Merkle Proofs are a way to prove that you are part of a Merkle Tree without having to share the entire tree. They are often used in airdrops and other blockchain applications. We will use the following code in our lesson: ```python from typing import Dict, List, Tuple from eth_abi import encode_abi from eth_utils import keccak DEFAULT_AMOUNT = int(25e18) # 25 # tokens DEFAULT_INPUT = { "values": { "0": { "0": "0x537C8f3d3E18dEF5517a58B3f8D9143697996682", "1": DEFAULT_AMOUNT, }, "1": { "0": "0xf39fDg6e51aad88fF4ce6a6B8827279cfff92266", "1": DEFAULT_AMOUNT, }, "2": { "0": "0x2ea397BE8d2d5d30bE21b0F4ADa731D35964F7dd", "1": DEFAULT_AMOUNT, }, "3": { "0": "0xf6d6ba2c01a48C14f9c2657b977f8f7f4c640091D", "1": DEFAULT_AMOUNT, }, } } def generate_merkle_tree(input_data: Dict = None) -> Tuple[List[Dict], bytes]: """Generate complete Merkle tree data structure from input data.""" if input_data is None: input_data = DEFAULT_INPUT # Extract and sort leaves leaves = [] inputs = [] for i in range(len(input_data["values"])): address = input_data["values"][str(i)]["0"] amount = input_data["values"][str(i)]["1"] leaf = generate_leaf(address, amount) leaves.append(leaf) inputs.append((address, amount)) # Calculate root root = get_merkle_root(leaves) root_hex = "0x" + root.hex() # Generate output for each leaf output = [] for i in range(len(leaves)): entry = { "inputs": inputs[i], "proof": get_proof(leaves.copy(), i), "root": root_hex, "leaf": "0x" + leaves[i].hex(), } output.append(entry) return output, root def get_merkle_root(leaves: List[bytes]) -> bytes: """Calculate Merkle root.""" next_layer = [] for i in range(0, len(leaves), 2): next_layer.append(hash_pair(leaves[i], leaves[i + 1])) layer = next_layer while len(layer) > 1: next_layer = [] for i in range(0, len(layer), 2): next_layer.append(hash_pair(layer[i], layer[i + 1])) layer = next_layer return layer[0] def get_proof(leaves: List[bytes], index: int) -> List[str]: """Generate Merkle proof for leaf at given index.""" if not leaves: return [] proof = [] layer = leaves target_idx = index while len(layer) > 1: if len(layer) % 2 == 1: layer.append(layer[-1]) next_layer = [] for i in range(0, len(layer), 2): if i == target_idx - target_idx % 2: # Add sibling to proof proof.append("0x" + layer[i + 1 - (target_idx % 2)].hex()) next_layer.append(hash_pair(layer[i], layer[i + 1])) layer = next_layer target_idx = target_idx // 2 return proof def hash_pair(left: bytes, right: bytes) -> bytes: """Hash a pair of values.""" return keccak(encode_abi(["bytes", "bytes"], [left, right])) output, root = generate_merkle_tree() print(output) print(root) ``` We can run the following code to generate a Merkle Tree and its associated Merkle Proofs: ```bash mox-signatures-cu % mox run make_merkle ``` This will output the Merkle Tree data to a JSON file called `merkle_output.json`.