Atomic Cross-Chain Swaps (1801.09515v4)

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) $O(|A|^2)$.

• The paper introduces a protocol that guarantees secure, atomic execution of cross-chain swaps using HTLCs.
• It employs a directed graph model with a feedback vertex set to maintain rational safety and strong Nash equilibrium.
• The protocol paves the way for blockchain interoperability, enhancing scalability and enabling trustless asset exchanges.

Atomic Cross-Chain Swaps: An Overview

The paper "Atomic Cross-Chain Swaps" by Maurice Herlihy provides a comprehensive theoretical framework for executing asset exchanges between multiple blockchain networks through atomic swap protocols. The primary objective is to ensure asset exchanges occur between multiple parties, enabling transactions such as trading Bitcoin for Ether without the need for a trusted intermediary.

Key Aspects of Atomic Cross-Chain Swaps

The core contribution of the paper is the development of a protocol that guarantees secure and atomic execution of cross-chain swaps. This protocol achieves three critical properties:

1. Atomicity: If all parties adhere to the protocol, all proposed swaps execute successfully.
2. Rational Safety: If a subset of parties deviates, no conforming party ends up in a less favorable position.
3. Strong Nash Equilibrium: No coalition of parties has an incentive to deviate from the protocol.

Conceptual and Technical Framework

The underlying model for atomic cross-chain swaps is represented by a directed graph where the vertexes denote parties involved and arcs represent proposed asset transfers. The significant requirement for the protocol's success is that the graph be strongly connected, ensuring that for any two parties involved, there are paths enabling reciprocal access to assets, thus validating the decentralized, trustless nature of the system.

The protocol utilizes Hashed Timelock Contracts (HTLCs) to ensure the secure transfer of assets. The HTLCs guarantee that the exchange only occurs if a secret, which corresponds to a hashlock, is revealed before a specified time. This functionality ensures that if a party does not receive the necessary secret within a designated period, the assets are reverted back, thus adhering to the atomicity principle.

The paper outlines a procedure where each party generates a secret and corresponding hashlock. These hashlocks are used to form a hashlock vector that is assigned to all transaction arcs. The leaders, a subset of parties forming a feedback vertex set, are tasked with generating these hashlocks.

Complexity and Protocol Properties

The protocol's time complexity is proportional to the diameter of the swap digraph, while the space complexity is quadratic relative to the number of arcs. The necessity of having leaders as a feedback vertex set ensures that both termination and safety properties are maintained. Importantly, if the digraph is not strongly connected, achieving atomicity is provably impossible.

Implications and Future Directions

The atomic cross-chain swap protocol has several implications for blockchain interoperability and potentially transformative applications beyond digital asset trading. For example, atomic swaps could facilitate improved scalability for blockchain through sharding and decentralized software upgrade management.

Potential future research directions include optimizing the protocol for privacy, reducing the need for digital signatures, applying the protocol to complex transaction sequences, and developing stronger incentives against denial-of-service attacks that temporarily lock up assets.

In conclusion, this paper presents a mathematically rigorous and security-focused approach to enabling decentralized cross-chain asset swaps, presenting a significant advance in blockchain technologies and distributed systems. The theoretical insights delivered serve as a stepping stone for developing practical implementations and augmenting the broader blockchain ecosystem with secure asset exchange capabilities.