Thresholding Post-Quantum Signatures

Abstract

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.