Two-Party Adaptor Signatures from Identification Schemes

Abstract

Adaptor signatures are a novel cryptographic primitive with important applications for cryptocurrencies. They have been used to construct second layer solutions such as payment channels or cross-currency swaps. The basic idea of an adaptor signature scheme is to tie the signing process to the revelation of a secret value in the sense that, much like a regular signature scheme, an adaptor signature scheme can authenticate messages, but simultaneously leaks a secret to certain parties. Recently, Aumayr et al. provide the first formalization of adaptor signature schemes, and present provably secure constructions from ECDSA and Schnorr signatures. Unfortunately, the formalization and constructions given in this work have two limitations: (1) current schemes are limited to ECDSA and Schnorr signatures, and no generic transformation for constructing adaptor signatures is known; (2) they do not offer support for aggregated two-party signing, which can significantly reduce the blockchain footprint in applications of adaptor signatures. In this work, we address these two shortcomings. First, we show that signature schemes that are constructed from identification (ID) schemes, which additionally satisfy certain homomorphic properties, can generically be transformed into adaptor signature schemes. We further provide an impossibility result which proves that unique signature schemes (e.g., the BLS scheme) cannot be transformed into an adaptor signature scheme. In addition, we define two-party adaptor signature schemes with aggregatable public keys and show how to instantiate them via a generic transformation from ID-based signature schemes. Finally, we give instantiations of our generic transformations for the Schnorr, Katz-Wang and Guillou-Quisquater signature schemes.

Atomic cross-chain swap based on private key exchange

“…For example, a HTLC-based ACCS scheme requires that both blockchain scripts must support the same hash function. In addition, due to the fact that on-chain scripts are public, using them may compromise users' privacy (Deshpande and Herlihy 2020;Thyagarajan et al 2022).…”

“…the verification of digital signatures. Unfortunately, his protocol does not provide an efficient solution for blockchains that do not support adaptor signatures (Erwig et al 2021;Hanzlik et al 2022).…”

“…-Privacy. In ACCS, users' privacy includes: (i) Onchain data privacy (Deshpande and Herlihy 2020). The process of cross-chain swap may leak users' on-chain data.…”

“…Moreover, using the same private key share will not compromise the privacy of the players. Because the other player can generate a random private key share, resulting in different final joint addresses and ensuring the unlinkability of cross-chain transactions (Deshpande and Herlihy 2020) . In this case, we can still use the solution employed in the same curve swaps.…”

Post-Quantum Two-Party Adaptor Signature Based on Coding Theory

“…Since the work by Poelstra, several articles on adaptor signature have appeared, e.g., [9][10][11][12][13][14][15][16][17]. In [10], the authors introduced two adaptor signature schemes based on Schnorr's signature and the elliptic curve digital signature algorithm (ECDSA), respectively.…”