Blockchain intercommunication systems enable the exchanges of messages between blockchains. This interoperability promotes innovation, unlocks liquidity and access to assets. However, blockchains are isolated systems that originally were not designed for interoperability. This makes cross-chain communication, or bridges for short, insecure by nature. More precisely, cross-chain systems face security challenges in terms of selfish rational players such as maximal extractable value (MEV) and censorship. We propose to solve these challenges using zero knowledge proofs (ZKPs) for cross-chain communication. Securing cross-chain communication is remarkably more complex than securing single-chain events as such a system must preserve user security against both on- and off-chain analysis. To achieve this goal, we propose the following pair of contributions: the DACT protocol and the SurferMonkey infrastructure that supports the DACT protocol. The DACT protocol is a global solution for the anonymity and security challenges of agnostic blockchain intercommunication. DACT breaks on- and off-chain analysis thanks to the use of ZKPs. SurferMonkey is a decentralized infrastructure that implements DACT in practice. Since SurferMonkey works at the blockchain application layer, any decentralized application (dApp) can use SurferMonkey to send any type of message to a dApp on another blockchain. With SurferMonkey, users can neither be censored nor be exposed to MEV. By applying decentralized proactive security, we obtain resilience against selfish rational players, and raise the security bar against cyberattacks. We have implemented a proof of concept (PoC) of SurferMonkey by reverse engineering Tornado Cash and by applying IDEN3 ZKP circuits. SurferMonkey enables new usecases, ranging from anonymous voting and gaming, to a new phase of anonymous decentralized finance (aDeFi).