Adapter Signatures and Their Applications in Cross-Chain Atomic Swaps

With the rapid development of Bitcoin Layer 2 scaling solutions, the frequency of cross-chain asset transfers between Bitcoin and its Layer 2 networks has significantly increased. This trend is driven by the higher scalability, lower transaction fees, and high throughput offered by Layer 2 technologies. These advancements promote more efficient and cost-effective transactions, facilitating broader adoption and integration of Bitcoin across various applications. Therefore, the interoperability between Bitcoin and Layer 2 networks is becoming a key component of the cryptocurrency ecosystem, driving innovation and providing users with a more diverse and powerful set of financial tools.

There are three typical solutions for cross-chain transactions between Bitcoin and Layer 2, namely centralized cross-chain trading, BitVM cross-chain bridge, and cross-chain atomic swaps. These three technologies differ in terms of trust assumptions, security, convenience, transaction limits, and can meet different application needs.

The advantages of centralized cross-chain trading lie in its speed and the relatively easy matching process, as centralized institutions can quickly confirm and process transactions. However, the security of this method entirely depends on the reliability and reputation of the centralized institution. If the centralized institution encounters technical failures, malicious attacks, or defaults, users' funds face a higher risk. Moreover, centralized cross-chain trading may also leak user privacy, requiring users to consider this method carefully when choosing.

The BitVM cross-chain bridge technology is relatively complex. It introduces an optimistic challenge mechanism, making the technology comparatively intricate. Additionally, the optimistic challenge mechanism involves a large number of challenge and response transactions, resulting in higher transaction fees. Therefore, the BitVM cross-chain bridge is only suitable for very large transactions and is used less frequently.

Cross-chain atomic swaps are contracts that enable decentralized cryptocurrency trading. This technology is decentralized, censorship-resistant, offers good privacy protection, and allows for high-frequency cross-chain transactions, making it widely used in decentralized exchanges. Cross-chain atomic swap technology mainly includes hash time locks and adapter signatures.

Hash Time-Locked Contracts (HTLC) based cross-chain atomic swaps allow two users to conduct time-restricted cryptocurrency transactions. While HTLC atomic swaps represent a significant breakthrough in the field of decentralized exchange technology, there are issues related to privacy leakage.

Adapter signature-based cross-chain atomic swaps have three advantages: first, it replaces the "secret hash" swaps that rely on on-chain scripts. Second, since such scripts are not involved, on-chain space usage is reduced, making adapter signature-based atomic swaps lighter and cheaper. Finally, the transactions involved in adapter signature atomic swaps cannot be linked, achieving privacy protection.

The adapter signature has security issues with random numbers, such as random number leakage and reuse problems, which can be addressed by using RFC 6979. In cross-chain scenarios, it is also necessary to consider the heterogeneity problem between UTXO and account model systems, as well as compatibility issues with different algorithms and curves.

The adapter signature can also be applied to non-interactive digital asset custody. This method allows for the instantiation of a subset of threshold spending strategies without interaction, offering the advantages of non-interactivity.

Overall, adapter signature technology provides an efficient, secure, and privacy-preserving solution for cross-chain atomic swaps and digital asset custody, but many technical details and security issues still need to be considered in practical applications.