Merkle trees, also known as hash trees or binary hash trees, are tree-like data structures used in computer science. They are named after their inventor, Ralph Merkle, who proposed the concept in 1979. Merkle trees enable efficient and secure verification of large datasets by breaking them down into smaller, manageable parts.
The Bitcoin whitepaper lists Merkle trees as a method for a simplified payment verification. If Merkle trees were not included, then every node on the network would have to retain a complete copy of every single Bitcoin transaction ever made, rendering transactions more or less unverifiable due to the scalability and storage limitations it would impose.
“It is possible to verify payments without running a full network node. A user only needs to keep a copy of the block headers of the longest proof-of-work chain, which he can get by querying network nodes until he’s convinced he has the longest chain” – Satoshi Nakamoto
Why Use a Merkle Tree?
- Efficiency: Merkle trees offer efficient ways to handle large datasets. By breaking down the data into smaller parts and employing hash functions, Merkle trees can verify data integrity without needing to access the entire dataset. This makes them particularly suitable for applications that involve large-scale data verification, such as blockchain technology and distributed systems.
- Integrity and Security: Merkle trees provide a secure way of verifying the integrity of data. By comparing hash values, it is possible to detect any tampering or alteration of data at any level of the tree. This property ensures the trustworthiness and authenticity of the data, making Merkle trees essential in applications that require secure data storage or transfer.
- Bandwidth Savings: Merkle roots require a slightly greater initial effort to construct, and then save on bandwidth when it comes to verification later on. For instance, consider the following comparison:
- Without a Merkle root: To verify that a transaction exists within a block on the bitcoin blockchain, it would need to download 75,232 bytes (2,351 x 32-byte TXIDs) of data to recreate the hash of all transactions in the block.
- With a Merkle root: Only 384 bytes (12 x 32-byte branches along the path of the Merkle tree) need to be downloaded to recreate the Merkle root hash.
The Structure of Merkle Trees
Bitcoin’s use of trees, roots, and proofs enables Simple Payment Verification (SPV). SPV allows lightweight clients to confirm if a transaction is part of a block without downloading the entire block or blockchain. This efficient verification process leverages the compact representation provided by Merkle proofs to validate transactions without requiring full data access.
Merkle trees consist of multiple layers, with each layer representing a level in the tree. The bottommost layer contains the original data elements or leaf nodes, while each subsequent layer is formed by hashing the nodes of the previous layer.
Merkle Trees
A Merkle tree, also known as a binary hash tree or Hash tree, is a specific type of data structure widely used in computer science. This mathematical data structure comprises hashes of various data blocks that summarize all transactions within a specific block. In blockchain technology, particularly within Bitcoin, Merkle trees enhance data encryption efficiency and security.
Merkle trees enable rapid and secure content verification across large datasets while ensuring consistency and data integrity. The concept forms the basis for several cryptographic protocols and applications. Additionally, these trees are a specific type of binary trees, where each non-leaf node is labeled with the cryptographic hash of the labels of its child nodes. This structure allows for efficient verification of dataset integrity by confirming that individual data pieces remain unaltered and correctly linked to the overall structure.
A Merkle tree is created by hashing pairs of nodes repeatedly, using a cryptographic hash function like SHA-256 until only one hash remains; this hash is known as the Merkle root or the “root hash.”
Merkle Roots
A Merkle root is a core concept in the context of Merkle trees, serving as a method for verifying the authenticity of data presented within a Merkle tree structure. In the realm of Bitcoin, Merkle roots play a crucial role in confirming that data blocks transmitted through the peer-to-peer network remain unaltered and undamaged. They are essential components in the computational processes necessary to maintain the functionality of the Bitcoin network.
By organizing data hierarchically in this manner, Merkle trees provide an efficient way to verify the integrity of an entire dataset without needing to access every individual element. Instead, you only need to compare the root hash with a trusted root hash to ensure the data has not been tampered with. This hierarchical structure ensures that any changes made to the dataset can be quickly identified and verified, maintaining the security and integrity of the network.
Nodes and Hashes
Nodes represent data. Consider a basic example with four leaf nodes, each containing a piece of data. Each of these nodes is then hashed, resulting in two new nodes, called the parent nodes. The parent nodes are then hashed, forming a single root node to represent the entire dataset.
This hierarchical structure allows for efficient verification, as only the root hash needs to be checked to confirm the integrity of the entire dataset. The hash values ensure that any tampering or alteration of the data will be detectable.
