## Introduction to Merkle Trees We will be covering the concept of Merkle Trees. They are a powerful tool that is used in various domains like blockchain technology, cryptography, and more. Merkle trees are like a hierarchical data structure that allows for efficient and secure verification of data integrity. It enables us to verify a large amount of data using a compact hash value, known as the root. Let's dive into the world of Merkle Trees and understand the key concepts behind them. ## What are Merkle Trees? Merkle trees essentially help us to efficiently verify a large amount of data using a small, compact hash value. They are like a hierarchical data structure that holds data and its hash values. We can use Merkle Trees in a variety of ways: * **Verification of data integrity:** If we make a change to any data, it will affect all hash values leading up to the root, thus allowing us to easily detect any manipulation or tampering. * **Efficient data comparison:** By comparing the root hash values of two Merkle Trees, we can quickly determine if the data sets are the same or different. * **Distributed ledger technology:** Merkle trees are used to verify transactions in blockchains. Each block in a blockchain contains a Merkle tree that represents all the transactions in that block. * **Secure data sharing:** By providing proof that a specific piece of data is included in a Merkle tree, we can share data securely without revealing the entire dataset. ## Building a Merkle Tree Let's consider a simple scenario where we have a set of data elements, and we want to construct a Merkle tree from them. We can build a Merkle Tree by: 1. **Hashing each data element:** This step involves applying a cryptographic hash function to each data element, producing unique hash values for each element. 2. **Pairing and hashing hash values:** We pair up the hash values, creating a new hash by combining the two hash values. The new hash can be created by sorting the hashes and then combining them using a cryptographic hash function. 3. **Continuing the process:** The newly generated hash values from step 2 are then paired up and hashed again, creating a new level in the tree. This process continues until we reach the root node. ## Example We are going to go over a simple Merkle Tree with four leaf nodes. The first step we will take is to create an input for our Merkle Tree. ```python DEFAULT_AMOUNT = int(25e18) # 25e18 tokens DEFAULT_INPUT = { "values": { "0": { "0": "0x537C8f3d3E18Df5517a58B37809143697996682", "1": DEFAULT_AMOUNT, }, "1": { "0": "0xF39F0de51aa0d88f6e4c6aB8827279cffb92266", "1": DEFAULT_AMOUNT, }, "2": { "0": "0x2ea3970e82D8d30b25b08e21FAAD4731035964f7dd", "1": DEFAULT_AMOUNT, }, "3": { "0": "0xf6d8ab2c0148C14FC92657f937f77c464c40091D", "1": DEFAULT_AMOUNT, }, } } ``` We can now use this input to build a Merkle Tree and print it to a `JSON` file for later use. ```bash patrick@kcu:mox-signatures-cu % mox run make_merkle ``` This will output a `JSON` file that contains the Merkle Tree data. ## Workshop We are now going to complete a workshop. We will build a Merkle Tree with eight leaf nodes. We will be using the code we've created above as a starting point. We can modify the `DEFAULT_INPUT` to include eight leaf nodes. We can also use the command `mox run make_merkle` to create the new Merkle Tree. Remember, you can try to complete this workshop without the aid of AI. If you get stuck, take a break and then you can use AI or the discussions to help you solve it. Good luck! This is just a basic introduction to Merkle trees and the concept of building them. There are more advanced topics and applications of Merkle trees that we will cover in later lessons.