## What’s A Merkle Tree?

If you’re a newcomer to the blockchain world, you may have come across the phrase *“Merkle Tree”* and felt a little lost. While Merkle Trees are not a widely-understood concept, they’re also not terribly complicated.

So, what’s a Merkle Tree? To put it very simply, a Merkle Tree is a method of structuring data that allows a large body of information to be verified for accuracy extremely quickly and efficiently.

Since Merkle Trees are such a crucial component of blockchain technology, it’s worth gaining an in-depth understanding of them. This post will help you do just that. Let’s get started.

## All About Merkle Trees

The story of Merkle Trees begins way back in 1979 with a person named Ralph Merkle. While in grad school at Stanford University, Merkle wrote an academic paper called “A Certified Digital Signature.” In this essay, Merkle described a new, extremely efficient method of creating proofs. In other words, he designed a process for verifying data that would allow computers to do their work much, much faster than ever before.

Merkle’s idea, now better known as a Merkle Tree, revolutionised the world of cryptography and, by extension, the way that encrypted computer protocols function. In fact, Merkle Trees are mentioned repeatedly in Satoshi Nakamoto’s 2008 essay that introduced Bitcoin to the world. They’re also used extensively in Bitcoin’s foundational code.

So, what exactly are Merkle Trees? First, it’s important to note that each transaction on a blockchain has its own unique transaction ID. With most blockchains, each transaction ID is a 64-character code *(SHA2 Hash)* that takes up 256 bits (32 bytes) of memory.

When you consider that blockchains are typically made up of hundreds of thousands of blocks, with each block containing as many as several thousand transactions, you can imagine how quickly memory space becomes a problem.

As such, it’s optimal to use as little data as possible when processing and verifying transactions. This minimises CPU processing times while also ensuring the highest level of security.

Well, that’s exactly what Merkle Trees do. To put it very simply, Merkle Trees take a huge number of transaction IDs and put them through a mathematical process that results in a single, 64-character code *(SHA2 Hash)*.

This code is extremely important because it allows any computer to quickly verify that a specific transaction took place on a particular block as efficiently as possible. This code is called the Merkle Root.

## What’s A Merkle Root?

The single code that a Merkle Tree produces is called the Merkle Root. Each block in a blockchain has exactly one. And, as we just mentioned, the Merkle Root is a crucial piece of data because it allows computers to verify information with incredible speed and efficiency.

Let’s dive a little deeper. How is a Merkle Root produced? The first step is to organise all of the data inputs.

Merkle Trees, by design, always group all of the inputs into pairs. **If there is an odd number of inputs, the last input is copied and then paired with itself.** This holds true for all the transaction IDs written onto a block of a blockchain.

*Example:*

*EvenNumber: 12345678 == 11223344 & 55667788*

*OddNumber: 1234567 == 12345677 == 11223344 & 55667777*

For instance, let’s suppose that a single block contains a total of 512 transactions. The Merkle Tree would begin by grouping those 512 transactions IDs into 256 pairs. Then, those 256 pairs of transaction IDs would go through a mathematical process, called a hashing function or hashing algorithm, that would result in 256 new, 64-character alphanumeric codes.

The same exact process would occur again. Those 256 new codes would be paired up and turned into 128 codes. The process would be repeated, cutting the number of codes in half each time, until only a single code remained. That single code is our Merkle Root.

## An Example Of A Merkle Tree

To make this concept clear, let’s look at a very simple example of a Merkle Tree. Imagine that there were 8 transactions performed on one particular block. In reality, transaction IDs are 64 characters long, but for the sake of simplicity, let’s pretend that they’re only 8 characters long. To make things even easier, let’s use only numbers (and ignore letters altogether).

So, in this example, our eight transactions IDs will be:

- 11111111
- 22222222
- 33333333
- 44444444
- 55555555
- 66666666
- 77777777
- 88888888

Now let’s suppose that the method for hashing transaction IDs together is to take the first, third, fifth, and seventh digits from each of the two IDs being combined, and then simply push those numbers together to form a new, 8-digit code.

Of course, in reality, the mathematics behind hashing algorithms is far more complicated than this. But for this simple demonstration, this elementary system will suffice.

This is what our Merkle Tree would look like:

Notice that the number of codes is cut in half each step down the Merkle Tree. We start with 8 transaction IDs and, after just 3 steps, end up with a single code—the Merkle Root. In this example, our Merkle Root is the code in the bottom box: 12345678.

The primary benefit of Merkle Trees is that they allow extremely quick verification of data. If we want to validate a single transaction ID, we wouldn’t need to double-check every single transaction on the block. Rather, we would only need to verify that particular “branch” of our Merkle Tree.

## Efficiency And Speed: The Benefits Of Merkle Trees

Let’s suppose that we want to validate a transaction ID in our current example. Suresh says that he paid Praveen a certain sum of Bitcoin and tells us that the transaction ID is 88888888. He also sends us 3 hashes: 77777777, 55556666, and 11223344. That’s all the info that needs to be sent or received to verify Suresh’s payment to Praveen.

These three hashes, along with the transaction ID in question and this particular block’s Merkle Root, are the only data needed to verify Suresh’s payment to Praveen. This is far less data than what would be required to verify the entire Merkle Tree. As a result, the verification process is much faster and far more efficient for everyone.

Here’s how it works. We already have the block’s Merkle Root, so Suresh doesn’t need to send us that. He sends us his transaction ID and the 3 additional hashes we listed above. He also sends a tiny bit of information about the order and placement in which to use the hashes. Now, all we have to do is run the hashing algorithm on the set of data Suresh provided.

We start by hashing the first code 77777777 with the transaction ID 88888888, which gives us the result 77778888. Suresh didn’t send us this code but he didn’t need to because we’re using the same hashing algorithm as him. Therefore, we receive the exact same results.

We then take the second code Suresh sent us, 55556666, and hash it with the new code 77778888 we just derived. This, of course, produces the number 55667788.

Finally, we hash the third code Suresh gave us, 11223344, with the other new code we received, 55667788, and we end up with the correct Merkle Root: 12345678.

Notice that we only need 3 codes from Suresh and only had to run the hashing algorithm three times to see that Suresh’s transaction is valid. That means our computer has done less than half the work that would’ve been required to verify the entire Merkle Tree. The original Merkle Tree diagram has 15 numbers and the hashing algorithm needs to be run 7 times. But more than half of that tree isn’t necessary to verify Suresh’s transaction!

This procedure is sufficient to verify that Suresh did, in fact, pay Praveen that certain sum of Bitcoin because we derived numbers that, when hashed together with the other codes Suresh sent us, produced the same Merkle Root that we already knew to be true for this particular block.

Suresh can’t fake a transaction because that would require finding a fake transaction ID and an additional set of fake codes that, when put through the hashing function, would produce the true Merkle Root. The chances of this happening are so astronomically small that we can confidently say it’s impossible.

In this simple example, the savings of computing power might not seem substantial. However, when you consider that blocks in a blockchain might contain several thousand transactions, it’s easy to see how Merkle Trees increase efficiency so dramatically.

In short, that’s the main benefit of a Merkle Tree. It allows computers to verify information extremely efficiently and with far less data than what would be required without the Merkle Tree.

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