Merkle Proofs
A Merkle proof, or Merkle path, is a concise representation that includes the minimum required hashes and nodes from a tree branch. It is a means to verify that a specific piece of data is in a dataset without broadcasting the entire dataset. To validate, all a user needs to do is provide the data and hashes that need to be combined in order to obtain the root. Then the verifier can combine and hash until a single node is left. If the proof matches the posted root, the data is valid.
Example: Merkle Proof
Imagine we have a block header (and therefore the Merkle root) for the block 000000000000000000abcd1234567890fedcba0987654321fedcba0987654321
..and we want to verify that the transaction 1f3a4b5c6d7e8f90123456789abcdef123456789abcdef123456789abcdef1234 is inside this block.
Here’s the Merkle proof that proves the transaction is inside the block:
Txid: 1f3a4b5c6d7e8f90123456789abcdef123456789abcdef123456789abcdef1234
(reverse byte order)
Merkle proof:
9a4b5c6d7e8f90123456789abcdef123456789abcdef123456789abcdef1234567 left
2b3c4d5e6f7a8b90123456789abcdef123456789abcdef123456789abcdef1234 right
3c4d5e6f7a8b90123456789abcdef123456789abcdef123456789abcdef1234567 left
4d5e6f7a8b90123456789abcdef123456789abcdef123456789abcdef12345678 left
5e6f7a8b90123456789abcdef123456789abcdef123456789abcdef1234567890 left
6f7a8b90123456789abcdef123456789abcdef123456789abcdef123456789abcd left
7a8b90123456789abcdef123456789abcdef123456789abcdef123456789abcdef left
8b90123456789abcdef123456789abcdef123456789abcdef123456789abcdef123 left
90123456789abcdef123456789abcdef123456789abcdef123456789abcdef1234 left
abcdef123456789abcdef123456789abcdef123456789abcdef123456789abcdef12 left
bcdef123456789abcdef123456789abcdef123456789abcdef123456789abcdef12 left
cdef123456789abcdef123456789abcdef123456789abcdef123456789abcdef123 left
Merkle root:
0987654321fedcba0987654321fedcba0987654321fedcba0987654321fedcba00
(reverse byte order)
The above Merkle proof example contains a sequence of nodes from the Merkle tree, specifying the path required to reach the Merkle root. Each node indicates whether it resides on the “left” or “right,” ensuring that the pairs are concatenated in the correct order before hashing.
To verify if the TXID is part of the Merkle root, you start with the TXID and concatenate and hash the nodes provided in the Merkle proof. This process continues until the final hash matches the Merkle root found in the block header.
Beyond Bitcoin, Other Applications of Merkle Trees
Beyond the Bitcoin protocol, Merkle trees feature in a number of other systems, including, but not limited to, the following:
The Stratum V2 Protocol
The Stratum V2 protocol relies on Merkle trees to ensure the integrity and authenticity of mining jobs and transactions. By using predefined data, such as the prevhash and the Merkle root for the transaction set, miners can trust that they are working on legitimate blocks. When a miner receives a mining.notify request from a pool, it includes an array of Merkle tree hashes that denote the transactions to be included in the current block.
It allows pools to verify the work submitted by miners and reduces the risk of fraud or malicious behavior. The inclusion of the coinbase transaction — which contains the mining reward — as part of the Merkle tree ensures that this critical component is also verified and secure.
Proof of Reserves
Proof of reserves is a mechanism that ensures the security and integrity of cryptocurrency exchanges by verifying that they hold the assets claimed on their balance sheets.
Merkle trees play a crucial role in proof of reserves, as they allow for efficient verification of the exchange’s reserves without revealing sensitive information about individual users. By using proofs based on Merkle trees, exchanges can demonstrate to users that their bitcoin are securely stored and that the exchange is solvent.
Content Distribution Networks (CDNs)
Content distribution networks (CDNs) use Merkle trees for efficient distribution of content and authentication of user requests. This ensures that CDNs can deliver content quickly and securely while maintaining data integrity.
Distributed Databases
In distributed databases, such as Amazon’s DynamoDB, Merkle trees are used to ensure consistency and fault tolerance across multiple nodes. By using Merkle tree-based proofs, database systems can verify the correctness and integrity of stored data without requiring a complete synchronization of all nodes.
Git Version Control System
Merkle trees are also employed in the Git version control system for efficient data verification and authentication. In Git, Merkle trees are used to represent the commit graph, enabling quick and secure verification of the repository’s history without requiring full duplication of files or data.
