Paper 2026/1067

GATOR: Group Action AdapTOR Signatures via MPC-in-the-Head

Abstract

Adaptor signatures are a foundational fairness primitive for blockchain applications. They enhance blockchain functionality by enabling applications such as atomic swaps, payment channels, and other fair-exchange protocols. At a high level, they allow a buyer to produce a pre-signature tied to a public statement, which a seller holding a corresponding witness can adapt into a valid signature. Once this signature is posted on-chain, the seller obtains payment, while the buyer can extract the witness from the finalized signature. Existing practical adaptor signature constructions are predominantly tied to discrete-logarithm-based signatures, such as ECDSA and Schnorr, reflecting their widespread use in current blockchain deployments. However, the threat of Shor's algorithm and the broader transition toward post-quantum cryptography raise the question of whether adaptor functionality can also be realized efficiently for post-quantum signature schemes. In this work, we answer this question for a broad class of signatures based on cryptographic group actions. Building on efficient MPC-in-the-Head-style group-action signatures, we obtain adaptor functionality through small modifications, yielding a general framework for adaptor signatures from arbitrary group actions. In particular, our construction supports selling group-action discrete logarithms, which in certain parameter regimes correspond to the secret keys of the underlying signature scheme. We further discuss concrete instantiations from several group-action families, including those underlying schemes such as CSI-FiSh, LESS, MEDS, and ALTEQ, and present a modular proof-of-concept implementation. We obtain a ~25kB pre-signature with ~100ms pre-signing time for LESS, MEDS and ALTEQ, while a ~4kB pre-signature with ~3.6s pre-signing time for CSI-FiSh.