What Is Merkle Proof?
Also known as: Merkle Path, Merkle Branch, Inclusion Proof
In short
A Merkle proof is a cryptographic proof that lets you verify a piece of data is included in a Merkle tree using only a few hashes on the relevant branch and the Merkle root, without needing the whole tree.
A Merkle proof consists of the hash of the data to be verified and the hashes of the sibling nodes at each level along the path from the leaf to the root. The verifier combines and rehashes these hashes in order; if the result matches the Merkle root known from a trusted source, it is proven that the data is in the tree. Because the number of hashes needed grows logarithmically with the amount of data, about 20 hashes are enough in a tree containing one million items.
Simplified payment verification (SPV) on Bitcoin relies on light clients checking with Merkle proofs that a transaction was included in a block. In airdrop and whitelist applications, not all eligible addresses are written on-chain; only the Merkle root is recorded in the smart contract, and each user presents their own proof at claim time. This method significantly reduces gas costs.
In cryptocurrency exchanges' proof of reserves practices, users can check with a Merkle proof that their own balances are included in the liability tree the exchange publishes. However, a proof shows only inclusion; if the tree's root was built from incorrect or incomplete data, the proof alone cannot be expected to reveal this.
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