International Association
for Cryptologic Research

A threshold verifiable random function (threshold VRF) is a VRF where the evaluation key is secret shared among $n$ parties, and a quorum of $t$ parties is needed to evaluate the VRF. Threshold VRFs are used widely in practice in applications such as randomness beacons and deterministic wallets. Despite their long history, the question of accountability for leaking key shares in a threshold VRF has not been studied. Specifically, consider a set of $f$ parties who use their key shares to create an evaluation box $E$ that lets anyone evaluate the VRF at any point in the domain of the VRF. When $f$ is less than the threshold $t$, this box $E$ must also take as input $t-f$ additional evaluation shares. Our goal is to design a threshold VRF where there is a tracing algorithm that can trace any such box $E$ to the coalition of $f$ parties that created it, using only blackbox access to $E$. The risk of tracing should deter the coalition from selling such a box. Questions in this vein were previously explored in the context of threshold decryption and secret sharing. Here we define and study traceability for a threshold VRF.

Our traceable threshold VRF is built from a VRF based on Paillier encryption. The starting point for our tracing algorithm is the tracing technique of Boneh-Partap-Rotem (Crypto 2024) designed for tracing leaks in the context of secret sharing. However, there are multiple technical challenges in making this approach work, and we develop the necessary tools to overcome all these challenges. The end result is a threshold VRF with a provably secure tracing algorithm.