Atomic Cross-Chain Swaps

TL;DR

This paper introduces a protocol for atomic cross-chain swaps ensuring secure asset exchanges across multiple blockchains, using graph theory and hashed timelock contracts, with proven limitations and efficiency analysis.

Contribution

It presents a novel protocol for atomic cross-chain swaps based on graph structures and feedback vertex sets, with proven correctness and complexity bounds.

Findings

Protocol guarantees atomicity and incentive compatibility.

No protocol exists if the graph isn't strongly connected or lacks a feedback vertex set.

Time complexity is proportional to the graph's diameter.

Abstract

An atomic cross-chain swap is a distributed coordination task where multiple parties exchange assets across multiple blockchains, for example, trading bitcoin for ether. An atomic swap protocol guarantees (1) if all parties conform to the protocol, then all swaps take place, (2) if some coalition deviates from the protocol, then no conforming party ends up worse off, and (3) no coalition has an incentive to deviate from the protocol. A cross-chain swap is modeled as a directed graph ${\cal D}$, whose vertexes are parties and whose arcs are proposed asset transfers. For any pair $({\cal D},L)$, where ${\cal D} = (V,A)$ is a strongly-connected directed graph and $L \subset V$ a feedback vertex set for ${\cal D}$, we give an atomic cross-chain swap protocol for ${\cal D}$, using a form of hashed timelock contracts, where the vertexes in $L$ generate the hashlocked secrets. We show that no such protocol is possible if ${\cal D}$ is not strongly connected, or if ${\cal D}$ is strongly connected but $L$ is not a feedback vertex set. The protocol has time complexity $O(diam({\cal D}))$ and space complexity (bits stored on all blockchains) $O(|A|^2)$.