Last Updated on August 18, 2022
In the bitcoin original paper, these trees are mentioned as a way to reclaim disk space.
Merkle roots are stored in Bitcoin block headers so as to enable efficient membership proofs for transactions in a block, which are necessary for Simple Verified Payment verification (SPV) nodes that only store block headers and not block contents.
The Merkle root is cryptographic proof of which transactions are in the block, and which order they are in. It provides a convenient piece of information to be included in the block header which is then hashed and included in the next block header. Without the Merkle root in the block header, we would have no cryptographic proof of which transactions are included in a block, nor proof that their contents haven’t been tampered with.
Using a Merkle tree is preferable over a hash chain or a hash of concatenated transactions because it allows for a much quicker and simpler test of whether a particular transaction is included in the set.
TECH: Membership proofs with respect to a hash chain are O(n) when there are n transactions in the chain, versus O(\log{n}) proofs with regards to a Merkle tree.
Miners, just like full nodes on the P2P network, receive new transactions from other full nodes and verify them by checking their digital signature and that they spend valid coins.
Merkle trees are not involved at this point. Later on, the miner takes all the verified transactions and creates a Merkle tree on top of them. As more transactions come to the miner, the miner verifies them and adds them to the Merkle tree.
The reason we have Merkle trees is so SPV nodes can efficiently verify that miners verified the transactions in the block