## TLDR - Cryptographic Hash Function

A cryptographic hash function is a mathematical algorithm that takes an input (or message) and produces a fixed-size string of characters, which is typically a sequence of numbers and letters. The output, known as the hash value or hash code, is unique to the input data and is generated in such a way that even a small change in the input will produce a significantly different hash value. Cryptographic hash functions are widely used in various applications, including data integrity verification, password storage, digital signatures, and blockchain technology.

## Properties of Cryptographic Hash Functions

Cryptographic hash functions possess several important properties that make them suitable for secure applications:

### 1. Deterministic

A cryptographic hash function always produces the same hash value for the same input. This property allows for easy verification of data integrity by comparing the computed hash value with the original hash value.

### 2. Fast Computation

Cryptographic hash functions are designed to be computationally efficient, allowing for quick generation of hash values even for large amounts of data.

### 3. Pre-image Resistance

A hash function should be computationally infeasible to reverse, meaning it should be extremely difficult to determine the original input data from its hash value. This property ensures that the hash value cannot be used to reconstruct the original data.

### 4. Collision Resistance

A collision occurs when two different inputs produce the same hash value. A good cryptographic hash function should have a negligible probability of collisions, making it highly unlikely for two different inputs to generate the same hash value.

### 5. Avalanche Effect

A small change in the input data should result in a significant change in the hash value. This property ensures that even a minor alteration in the input will produce a completely different hash value, making it difficult to tamper with the data without detection.

### 6. Fixed Output Size

Cryptographic hash functions produce a fixed-size output, regardless of the size of the input data. This allows for efficient storage and comparison of hash values.

## Applications of Cryptographic Hash Functions

Cryptographic hash functions find applications in various domains:

### Data Integrity Verification

Hash functions are commonly used to verify the integrity of data. By computing the hash value of a file or message, one can compare it with the original hash value to ensure that the data has not been modified or corrupted.

### Password Storage

Instead of storing passwords in plain text, systems often store the hash values of passwords. When a user enters their password, the system computes the hash value and compares it with the stored hash value. This way, even if the password database is compromised, the actual passwords remain secure.

### Digital Signatures

Cryptographic hash functions are an essential component of digital signature schemes. They are used to generate a unique hash value of a message, which is then encrypted with the sender's private key. The recipient can verify the integrity of the message by decrypting the hash value using the sender's public key and comparing it with the computed hash value of the received message.

### Blockchain Technology

Cryptographic hash functions play a crucial role in blockchain technology. They are used to link blocks together by including the hash value of the previous block in the current block. This ensures the immutability and integrity of the blockchain, as any change in a block's data would require recalculating the hash values of all subsequent blocks.

## Common Cryptographic Hash Functions

There are several widely used cryptographic hash functions:

### 1. SHA-256 (Secure Hash Algorithm 256-bit)

SHA-256 is a widely used cryptographic hash function that produces a 256-bit hash value. It is commonly used in blockchain technology, including Bitcoin.

### 2. MD5 (Message Digest Algorithm 5)

MD5 is a widely used cryptographic hash function that produces a 128-bit hash value. However, it is considered insecure for many applications due to vulnerabilities.

### 3. SHA-3 (Secure Hash Algorithm 3)

SHA-3 is the latest member of the Secure Hash Algorithm family. It offers improved security and resistance against certain types of attacks compared to its predecessors.

### 4. Blake2

Blake2 is a cryptographic hash function that is faster than many other hash functions while maintaining a high level of security. It is often used in applications where speed is a critical factor.

## Conclusion

Cryptographic hash functions are fundamental tools in modern cryptography. They provide essential properties such as data integrity, password security, and digital signatures. Understanding the properties and applications of cryptographic hash functions is crucial for building secure systems and ensuring the integrity of data.