What is a hash function and what properties must it have?

A cryptographic hash function takes input of any size and produces a fixed-length output called a digest. It must have three properties: it must be one-way, meaning you cannot derive the input from the output; it must be collision-resistant, meaning it is computationally infeasible to find two different inputs that produce the same output; and it must exhibit the avalanche effect, where a tiny change in input produces a dramatically different output. SHA-256 produces a 256-bit digest. Hashing verifies file integrity, stores passwords securely, and is the foundation of digital signatures.