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# Introduction to Hashing

## What is Hashing

Hashing is the process of converting input data of any size into a fixed-size output using a mathematical function.

```
h = H(m)
```

* `m` = message (input)
* `H` = hash function
* `h` = hash (output)

The output is also called a **digest**.

## Simple Example

```python
import hashlib

m = b"hello"

h = hashlib.md5(m).hexdigest()
print(h)
```

Output:

```
5d41402abc4b2a76b9719d911017c592
```

The same input will always produce the same hash.

## Why Hashing is Used

Hashing is widely used in cryptography and systems:

* Password storage (store hash, not password)
* Data integrity (verify file hasn’t changed)
* Digital signatures
* Blockchain
* Caching and indexing

## Key Idea

Hashing is **not encryption**.

Encryption:

```
reversible (you can decrypt)
```

Hashing:

```
one-way (you cannot reverse it)
```

## Important Characteristics

A good cryptographic hash function has:

### 1. Deterministic

Same input → same output

### 2. Fixed Length

No matter input size, output size is constant

Example:

```
MD5 → 128 bits
SHA256 → 256 bits
```

### 3. Fast Computation

Efficient to compute

### 4. One-Way Function

Given hash, you cannot get original input

### 5. Avalanche Effect

Small change in input → completely different hash

## Example of Avalanche Effect

```
Input 1: hello
Input 2: hello1
```

Hashes:

```
5d41402abc4b2a76b9719d911017c592
203ad5ffa1d7c650ad681fdff3965cd2
```

A tiny change → completely different output.

## Common Hash Functions

* MD5 (broken, but common in CTFs)
* SHA-1 (broken)
* SHA-256 (secure)
* SHA-512 (secure)
* SHA-3 (modern)

## Important Clarification

You do NOT "decrypt" hashes.

Instead:

```
You guess the input and compare hashes
```

## Mental Model

Think of hashing like a machine:

```
Input → Black Box → Fixed Output
```

You can go forward easily, but not backward.

## Summary

* Hashing converts data into fixed-size output
* It is one-way and irreversible
* Used for security, integrity, and verification
* Core concept for almost all cryptographic systems


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