Threshold/Multi Adaptor Signature and Their Applications in Blockchains

Abstract

Adaptor signature is a variant of digital signatures and useful for fair excheng in financial applications such as cryptocurrencies, to name a few, off-chain transaction protocols, atomic swaps and other privacy-enhancing mechanisms. However, similar to normal digital signatures, an adaptor signature also suffers from the loss of the secret key and single-point failure, which is insufficient in practice. In this paper, we address this constraint by introducing two new concepts as enhancements: multi-adaptor signatures and threshold adaptor signatures. First, we propose the formal security models for multi-adaptor signature and threshold adaptor signature. Then, we present specific schemes for these two primitives based on the commonly used blockchain signature scheme Schnorr and the post-quantum signature scheme Dilithium, respectively. Furthermore, we provide security proofs for these four schemes. Finally, we demonstrate interesting applications for blockchains, such as oracle-based conditional payment and n to n atomic swap.