$BitML^{x}$: Secure Cross-Chain Smart Contracts for Bitcoin-Style Cryptocurrencies

A smart contract is an interactive program that governs funds in the realm of a single cryptocurrency. Yet, the many existing cryptocurrencies have spurred the design of cross-chain applications that require interactions with multiple cryp-tocurrencies simultaneously. Currently, cross-chain applications are implemented as use-case-specific cryptographic protocols that serve as overlay to synchronize smart contract executions in the different cryptocurrencies. Hence, their design requires substantial expertise, as well as a security analysis in complex cryptographic frameworks. In this work, we present <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$BitML^{x}$</tex>, the first domain-specific language for cross-chain smart contracts, enabling interactions with several users that hold funds across multiple Bitcoin-like cryptocurrencies. We contribute a compiler to automatically translate a <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$BitML^{x}$</tex> contract into one contract per involved cryp-tocurrency and a user strategy that synchronizes the execution of these contracts. We prove that an honest user, who follows the prescribed strategy when interacting with the several contracts, ends up with at least as many funds as in the corresponding execution of the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$BitML^{x}$</tex> contract. Last, but not least, we implement the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$BitML^{x}$</tex> compiler and demonstrate its utility in the design of illustrative examples of cross-chain applications such as multi-chain donations or loans across different cryptocurrencies.