A Technical Review of FROST Threshold Signatures: Variants, Extensions, Security, and RFC9591

Threshold signature schemes enable a group of participants to collaboratively generate a signature if a subset of t out of n participants willingly participate in the signing process. Among recent developments, FROST (Flexible Round-Optimised Schnorr Threshold signatures) stands out for its efficiency, flexibility, and strong security guarantees in both theoretical and applied settings. This survey provides a comprehensive overview of FROST, starting from its cryptographic foundations in Schnorr signatures and the discrete logarithm problem to its formal security models and threat assumptions, including the unique robustness properties of FROST in the presence of malicious or aborting signers. We examine its two- round signing protocol, distributed key generation (DKG), and integration with secure multiparty computation frameworks. Furthermore, the survey categorises and analyses key extensions and adaptations of FROST, such as proactive and dynamic group configurations, post-quantum variants, compatibility with verifiable secret sharing, and deployments over alternative curves and signature primitives. We also evaluate practical implementations, standardisation efforts (e.g., by the IRTF CFRG), and real-world applications in blockchain and distributed systems. By mapping out current research and highlighting open challenges, this survey aims to guide future work in robust, scalable threshold signature protocols anchored in the FROST paradigm.