Contingent payments from two-party signing and verification for abelian groups

The fair exchange problem has faced for a long time the bottleneck of a required trusted third party. The recent development of blockchains introduces a new type of party to this problem, whose trustworthiness relies on a public ledger and distributed computation. The challenge in this setting is to reconcile the minimalistic and public nature of blockchains with elaborate fair exchange requirements, from functionality to privacy. Zero-knowledge contingent payments (ZKCP) are a class of protocols that are promising in this direction, allowing the fair exchange of data for payment. We propose a new ZKCP protocol that, when compared to others, requires less computation from the blockchain and less interaction between parties. The protocol is based on two-party (weak) adaptor signatures, which we show how to instantiate from state of the art multiparty sign- ing protocols. We improve the symbolic definition of ZKCP security and, for automated verification with Tamarin, we propose a general security reduction from the theory of abelian groups to the theory of exclusive or.