## 2 Related Work  
Communication between blockchains involves two blockchains: the source and the target [1]. The source chain initiates a transaction that can be executed on the target chain. At present, \"cross chain\" refers to \"asset transfer\" and \"asset exchange\". A cross-chain asset transfer involves three atomic transactions: (1) a source chain asset lock, (2) transaction confirmation on the blockchain, and (3) the creation of assets on the target chain [2; 3; 4]. According to a technical report from the National Institute of Standards and Technology (NIST), blockchain interoperability is defined as \"the composition of distinguishable blockchain systems, each representing a unique distributed data ledger, in which atomic transaction execution can span multiple heterogeneous blockchain systems, where data is recorded in a system [where] the blockchain is semantically reachable, [is] verifiable, and can be referenced by another possible external transaction\" [5]. In the general communication protocol proposed by [PERSON] et al., interoperability is defined as the \"transmission or exchange of data or value between different ledgers with guaranteed validity\" [6]. [PERSON] and [PERSON] noted that \"the purpose of cross-communication is not to directly change the state of another blockchain system. Instead, cross-communication should trigger some set of functions on the other system that are expected to operate within its own network\" [7]. [PERSON] et al. define blockchain transaction activity as \"the completion of an application-level transaction that is independent of the participating blockchain system\" [8]. Both transactions and sub-transactions are guaranteed to be completed within a specified time, i.e., with a \"best effort to deliver\". Two blockchain cross-chain protocols include the cross-chain communication protocol (CCCP) and the cross-blockchain communication protocol (CBCP). [PERSON] et al. made the distinction that the CCCP process communicates against a homogeneous blockchain. The CBCP targets heterogeneous blockchain communication [1]. [PERSON] et al. demonstrated that \"there is no asynchronous cross-chain communication (CCC) protocol that tolerates [the] abnormal behavior of nodes\" [9]. The authors use the simplification of the fair exchange problem to show that correct cross-chain communication is just as difficult as the fair exchange problem [10]. As a result of the proposed theorem, the authors state that, \"without trusted third parties, there can be no CCC protocol for tolerating misbehaving nodes\". Trusted third parties can be centralized or decentralized. For example, a centralized trusted party is a trusted validator [11], and a decentralized trusted party can be another blockchain. [PERSON] and [PERSON] [12] formalize the issue of blockchain interoperability, arguing that a fully decentralized source blockchain cannot verify the existence of data on the target blockchain through practical efforts. More specifically, no protocol assumes that a complete client can implement its interoperable functions, such as asset transfers, without the assistance of third parties. For these two cross-chain operations, there are several mainstream cross-chain technologies: (1) notary schemes, (2) hash-locking, (3) sidechains/relays, and (4) distributed private key control. The notary scheme involves a notary, an entity that monitors multiple chains, triggering transactions in the chain when an event occurs on another chain [13]. Exchanges facilitate signaling among market participants by managing order books and matching buyers and sellers. If the trust anchor is placed on a centralized party that holds the user's private key or funds, the notary is a centralized exchange. Otherwise, if the exchange does not perform trades on behalf of the user and only provides matching services, it is considered a decentralized exchange [14]. In layman's terms: A trusted third party who tells Chain B what is happening to Chain A, or who tells Chain B whether certain information is true.