A Merkle proof is a cryptographic proof that allows a user to verify the inclusion of a specific piece of data in a Merkle tree without needing the entire tree. The Keccak-256 algorithm (also known as SHA-3) is commonly used as the hashing function to build Merkle trees due to its cryptographic properties.

To generate a Merkle proof in Python using Keccak-256, you can use the following steps:

  1. Install Required Libraries: First, make sure you have the required libraries installed. You can use the eth_hash library to compute the Keccak-256 hash.

    bash
    pip install eth-hash
  2. Implement the Merkle Proof:

python
import hashlib from eth_hash.auto import keccak def compute_hash(data): return keccak(data) def generate_merkle_proof(merkle_tree, target_leaf_index): proof = [] node_index = target_leaf_index for level in range(len(merkle_tree) - 1, 0, -1): is_right_node = node_index % 2 sibling_index = node_index - 1 if is_right_node else node_index + 1 if sibling_index < len(merkle_tree[level]): proof.append(merkle_tree[level][sibling_index]) node_index //= 2 return proof def verify_merkle_proof(merkle_root, target_data, proof): current_hash = compute_hash(target_data) for sibling in proof: current_hash = compute_hash(current_hash + sibling) return current_hash == merkle_root # Example usage: if __name__ == '__main__': merkle_tree = [ # Merkle tree layers (from bottom to top) [compute_hash(b'data1'), compute_hash(b'data2'), compute_hash(b'data3'), compute_hash(b'data4')], [compute_hash(compute_hash(b'data1') + compute_hash(b'data2')), compute_hash(compute_hash(b'data3') + compute_hash(b'data4'))], [compute_hash(compute_hash(compute_hash(b'data1') + compute_hash(b'data2')) + compute_hash(compute_hash(b'data3') + compute_hash(b'data4')))] ] target_leaf_index = 1 # Index of the target leaf whose inclusion needs to be proven target_data = b'data2' # Data of the target leaf proof = generate_merkle_proof(merkle_tree, target_leaf_index) merkle_root = merkle_tree[-1][0] is_verified = verify_merkle_proof(merkle_root, target_data, proof) print(f"Is verified: {is_verified}")

This code demonstrates how to generate and verify a Merkle proof for a specific data (leaf) in a Merkle tree built using the Keccak-256 algorithm. The generate_merkle_proof function generates the proof, and the verify_merkle_proof function verifies the proof against the Merkle root. The example uses hardcoded data, but in practice, you would replace the data with the actual data from your application.

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