Merkle Trees and Merkle Roots Explained

What Is a Merkle Tree?

The concept of a Merkle tree was introduced by computer scientist Ralph Merkle in the early 1980s. This structure effectively verifies the integrity of datasets, making it especially suitable for peer-to-peer networks where participants need to share and independently verify information. Hash functions are at the core of Merkle trees, so it is advisable to familiarize yourself with the basics of hashing before diving deeper into Merkle trees.

How Does a Merkle Tree Work?

Imagine you want to download a large file. When using open-source download software, you typically check whether the hash of the downloaded file matches the hash provided by the developer. If the hashes match, it indicates a successful download.

If the hash values do not match, there may have been an issue. You might have downloaded a malicious file disguised as software or the wrong file, resulting in an unusable file. If it was a download error, you would certainly feel frustrated, especially after waiting a significant amount of time for the download to complete. Now you have to start over, hoping not to encounter the same error again.

Have you ever wondered if there is a simpler way to address this problem? This is where the Merkle tree comes into play. A Merkle tree can break the file into multiple data blocks. For example, a 50GB file can be divided into 100 smaller 0.5GB chunks, allowing for sequential downloads, similar to how torrent files work.

At this point, the source of the file is a hash value known as the Merkle root. This single hash value represents all the data blocks that make up the file, simplifying data verification.

To clarify further, let's consider an example. Suppose an 8GB file is divided into eight parts, named A through H. Next, each segment is fed into a hash function to generate eight distinct hash values.

This example should help illustrate the concept. If we obtain the hash values of all segments, can we identify the problem by comparing them to the original file when one hash value fails? Perhaps, but the efficiency would still be low. If the file has thousands of segments, would we really need to hash and compare each segment one by one?

In fact, we do not need to do that. We can combine pairs of hash values and perform a merge hash operation. Specifically, we hash hA + hB, hC + hD, hE + hF, and hG + hH to get four new hash values. Then, we perform another round of merging until we eventually arrive at two hash values, which are then merged to produce a single master hash value, known as the Merkle root (or root hash).

Now we have the Merkle root representing the downloaded file. By comparing this root hash value with the original file's value, if they match, everything is normal! If the hash values differ, it indicates that the data has been tampered with. In other words, one or more segments generated different hash values, meaning even minor modifications in the data will completely change the Merkle root.

Fortunately, identifying the erroneous segment is also straightforward. Suppose the issue lies with hE. First, we request the two hash values that generated the Merkle root from others (hABCD and hEFGH). If our hABCD value matches with theirs, it confirms that the subtree is error-free. If hEFGH does not match, we can start troubleshooting from there. Next, we ask for the hEF and hGH hash values from others and compare them with our own. If hGH is fine, then hEF is the problem. Finally, we compare the hash values of hE and hF; once we identify that the error source is hE, we can re-download that data block.

Why Use Merkle Roots in Bitcoin?

The applications of Merkle trees are quite extensive, but this article will focus on their important role in blockchain technology. Bitcoin and many other cryptocurrencies rely heavily on Merkle trees. The Merkle tree is a component of every block and is typically located in the block header. Through the transaction hash values (TXIDs) of each transaction, we can derive the leaves of the tree.

In this context, the Merkle root serves multiple purposes. Next, we will examine the applications of the Merkle root in cryptocurrency mining and transaction verification.

Mining

Bitcoin blocks consist of two main components. The first part is a fixed-size block header that contains metadata about the block; the second part is a variable-size block body, which is typically much larger than the header, containing a series of transaction records. Miners continuously perform hashing operations until they find a result that meets specific criteria, thereby mining a valid block. To achieve the correct result, they may need to attempt trillions of combinations. Each attempt requires the miner to modify a random number in the block header—the nonce value—to generate different outputs. However, the other parts of the block, including thousands of transactions, remain unchanged.

The introduction of the Merkle root significantly simplifies this process. At the start of mining, all transactions are packaged and constructed into a Merkle tree, and the resulting 32-byte root hash is placed in the block header. This way, miners do not need to hash the entire block but can focus solely on the block header for calculations.

This method effectively prevents data tampering, allowing all transactions to be efficiently summarized in a compact form. The list of transactions in a valid block header cannot be modified; otherwise, the value of the Merkle root would change. When the block is sent to other nodes, they compute the root hash from the transaction list, and if it does not match the value in the block header, the block will be rejected.

Verification

We can also leverage another interesting feature of the Merkle root, particularly useful for lightweight clients (nodes that do not store a full copy of the blockchain). If you are running a node on a resource-limited device, you certainly do not want to download all transactions in the block and perform hash calculations. Instead, you can request a Merkle proof, which is provided by full nodes, serving as evidence that a specific transaction was included in a given block. This proof is known as "Simple Payment Verification" (SPV), a concept that Satoshi Nakamoto detailed in the Bitcoin white paper.

Suppose we want to obtain information for a transaction with the TXID hD. If we know hC, we can compute hCD. Next, using hAB, we can derive hABCD. Finally, by referencing hEFGH, we can confirm whether the computed Merkle root matches the root hash value in the block header. If the match is successful, it indicates that the transaction has been included in the block, as it is virtually impossible to generate the same hash value using different data.

In this example, we performed only three hash operations. Without the Merkle proof, seven operations would be necessary. Given that the current block contains thousands of transactions, Merkle proofs save us a considerable amount of time and computational power.

Conclusion

The significance of Merkle trees in the field of computer science has been validated, and as we have seen, they hold great value in blockchain technology as well. Merkle trees facilitate easier information verification in distributed systems, avoiding congestion from redundant data across the network.

Without Merkle trees and Merkle roots, the blocks of Bitcoin and other cryptocurrencies would not be as compact as they are today. Although lightweight clients may face disadvantages in terms of privacy and security, Merkle proofs enable users to verify whether transactions have been successfully included in blocks at minimal cost.

Risk Warning

While the cryptocurrency market offers significant growth potential and innovation opportunities, it also carries a high level of market risk and price volatility. The value of crypto assets can fluctuate dramatically in a short period, potentially leading to substantial financial losses for investors. Additionally, the cryptocurrency market faces multiple risk factors, including technical risks, legal and regulatory uncertainties, cybersecurity threats, and market manipulation. We strongly advise users to conduct thorough research and due diligence before making any investment decisions and to consult professional financial advisors. All investment decisions are made at the user’s own risk. Thank you for your trust and support of Venkate!

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