Summary  
This chapter covers the programming concept of cryptographic hash functions—how they produce fixed-size, unpredictable outputs with properties like determinism, pre-image resistance, collision resistance, and the avalanche effect—and illustrates building Merkle trees and performing double SHA-256 hashing to structure and verify data integrity.  

General domain of usage  
Blockchain technology

We have already mentioned **hashing** and **block hashes** a few times, but didn't really pay much attention to that, so it's time to discuss what hashing actually is.

## Properties of Hash Functions
In blockchain, hash functions are used to:
- Secure transactions by creating a unique fingerprint for each one;
- Generate addresses from public keys;
- Create the links in the blockchain through block hashes.

With this in mind, a good hash function for blockchain has several key properties:



Hashing, especially using a good hash function, can be compared to making a smoothie. Let's take a look at the following illustration:

Well, in fact, it is possible to find the original input given a hash, however, it would take too much time to actually be somewhat practical.

## Block Hashing

In order to get the hash of a certain block, Bitcoin uses the **SHA-256** hash function, which outputs a **256-bit** (32-byte) hash. It's a part of the SHA-2 family designed by the **National Security Agency (NSA)** and known for its strong security properties, making it resistant to collisions, preimage attacks, and other cryptographic vulnerabilities.

The hash of a Bitcoin block is computed by taking the **block header** data. This data is input into the **SHA-256** hash function **twice** in a process known as double SHA-256. 

Here is an image to make things clear:




The resulting **256-bit hash** must meet certain criteria defined by the network's difficulty target. If the hash is not below the target, the **nonce** is adjusted and the hash is recomputed until a qualifying hash is found. This final hash is the block's **unique identifier**.


## Merkle Root

As we have mentioned before, **Merkle root** is a single hash  that represents all the transactions included in the block. Computation of  a Merkle root starts with the hashes of each transaction in a block. **Double SHA-256** is used here as well. 

Each hash is then **paired** with another and they are hashed together to form a new hash. This process of pairing and hashing the new hashes continues until only one hash remains. The final hash is the **Merkle root**, representing all transactions in the block and ensuring their integrity by encoding the entire set of transactions into a single hash. Such process forms a **Merkle tree**. 

Let's take a look at an example of a Merkle tree:

As you can see, our block contains 6 transactions (each labeled as **Tx**) and via hashing and pairing new hashes a Merkle  root is computed. 

What is the output size of the SHA-256 hash function used in Bitcoin's blockchain?

Explore the revolutionary world of blockchain technology and its first and most prominent application, Bitcoin. Delve into the intricacies of how blockchain functions, the technical underpinnings of Bitcoin, and the broader implications and future trends in this dynamic field. Gain a well-rounded understanding of the technology that is reshaping industries and challenging traditional notions of currency and data security.

First, we will explore the evolution of the Web and how blockchain technology ushered in a new era known as Web 3.0. Additionally, we will gain a basic understanding of how blockchain, and specifically Bitcoin, works.

Now, it's time to explore the key components of a blockchain: blocks and transactions, specifically their structure and the processes related to them, such as verification and mining.

Finally, we will go through some of the more advanced blockchain concepts, including consensus mechanisms, blockchain security, and groundbreaking technologies like smart contracts, tokens, and digital assets.

Overview of Hashing

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Overview of Hashing