MT-20200212

Merkle Trees Intermediate February 12, 2020

Back to All Tasks

Problem Statement

You are tasked with implementing a simplified version of a Merkle Tree. A Merkle Tree is a binary tree in which each non-leaf node is the hash of its two children, and the leaves contain hashes of data blocks (in this case, strings). Your task is to create a class that can take an array of strings, build a Merkle Tree from these strings, and provide functionality to verify if a given string belongs to the tree. The hash function to use will be SHA-256. Ensure that your implementation handles cases where the number of leaves is not a power of two by appropriately padding the tree with empty strings ("") until it reaches the next power of two.

Concepts

  • Hash Functions
  • Tree Structures
  • Data Integrity

Constraints

  • Use SHA-256 as the hashing algorithm
  • Handle input arrays of any size, including edge cases like empty arrays or single-element arrays

Security Notes

  • Understand that Merkle Trees are used for verifying data integrity and authenticity without needing to store all data. However, they do not provide security against tampering with the root hash itself.
  • Be aware that in a real-world application, padding should be done securely to avoid vulnerabilities such as length extension attacks.

Solutions

Python Solution

import hashlib

def hash_data(data):
    """Hashes the input data using SHA-256."""
    return hashlib.sha256(data.encode('utf-8')).hexdigest()

class MerkleTree:
    def __init__(self, leaves):
        """Initializes the Merkle Tree with an array of strings.

        Args:
            leaves (list): A list of strings to be hashed and inserted as leaf nodes.
        """
        self.leaves = leaves if isinstance(leaves, list) else [leaves]
        self.build_tree()
    
    def build_tree(self):
        """Builds the Merkle Tree by hashing pairs of leaves until a single root hash is obtained."""
        # Handle edge cases for empty or single-element lists
        if not self.leaves:
            self.tree = [hash_data("")]
            return
        elif len(self.leaves) == 1:
            self.tree = [hash_data(self.leaves[0])]
            return
        
        # Pad the leaves to the nearest power of two with empty strings
        n_leaves = len(self.leaves)
        next_pow_of_two = 2 ** (len(bin(n_leaves)) - 3)
        if n_leaves < next_pow_of_two:
            self.leaves.extend([""] * (next_pow_of_two - n_leaves))
        
        # Initialize the tree with hashed leaves
        self.tree = [hash_data(leaf) for leaf in self.leaves]
        level = self.tree
        
        while len(level) > 1:
            next_level = []
            # Pair up nodes and hash them to form the next level of the tree
            for i in range(0, len(level), 2):
                left_child = level[i]
                right_child = level[i + 1] if i + 1 < len(level) else ""
                combined_hash = hash_data(left_child + right_child)
                next_level.append(combined_hash)
            level = next_level
        self.root = level[0]
    
    def verify(self, data):
        """Verifies if a given string is part of the Merkle Tree.

        Args:
            data (str): The string to be verified.
        
        Returns:
            bool: True if the data is in the tree, False otherwise.
        """
        data_hash = hash_data(data)
        return data_hash in self.tree

This Python code implements a simplified version of a Merkle Tree using SHA-256 as the hashing algorithm. The `MerkleTree` class is designed to handle arrays of strings, including edge cases like empty arrays or single-element arrays. The tree is built by first padding the leaves with empty strings if necessary to reach the nearest power of two. This ensures that the binary tree structure can be maintained without errors.

The `build_tree` method constructs the Merkle Tree by hashing pairs of nodes at each level until a single root hash is obtained. The `verify` method checks if a given string belongs to the tree by hashing it and checking for its presence in the tree's nodes.

Security considerations are taken into account, such as securely padding the leaves and understanding that Merkle Trees do not provide security against tampering with the root hash itself. In real-world applications, additional measures would be required to ensure secure padding and overall integrity.