Blockchain pills — Merkle Tree
A Merkle tree, also known as a binary hash tree, is a data structure used to efficiently index and verify the integrity of large datasets. In computer science, a “tree” is often depicted upside down, with the “root” at the top and the branches extending downward.
Understanding the Merkle Tree Structure
A hash function transforms input data into a fixed-size string of characters, which is called a hash. Each unique input yields a unique hash, allowing for efficient data identification. In a Merkle tree, transactions are paired, and the hash for each pair is computed and stored in the parent node. These parent nodes are then paired, hashed, and stored at the next level up, continuing until reaching the root of the tree.
The Merkle tree nodes include:
- Root Node: The root, known as the Merkle root, is stored in the block header.
- Leaf Nodes: These nodes contain hash values of transaction data. Each transaction’s data is hashed, and this hash (also known as the transaction ID) is stored in the leaf nodes.
- Non-Leaf Nodes: These nodes contain the hash values of their child nodes and are also known as intermediate nodes. They store the intermediate hash values, continuing the hashing process up to the tree’s root.
Efficiency and Security
In a Merkle tree, every leaf node is labeled with the cryptographic hash of a data block, and each non-leaf node is labeled with the cryptographic hash of its child nodes’ labels. This structure allows for secure and efficient verification of large data sets. Merkle trees are a generalization of hash lists and chains. For instance, in Bitcoin, they are used to index transactions within a block, creating a digital fingerprint of the entire set of transactions and enabling efficient verification of whether a transaction is included in the block.
The Merkle Root
Hashing starts at the leaf level, and all hashes are included in the hash of nodes at the next level. This process continues, creating hashes of hashes, until reaching the single top root hash. This root hash, known as the Merkle root, contains all the information about every transaction hash in the block. It provides a single-point hash value that validates everything in the block. Despite the tree’s growth, the Merkle root remains constant at 32 bytes.
Balanced Merkle Trees
A Merkle tree must have an even number of leaf nodes. If the number of leaf nodes is odd, the last hash is duplicated to create an even number of leaf nodes, resulting in a balanced tree. To prove a transaction’s inclusion in the block, a node only needs to produce 32-byte hashes in a logarithmic number of steps relative to the total number of transactions.
This constitutes an authentication path or Merkle path, connecting the specific transaction to the tree’s root. This method is efficient as the logarithmic growth rate is much slower compared to the increase in the number of transactions, allowing nodes to produce a verification path with just 10 to 12 hashes for over a thousand transactions within a megabyte-sized block.
Applications in Blockchain Technology
Nodes that do not store the entire blockchain (SPV nodes in Bitcoin) use the Merkle path to verify transactions without downloading entire blocks. The Merkle tree’s utility lies in enabling users to verify specific transactions efficiently, without needing to download the entire blockchain.
Merkle tree is a powerful data structure that enhances the efficiency and security of data verification in large data sets. Its application in blockchain technology, show its ability to manage transaction verification processes, making it an fundamental component of modern Blockchain.
