Use cases for blockchain-based cryptocurrencies have evolved beyond simple transfers into complex financial applications. Traditionally, these applications are implemented using blockchain-specific features. As a drawback, the same application required multiple implementations, each tailored to a different blockchain. This increases efforts in development, security analysis and limits the deployment of applications on blockchains with restricted features. An alternative consists of implementing the application logic in an off-chain cryptographic protocol. The protocol would output one (or more) payment authorization as required by the logic of the application. These protocols solely depend on the payment authorization mechanism of the blockchain. This enables implementing applications in a blockchain-agnostic manner. Moreover, automatic formal verification tools can help prove the security guarantees of these off-chain protocols. Ultimately, blockchain-agnostic off-chain protocols would enable applications to be implemented once, analyzed once and be deployed on virtually all blockchains. To achieve this vision, remaining challenges are that not all blockchains share the same authorization mechanism, and the existing verification tools fail to capture subtle functionality beyond cryptography (e.g., time when an authorization can be included in the blockchain) that is nevertheless crucial for the security of off-chain protocols. Our research aims to fill these gaps by investigating how to design off-chain protocols over a unified cryptographic foundation for payment authorizations, and their security analysis with automatic formal verification tools.