Vitārit: Paying for Threshold Services on Bitcoin and Friends

Blockchain service offerings have seen a rapid rise in recent times. Many of these services realize a decentralized architecture with a threshold adversary to avoid a single point of failure and to mitigate key escrow issues. Although payments to such services are straightforward in systems that support smart contracts, achieving fairness poses challenges in systems like Bitcoin, which use the UTXO model with limited scripting capabilities. This is especially challenging without smart contracts, as we wish to pay only the required threshold of $t$ + 1 out of the $n$ servers offering the service, without any server claiming payment twice. In this paper, we introduce Vitārit¹1.A Sanskrit word for ‘distributed’, a novel payment solution tailored for threshold cryptographic services in UTXO systems like Bitcoin. Our approach guarantees robust, provable security while facilitating practical deployment. We focus on the t-out-of-n distributed threshold verifiable random function (VRF) service with certain properties, such as threshold BLS signatures, a recently highlighted area of interest. Our protocol enables clients to request verifiable random function (VRF) values from the threshold service, triggering payments to up to $t$ + 1 servers of the distributed threshold VRF. Our efficient design relies on simple transactions using signature verification scripts, making it immediately applicable in Bitcoin-like systems. We also introduce new tools and techniques at both the cryptographic and transaction layers, including a novel signature-VRF exchange protocol for standard constructions, which may be of independent interest. Additionally, our transaction flow design prevents malicious servers from claiming payments twice, offering broader implications for decentralized payment systems. Our prototype implementation shows that in the two-party interaction, the client takes 126.4 msec, and the server takes 204 msec, demonstrating practicality and deployability of the system.