architects the feasibility of time-sensitive on-chain mechanisms, enabling practical, resource-efficient protocols for future-dated transactions and decentralized governance.
Context
Before this work, the established VTS model, which allows a signature to be verifiably time-locked for a duration $T$, relied on schemes that exhibited a linear increase in proof size and computational overhead proportional to the complexity or number of shares used in the time-lock mechanism. This fundamental theoretical limitation meant that implementing VTS for long-duration time-locks or in high-throughput environments was computationally prohibitive, creating a trade-off between the desired time constraint $T$ and the on-chain resource consumption required for verification.
Analysis
The core mechanism achieves constant size by replacing the linear-scaling cut-and-choose protocols of prior VTS schemes with a unified cryptographic structure. The process involves a sender creating a commitment to a valid RSA signature. This commitment is constructed using a Trapdoor Verifiable Delay Function (TVDF), where the signature is only extractable after the sequential computation of the delay function is complete.
The crucial step is the non-interactive Zero-Knowledge Proof of Knowledge (ZKPoK) that proves the commitment correctly contains a valid RSA signature without revealing the signature itself. This proof has a constant size, ensuring the verifier can confirm the signature’s validity and extractability at any point without performing the time-consuming sequential computation.
Parameters
- Signature Size Reduction → At least 90.5% reduction in size compared to the previous state-of-the-art (CCS 2020).
- Computational Cost Reduction → At least 77% reduction in verification costs compared to the previous state-of-the-art (CCS 2020).
- Core Cryptographic Primitive → Verifiable Timed Signature (VTS) , which time-locks a signature with public verifiability.
- Underlying Cryptographic Assumption → RSA Group and the hardness of the sequential squaring problem for the TVDF.
Outlook
This constant-size primitive immediately unlocks new applications where time-sensitive execution must be coupled with on-chain efficiency. In the next 3-5 years, this will enable the deployment of truly scalable decentralized governance mechanisms, such as on-chain voting where votes are committed instantly but only revealed after a set time $T$. It also facilitates more robust and private payment channel networks and advanced escrow services, shifting the architectural focus from relying on block height as a time proxy to using cryptographically enforced, constant-cost time delays. Future research will likely focus on achieving post-quantum VTS with similar constant-size properties.
Verdict
The achievement of constant-size verifiable timed signatures represents a foundational advance in timed cryptography, establishing a highly efficient and practical primitive for future-proof, time-constrained decentralized applications.
