This also means that the Merkle tree is inverted down where the leaf nodes are the lowest node. At the core of Merkle trees, we need to learn three important terms. They are as below:. If you take a look at the Merkle tree as a whole, it is an upside-down tree. The tree is capable of summarizing a whole set of transactions by itself. This means that the user can verify if a transaction is part of the block or not.
To make Merkle trees work, hashing is used. It simply does the hashing pairs of nodes repeatedly until only one hash value is left. The left hash value is known as Merkle Root or the Root Hash. The tree is created from the bottom up using the individual transactions hashes. The individual transaction hashes are also known as Transaction IDs. The leaf nodes are the nodes that contain transactional data hashes. In the case of the non-leaf nodes, they store the hash of the two previous hashes.
Another important property of Merkle trees is that it is binary in nature. This means that it requires leaf nodes to be even for it works. In case, if there is an odd number of leaf nodes, it will simply duplicate the last hash and make it even. Here, we see that four transactions have taken place in the block. These transactions are named X, Y, Z, and W.
Finally, these two hashes are used to create the Merkle Root or Root Hash. The whole process of hashing can be done on a very large data set which makes the Merkle Trees data structure useful in the case of decentralized networks. As we discussed earlier, hashing algorithms usage depends on the implementation. However, one of the most common hash functions that are used includes the SHA-2 cryptographic hash function. So, a transaction can be verified if the previous transactions are verifiable, thanks to the hash values.
Merkle tree is ideal for data integrity. Also, there is no need to go through the whole transaction to see its verifiability. The transactions can be verified with the use of the information stored in the block header. The Merkle root value is also changed depending on the previous transactions. This also means that the root values are changed frequently and can be used to verify transactions almost instantly.
All of these can sound a little bit similar to hash-list, however, this is not true. For a hash-list, you need to download the full list to verify transactions or data. In the case of the Merkle tree, you can download the branch and then use it to verify the transactions. There is no need to download the whole tree to verify transactions.
This also means that the whole tree can be divided into small data blocks which can be used to verify transactions all across the network. The concept is known as Merkle proofs. You can also check out Merkle tree python — a Merkle tree implementation in Python article. Bitcoin was the first cryptocurrency that employed Merkle trees effectively. To ensure that the hash values are protected and cannot be reversed easily, it utilizes the famous Secure Hashing Algorithm SHA This also means that the hash values output is bits long.
At the core, Merkle trees are used to store data and also prune transactions. In bitcoin, each block is connected to previous blocks using hash values. This is how the whole blockchain is created. In a block, there are block headers which contain important information such as:.
It is taken from the Bitcoin whitepaper itself. As you can see, it requires miners to include the transactions into the block. Once done, it is hashed and becomes part of the Merkle tree. The use of Merkle Trees, this way, can lead to multiple benefits. This includes one notable benefit, i. So, what do they do? They simply download the longest chain block headers and hence do not have to download the whole blockchain. To do all of these, they need to verify if it has the stored block headers for the longest chain.
This is how Merkle tree implementation is done in bitcoin. Ethereum blockchain also utilizes Merkle trees. However, the approach here is different than that of how bitcoin utilized it. In other words, a Merkle tree lets us represent arbitrarily many blocks while only transmitting a single hash across the wire. Merkle trees are also known as hash trees , because they hash data upwards in a tree.
It's easy to explain in code—here's how you can create a hash tree with only two elements. By concatenating the two digests and taking their hash, the root of the hash tree commits to both digests. Think about it: if there were some other way to produce this same root, then that would imply the existence of a hash collision.
Hash collisions should be impossible for a strong cryptographic hash function. Thus, the root of this hash tree, known as the Merkle root , must be a unique identifier of this exact tree. If you don't follow this argument, play around with another example in code! This intuition is really important, and we'll continue to build on it. The Merkle root is therefore an accumulator over all of the original data that was hashed to produce this tree.
It also commits to that data in order, since we used string concatenation on the underlying blocks to combine their values. If you had used a commutative operation like addition or XOR instead of concatenation, then technically you could've switched the order of some blocks and gotten the same root. This is undesirable, so don't make that mistake.
How does this scale up to many blocks though? Pretty simple. We repeat this same operation across the data in layers until we get a single root. So the root of this tree is 6c2d5a56fdfaebb4dba. Notice that if you modified any element of the tree, even by 1 bit, then the avalanche effect of the hash would cause every hash upstream to change, all the way up to the root.
Now, say we downloaded the Linux distro along with its Merkle root a single hash. We recompute the Merkle tree over the Linux distro on our side, and we find that our root doesn't match the one we were provided. This means our file is corrupted. How can we quickly diagnose which of the blocks we downloaded was faulty? See if you can figure this out for yourself. Here's the answer: we have to request the two hashes below the root in the canonical Merkle tree, and figure out which hash doesn't match up with our client-side tree.
Once we've figured it out which subtree is faulty, we can repeat this for the two children of that subtree, and so on until we reach the base. We've seen how powerful Merkle trees are for verifying file integrity. But the real power of cryptographic accumulators comes not just in accumulating data, but in then being able to efficiently prove claims about the data. Imagine an accumulator as an opaque box full of items. You can't directly look inside this box, but with the magic of cryptography, you can query it in specific ways.
One of the operations you can perform with a cryptographic accumulator is an inclusion proof. This is a small proof that decisively attests that an item exists in the accumulator. If you know the Merkle root of an e-book, how can I efficiently prove to you that a certain quotation comes from that e-book?
I can do this without providing you the entire e-book or even the entire Merkle tree. We only need to provide the data we're proving exists, the Merkle root, and sibling hashes along the path from the leaf up to the root. If you redo all of the hashing and the roots match, you will know with certainty that quotation was indeed part of the e-book. This kind of proof is known as a Merkle proof. You should be asking: why is this sufficient for an inclusion proof?
What if someone just makes up the sibling hashes to make the roots match? How do we know they came from the real Merkle tree? Inclusion proofs are a powerful primitive enabled by Merkle trees. We'll do a quick sneak preview of how this works. These blocks can be quite large, since they potentially contain thousands of transactions. To save on bandwidth, Bitcoin pulls off a clever trick: instead of transmitting all of the transactions, the transmitted block only includes a Merkle root of that block's transactions.
In practice, this transmitted data is known as a block header , while the transactions themselves are transmitted separately on request. We'll learn more about this later. Since a Merkle root is a cryptographic accumulator over all the underlying ordered data, every block header includes a commitments to all the transactions in that block.
Because of this optimization, lightweight clients only need to keep track of block headers and can selectively verify Merkle proofs that a certain transaction was included in a given block. This optimization is essential for mobile phones or web wallets to be able to use the Bitcoin network without having to download everything.
Don't worry if that's confusing; there's a lot of structure to Bitcoin that we'll explain in upcoming lessons. But by now you have gotten a glimpse of how useful Merkle trees can be. There are many more innovations on Merkle trees that are worth exploring, including proofs of non-inclusion, online updates, and n-ary Merkle trees.
We'll provide resources in the additional reading if you want to see how the state of the art has evolved. We will also provide reading on a subtle second preimage attack against a naive implementation of a Merkle tree though it's not of practical use in a blockchain setting.
In our next assignment, you'll be writing your own implementation of a Merkle tree.
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