gen-define-a-cryptographic-hash-function-and-give-one-short-work-0bbf

Define a cryptographic hash function and give one short worked example.

# Cryptographic Hash Function ## Definition A **cryptographic hash function** is a mathematical algorithm that takes an input (message) of any length and produces a fixed-size output (hash/digest) with these key properties: 1. **Deterministic**: Same input always produces the same output 2. **Fast to compute**: Quick to calculate the hash 3. **Pre-image resistant**: Computationally infeasible to reverse (find input from hash) 4. **Small change avalanche**: Tiny input change completely changes the output 5. **Collision resistant**: Nearly impossible to find two different inputs with the same hash ## Short Worked Example Using **SHA-256** (a common cryptographic hash function): **Input:** `hello` **Process:** The SHA-256 algorithm processes the input through multiple rounds of bitwise operations, modular additions, and compression functions. **Output (hash):** ``` 2cf24dba5fb0a30e26e83b2ac5b9e29e1b161e5c1fa7425e73043362938b9824 ``` **Input:** `hello!` *(just added one character)* **Output:** ``` ce06092fb948d9ffac7d1a376e404b26b7575bcc11ee05a4615feda4e8c9f2ac ``` Notice how adding a single exclamation mark completely changed the entire hash—this demonstrates the avalanche effect. These hashes are always 256 bits (64 hexadecimal characters) regardless of input size.