Blockchain intercommunication systems listen to messages from Blockchain A and insert them in Blockchain B. This interoperability promotes innovation, unlocks liquidity and access to assets. As of March 2022, the Total Value Locked (TVL) in these systems was of $21.8 billion [22]. However, Blockchains are isolated systems that originally were not designed for interoperability. This makes cross-chain communication (Bridges) insecure by nature. More precisely, cross-chain systems face security challenges in terms of selfish Rational Players from a Game Theory perspective, Maximal Exctractable Value (MEV) and Censorship. As of July 2022, the top 3 Bridge hacks account for more than $1.5 billion in losses [20] and the aggregated value extracted from the users using MEV techniques is $663 million [12]. We propose to solve these challenges by using Zero Knowledge Proofs (ZKPs) for cross-chain communication. However, an agnostic anonymous cross-chain communication is more complex than an anonymous single-chain payment, or than a public cross-chain message, as user privacy must be preserved against on/off-chain analysis. Our first contribution is the Decentralized Anonymous Agnostic Cross-Chain Transfer (DACT) protocol. The DACT protocol is a global solution for the anonymity and security challenges of agnostic Blockchain intercommunication. The DACT messages break the on/off-chain analysis thanks to ZKPs. Our second contributions is SurferMonkey, a decentralized infrastructure that supports the DACT protocol. Since SurferMonkey works at the Blockchain application layer, any dApp can use SurferMonkey and send any type of message to a dApp on another Blockchain. Users cannot 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 Tornadocash and by applying IDEN3 ZKP circuits. SurferMonkey opens new projects, ranging from anonymous voting and gaming, to a new phase of Anonymous Decentralized Finance (aDeFi).