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This paper classifies existing post-quantum signature schemes suitable for threshold signature applications, analyzing methods based on lattice problems, one-way functions, cryptographic group actions, isogenies, and multivariate systems. The motivation stems from the need for secure alternatives in light of recent NIST calls for post-quantum cryptography, as traditional pre-quantum signatures are no longer adequate. The key result is a comprehensive categorization of tools that can facilitate the construction of T-out-of-N threshold schemes, incorporating advanced techniques like fully homomorphic encryption (FHE), multi-party computation (MPC), and zero-knowledge proofs (ZKP).
Post-quantum signatures could redefine secure distributed signing, but existing methods are often overlooked in favor of pre-quantum solutions.
Threshold signature schemes distribute the signing process among $T$ parties out of $N$. They enable a variety of applications and their research is also motivated by a recent NIST call. However, applications are dominated by pre-quantum signatures, which are more efficient but not secure in the post-quantum setting. This paper investigates existing post-quantum signatures, based on a variety of paradigms: lattice problems, one-way (hash) functions, cryptographic group actions, isogenies and multivariate systems. We propose a classification (divided by paradigm) of existing tools that are used to build $T$-out-of-$N$ schemes from digital signatures. We also include general approaches based on FHE, MPC or ZKP.
