Understanding Merkle-Patricia Trees
Last updated
Last updated
In the realm of blockchain technology, an advanced data structure known as the Merkle-Patricia Tree forms a pivotal part of the infrastructure. This structure combines the properties of Merkle Trees and Patricia Tries, culminating in a highly efficient and secure model for data representation and verification. Although they are primarily associated with Ethereum, their usefulness extends far beyond just this single blockchain.
Merkle-Patricia Trees play an integral role in various Layer 2 solutions, side chains, and other scalability enhancements. Layer 2 solutions, for instance, such as Rollups, Plasma chains, and state channels, leverage these structures for creating compact proofs of data availability and state transitions. Similarly, side chains, which are distinct blockchain networks designed to operate alongside the main chain, also utilize Merkle-Patricia Trees for ensuring data consistency and secure interoperability.
But what exactly are Merkle-Patricia Trees and why are they so crucial for these systems? To answer these questions and more, let's unravel this concept piece by piece, exploring their properties, uses, and their significance in maintaining the security and integrity of blockchain ecosystems.
Before we dive into the intricacies of Merkle-Patricia Trees, it's imperative to have a solid grasp on Merkle Trees and their functionality, as they form the foundation of our subject. If you haven't already explored , we strongly encourage you to do so to enhance your understanding and derive the maximum benefit from this guide.
For those who have completed the tutorial on Merkle Trees, let's proceed with a quick recap to refresh your memory and provide a smooth transition into the complex world of Merkle-Patricia Trees.
A Merkle Tree is a kind of data structure used in computing. A data structure is simply a way of organizing and storing data so it can be used efficiently.
Let's break down the definition of Merkle Tree into simpler parts:
What is a tree in computing? Imagine a family tree, with the "ancestors" at the top and "descendants" below. A tree in computing is similar. It starts with a single "root" node at the top, which branches out to "child" nodes, and each of those can have their own "child" nodes, and so on. The nodes at the very bottom that have no children are called "leaves".
What is a cryptographic hash? A hash is a way of taking any amount of input data (like a sentence, a document, or a whole book), and creating a fixed-size string of characters from it, which looks random. What's special about it is that any small change to the input will completely change the hash, and you can't go backwards from the hash to the original data. Cryptographic hash functions are special types of hash functions that are particularly secure, meaning they're very hard to reverse or find collisions (two different inputs producing the same hash).
How is a Merkle Tree built? You start with your data blocks at the bottom as the "leaves" of the tree. Each of these data blocks is turned into a hash. Then, each pair of these hashes is combined and hashed again to get the hash for the node above them. This process continues up the tree, until you get a single hash at the top, which is the "root" of the tree.
What is a Merkle Tree used for? Merkle Trees are used in places where you need to verify data quickly and securely. For example, they are used in blockchain technology (which underlies cryptocurrencies like Bitcoin) to ensure all transactions are valid without having to check every single one.
In essence, Merkle Trees allow you to check if a small piece of data is part of a large dataset very quickly and with a high degree of certainty. If you have the top hash and a way to move down the tree, you can check if a piece of data is included in the original dataset without needing to have the entire dataset.
1. Basic Terminology: In a Merkle tree:
Leaf nodes are the lowest nodes in the tree (they have no children) and represent the data blocks.
Parent nodes are labeled with a cryptographic hash of their child nodes.
The root node (the top node of the tree) is known as the Merkle root.
2. Construction of a Merkle Tree:
Let's consider we have 4 data blocks - L1, L2, L3, and L4.
Step 1: We start by taking the cryptographic hashes of the data blocks.
HL1 = Hash(L1)
HL2 = Hash(L2)
HL3 = Hash(L3)
HL4 = Hash(L4)
Here, 'Hash' can be any cryptographic hash function like SHA256.
Step 2: The hashes are paired and concatenated, and the hash of the resulting strings are calculated.
HL12 = Hash(HL1 + HL2)
HL34 = Hash(HL3 + HL4)
Here, '+' represents concatenation.
