Cryptographic hash functions

Cryptographic hash functions are a fundamental component of modern cryptography, providing a way to secure digital data in adverserial environments. They provide the ability to verify the integrity of data, and are used in a wide range of applications, including digital signatures, message authentication codes, and password hashing.

A cryptographic hash function is a mathematical algorithm that takes input data of any size and produces a fixed-size output, often referred to as the "hash" or "digest". The output is unique to the input data; even a small change in the input will result in a completely different output.

Hash functions are designed to be fast to compute, but difficult to reverse-engineer. This means that given the output of a hash function, it should be computationally infeasible to determine the input data that produced it. This property is known as "pre-image resistance".

In addition to pre-image resistance, cryptographic hash functions should also exhibit the following properties:

Second pre-image resistance: Given an input, it should be computationally infeasible to find another input that produces the same hash.
Avalanche effect: A small change in the input should produce a significant change in the output.
Deterministic: For a given input, the hash function should always produce the same output.
Efficient: The hash function should be fast to compute.
Non-reversible: It should be computationally infeasible to reverse-engineer the input from the output.

There are many cryptographic hash functions in use today, each with its own strengths and weaknesses. Some of the most widely used hash functions include:

SHA-256: A member of the SHA-2 family of hash functions, SHA-256 is widely used in blockchain technology, including Bitcoin.
SHA-3: The latest member of the Secure Hash Algorithm family, SHA-3 was designed as a replacement for SHA-2.
BLAKE2: A high-speed cryptographic hash function that is faster than MD5 and SHA-1.