Paper 2026/563

Optimizing FROST for Message Capacity

Abstract

The FROST threshold signature scheme achieves round optimal Schnorr signing through a double-nonce construction, but requires two presignatures per signature. Since each presignature demands an expensive distributed key generation (DKG) protocol, this overhead is significant for high-throughput applications. FROST builds on a core presignature protocol (that we call FROST-core) that uses hash-based re-randomization of presignatures. We investigate whether fewer presignatures can be used to sign multiple messages, improving FROST-core's message capacity. We first show that the natural generalization of using $k$ presignatures for $k$ messages is insecure: an extended ROS attack enables forgery even for $k=2$. However, we prove that using $k+1$ presignatures for $k$ messages achieves security in the Generic Group Model combined with the Random Oracle Model. This improves message capacity from 50% (standard FROST-core) to $\frac{k}{k+1}$, approaching 100% as $k$ grows. We further extend our analysis to a modified FROST-core protocol in which a set of presignatures is generated by different parties and used for signing $k$ messages. Security holds as long as at least $k+1$ presignatures were created by honest parties.