# Integrating Merkle Trees with Transformer Networks for Secure Financial Computation
## 2 Related Works
### Merkle Tree  
In this section, we describe how Merkle trees (which are hash-based data structures) are extensively utilized in various scenarios for security and data integrity verification [19], particularly in the fintech sector. Essentially, Merkle trees are a special type of binary tree where each non-leaf node is the hash of the hash values of its child nodes, as depicted in Figure 1.  
Within a Merkle tree, leaf nodes contain hash values of data blocks (such as transaction records or file segments), while each non-leaf node contains the combined hash of the hash values of its two child nodes. The top of the tree features a single node, known as the root node or Merkle root, representing a unique fingerprint of the entire dataset. The construction of a Merkle tree can be mathematically expressed as follows:  
\[MerkleTree=Hash(Hash(A)\oplus Hash(B)\oplus Hash(C)\oplus\ldots) \tag{1}\]  
Here, \(A\), \(B\), \(C\), etc., represent data blocks, \(\oplus\) represents concatenation, and the \(Hash()\) function is utilized to generate hash values.  
In the context of financial attack detection, Merkle trees can ensure the integrity and immutability of transaction records. Consider, for example, a blockchain system comprising multiple transaction records. Each block in the blockchain can utilize a Merkle tree to store the hash values of transactions [20]. To verify whether a specific transaction is included in a block, only a path from that transaction record to the Merkle root (i.e., a Merkle proof) is required.  
Figure 1: Illustration of a Merkle tree.  
This process can be represented by the following equation:  
\[\textit{MerkleProof}=Hash(Hash(Transaction)\oplus Hash(Sibling_{1})\oplus\ldots \oplus Hash(Sibling_{n})) \tag{2}\]  
Here, _Transaction_ is the transaction record being verified, and \(Sibling_{1},\ldots,Sibling_{n}\) are sibling nodes on the path from the transaction record to the root. In practical applications, Merkle trees offer an efficient and secure way to verify the integrity of large volumes of data. In the financial domain, this characteristic is especially significant. It not only ensures the security of transaction data but also effectively guards against financial fraud and tampering activities [21]. For instance, in distributed ledger technologies (such as blockchain), Merkle trees are used to ensure the integrity of transaction records in each block. Through this method, participants can verify the validity of individual transactions, even without downloading the entire blockchain. A key advantage of Merkle trees is their \"avalanche effect\": any change in a data block within the tree leads to a change in the entire tree's root hash value. This feature allows for any unauthorized modifications to the data to be rapidly detected, thereby providing a robust mechanism for data integrity protection.  
In the Merkle-Transformer model, these characteristics of Merkle trees are leveraged to enhance the security of financial data processing. By combining Merkle trees with the Transformer model, a secure and efficient method for processing complex financial data is provided, particularly when dealing with large-scale and high-frequency transaction data.