Merkle Trees and Merkle Roots

The Merkel tree is one of those data structures that work based on pure mathematics and public-key cryptography. This algorithm develops by Ralph Merkel in the early 1980s. The Merkel tree is also a structure for validating a set of data integrity used in digital currencies for peer-to-peer transactions. Merkel trees generally use hash functions.

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How the Merkel Tree Works?

Imagine you want to download a large file from the server. To authenticate this file in an open-source system, the entire file must be downloaded and then verified. the file entered into your system, if it is not approved, the file will have no use. In this case, you have to re-download another file with the same amount of information, which is very scary!

The Merkel tree offers a much better solution to such problems. your file splits into much smaller chunks, each of which must be approved or rejected separately. Suppose that instead of a large 100 GB file, you have to download small 100 MB files and certify each one in the open-source system. Torrent systems work the same way today.

In the Merkel tree, the Merkel root is considered as the main hash so that the data authentication faces a much lower volume. Imagine your file splits into twelve thousand parts. you need to authenticate every twelve thousand nodes with a specific hash in your system. What happens in this case? Everything will be destroyed. for easing this, a binary system is used, and both nodes together form a hash. Similarly, the nodes come up and all four nodes form a hash to reach the root and get a single hash.

All you have to do is to download the bulk file in this way. Then check the Merkel root hash with the hash of the file on the system to increase the speed of work. If any fragment of the data changes, the hash in the Merkel root will change in general, so there is no need to worry about changing part of a file.

The Merkel tree breaks large files into smaller files in open-source systems. The best algorithm for comparing data without having to download it and receive information from another sender is the same algorithm.

The reason for using Merkel root in Bitcoin

The vital part of a block in a Bitcoin blockchain is the Merkel root, which is located in the block header. with this algorithm, various transactions are addressed and performed. But there are benefits to Merkel’s roots that we will explore below:

Mining

Each Bitcoin block consists of two parts, the header, and the body. The structure of the header is fixed and contains metadata related to transactions, but its body includes all transactions related to a block. Mining is a digital currency in which different numbers of hashes randomly generate to match the target block. For example, more than a trillion times a different hash generates to reach a block. Merkel root is in the block header to hash all the block transactions, so miners no longer need to target all the transactions in a block and check the hash of each. Compare the hash with Merkel’s root to discover the block.

For this reason, the speed of mining is increased. In a complete compact system, you find a block header, compare its hash, which is certified by Merkel root, to your production hash, and then simply discover the block if it were the same. If this operation did not have Merkel roots, the trillions of transactions per block would have to be compared with the trillions of random hashes generated, which was considered extremely cumbersome and inefficient.

verification

In the blockchain, some nodes are light clients. This means that all these nodes do is completely copy the blockchain. If you do not have enough resources, you do not need to download the entire blockchain to your system. In that case, all that needs to be done is to verify the Merkel root, which will let you know if the transaction you have made is on the block or not. This system is in Bitcoin SPV processes, also known as simple payment authentication.

Consider an example in the image below. Suppose we want to examine the information of a transaction whose TXID is equal to hD. If you have hC, you can get hCD, then we go for hAB so we can get hABCD. Finally, with hEFGH, we can find the hash and compare it to the Merkel root. If the comparison is acknowledged, then the transaction is in this block.

Conclusion

The Merkel tree is one of the most widely used mathematical algorithms in Bitcoins and cryptocurrencies. This algorithm is best used to reduce transaction costs as well as increase productivity in mining. Of course, we examined its different applications in this article. If this hash algorithm did not exist, Bitcoin blocks would be several hundred times larger than the current volume or perhaps larger.