Merkle trees are a fundamental data structure in Bitcoin and many other cryptocurrencies. They are used to improve the efficiency of verification of transactions and to enable what is known as “lightweight clients”, which do not need to download the entire blockchain to verify that a transaction is valid.
A Merkle tree is a binary tree, in which each non-leaf node is the hash of the concatenation of the hashes of its two child nodes. The leaves of the tree are hashes of the data blocks in the blockchain.
In Bitcoin, each transaction has a unique hash, and so each leaf node in the Merkle tree represents a single transaction.
The root node of the tree is called the Merkle root, and it represents the entire set of transactions in the blockchain. When a new block is added to the blockchain, its hash is calculated and added as a new leaf node to the Merkle tree.
The hashes of all the other nodes in the tree are then recalculated all the way up to the root node. This process is repeated for every new block that is added to the blockchain.
Lightweight clients only need to download a small part of the blockchain, called the block header, in order to verify that a particular transaction is included in a block. The block header includes the hash of the Merkle root, which represents all the transactions in that block.
The lightweight client can then calculate all of the hashes in the path from that transaction’s leaf node to the Merkle root, and compare them against those in the block header. If they match, then that transaction has been successfully verified.
The use of Merkle trees makes it possible for Bitcoin users to verify transactions without having to download and store the entire blockchain. This makes Bitcoin much more scalable than it would otherwise be, and has been crucial in its adoption as a global payment system.