I'd be happy to break down how hash functions work, their security properties, and their applications in password hashing and data integrity checks.
What is a Hash Function?
A hash function is a one-way mathematical algorithm that transforms input data of any size (variable length) into a fixed-length, unique string of characters, known as a hash value, digest, or message digest.
The Hashing Process: Step-by-Step
Here's a simplified overview of how a hash function works:
1. Input: You provide the input data, which can be of any size (e.g., a password, a file, or a message). This input is often referred to as the message.
2. Preprocessing: The input message might undergo some initial processing, such as:
- Padding: Adding a fixed pattern to ensure the input length is a multiple of a certain block size.
- Encoding: Converting the input into a consistent format (e.g., ASCII to binary).
- Block Division: The preprocessed input is divided into fixed-size blocks (e.g., 512 bits or 64 bytes).
3. Hash Computation: Each block is passed through a series of mathematical operations, which can include:
- Bitwise operations (AND, OR, XOR, shifts, etc.)
- Modular arithmetic (additions, multiplications, etc., with modulus operations)
- Compression functions (reducing the block size while preserving entropy)
4. Block Chaining: The output from each block's computation is chained together, meaning the output of one block is used as input for the next block's computation. This ensures the entire input message influences the final hash value.
5. Finalization: After processing all blocks, the last output is finalized to produce the fixed-length hash value (e.g., 256 bits or 64 hexadecimal characters).
Security Properties of Hash Functions
To be considered secure, a hash function should exhibit the following properties:
- Deterministic: Given a specific input, the hash function always produces the same output hash value.
- Non-Invertible: It's computationally infeasible to recreate the original input from its hash value.
- Fixed Output Size: The hash value always has a fixed length, regardless of the input size.
- Collision-Resistant: It's computationally infeasible to find two different inputs with the same output hash value (known as a collision).
- Preimage-Resistant: Given a specific hash value, it's computationally infeasible to find an input that produces that hash value (known as a preimage).