Step 3: These hashes are again concatenated and hashed to form the root.
ROOT = Hash(HL12 + HL34)
This ROOT is the Merkle Root of our Merkle Tree.
Just like before, you can use this tree for efficient and secure verification of the contents of these data blocks. The process is exactly the same, but with the updated block names.
In simple terms, a Trie is a special type of tree used to store strings. What makes Tries interesting is how they organize and store the strings to allow quick look-ups, insertions, and deletions.
How Does a Trie Work?
Imagine we have an empty Trie. The root of the Trie does not contain any letters but serves as a starting point for storing our strings.
Let's start with the first string "an".
From the root node, we would check if there's a branch for the first letter, "a". In this case, there isn't, so we create a new node for "a".
We then check if there's a branch for the second letter "n" coming off the "a" node. Since there isn't, we create another node for "n".
Our Trie now represents the word "an".
To add the second word "ant", we start from the root again:
We check for a branch for "a". It already exists this time, so we follow it.
We then look for a branch for "n" from "a". This also exists, so we follow it.
Finally, we look for a branch for "t" from "n". It doesn't exist, so we add a new node for "t".
Our Trie now contains "an" and "ant".
We continue the process for "dad" and "do":
Starting with "dad", we don't find a branch for "d" at the root, so we add it.
We don't find a branch for "a" from "d", so we add it.
We don't find a branch for "d" from "a", so we add it.
For "do", we already have a "d" at the root, so we follow it.
We don't have an "o" branch from "d", so we add it.
Our Trie now contains "an", "ant", "dad", and "do".
That's how we create a Trie! If we want to check whether a word is in the Trie, we start at the root and follow the branches corresponding to the word's letters. If we can do this without hitting a dead-end, then our word is in the Trie.
By this, we can conclude that a Trie stores words by sharing the common letters among them. This shared structure allows for efficient storage and quick look-ups.
This is a basic explanation of Tries. Advanced topics include adding a marker to the end of each word in the Trie to distinguish, for example, "an" and "ant", as separate words.
A Patricia Trie (also known as a Radix Tree or Compact Prefix Tree) is a type of Trie that adds some optimizations to save space and potentially enhance search efficiency. The name "Patricia" is an acronym for "Practical Algorithm to Retrieve Information Coded in Alphanumeric."
How Does a Patricia Trie Work?
A Patricia Trie differs from a standard Trie by collapsing any node that has only one child. Instead of storing a single character in each node, a Patricia Trie can store entire strings or parts of them, significantly reducing the number of nodes.
let's see how a Patricia Trie handles the words: "romane", "romanus", "romulus", "rubens", "ruber", "rubicon", "rubicundus".
In a Patricia Trie, we start with an empty root node. Then we begin to add our words:
Inserting "romane": The Trie is currently empty, so we create a new node branching from the root that contains the string "romane".
Inserting "romanus": We notice that "romanus" shares a prefix, "roman", with "romane". So, we create a node branching off from "roman" that contains the suffix "us". We also update the existing "romane" branch to now start from "roman" and contain the suffix "e".
Inserting "romulus": This word shares the prefix "rom" with the existing words. Therefore, we add a branch off from "rom" that contains "ulus".
Inserting "rubens": This word doesn't share any prefix with the existing words, so it branches directly off from the root.
Inserting "ruber": "ruber" shares a prefix "rub" with "rubens", so we create a node branching from "rub" that contains "er". The "rubens" branch now also starts from "rub" and contains the suffix "ens".
Inserting "rubicon": "rubicon" shares a prefix "rubi" with "ruber", so we create a node branching from "rubi" that contains "con".
Inserting "rubicundus": This word shares a prefix "rubi" with the others. We branch off from "rubi" and add a node with "cundus".
Now, our Patricia Trie contains all seven words, each with its own unique path from the root. The Trie is efficient, compact and, compared to a regular Trie, much easier to traverse. Note that Patricia Tries significantly reduce the number of nodes and thus make operations more efficient by collapsing nodes with only one child.
