Merkel Tree: What is it, and how does it work?

A hash function is like a fingerprint machine. It takes any input, such as a file, a text, or a number, and produces a unique output, called a hash, that is much shorter than the input. The hash is like a fingerprint of the input. It is tough to find two different inputs that have the same hash. And it is impossible to get the original input from the hash.

But what if you have many files? Calculating and storing the hash for each file separately would be tedious. That's where Merkle trees come in handy.

A Merkle tree is like a family tree of hashes. You start with the hashes of each file as the leaves of the tree. Then you pair up the hashes and combine them to get new hashes. You repeat this process until you reach the top of the tree, where you have only one hash left. This hash is called the Merkle root.

But how do you verify a specific file? You don't need to download and check all the files in the tree. You only need to download and check a few hashes along the path from the file to the Merkle root. This path is called a Merkle proof.

Then you can calculate H AB by combining H A and H B and calculate H ABCD by combining H AB and H CD . If H ABCD matches the Merkle root, you can be sure that."cat.jpg" is correct.

You can use the same analogy to verify if the transaction present in the block is tempered by verifying the Merkle root instead of cat.jpg or dog.txt. It'll be a bunch of transactions at the leaf nodes.

What if I only have three leaf nodes? How will I create a Merkle Tree?

This scenario can quickly be addressed by duplicating one node, thus making the total number of nodes four.

For example, suppose you have transactions. T A, T B, and T C. You can calculate their hashes. H A, H B, and H C. Then you can duplicate H C to get H C'. Afterward; you can pair up and combine the hashes to get H AB, H CC’, and H ABCC’. The Merkle root is H ABCC’.

Summing up, Merkle trees benefit blockchain and other distributed systems, where many computers must share and verify large amounts of data. By using Merkle trees, they can save bandwidth, storage, and computation time.

Here's a quick Java example to show how you can create your own Merkle tree:

Output of the above code:

Thank you for taking the time to read my article.

Part 2: Merkle Tree: A Blockchain Perspective

Merkle Tree: How Blockchain Ensures Data Integrity and Security

In a blockchain context, a Merkle tree is constructed for the transactions within a block. Let's take an example to illustrate this process. Consider a block containing four transactions: