Hash functions

A hash function is a mathematical algorithm that takes in input data of any size and produces a fixed-size output, known as a hash or hash value. The output is typically a unique, deterministic representation of the input data. Hash functions are commonly used in cryptography to ensure data integrity and in data structures like hash tables to efficiently store and retrieve data. They are also used in digital signatures, data fingerprinting, and password hashing. A good hash function should be fast, produce evenly distributed outputs, and be resistant to collisions (when two different inputs produce the same output).

Properties of a hashing algorithm

• Stable: the same input generates the same output every time
• Uniform: the hash values should be uniformly distributed through the available space
• Efficient: the cost of generating a hash must be balanced with application need
• Secure: the cost of finding data that produces a given hash is prohibitive

String hashing

• Sum ASCII values: not uniform, not secure
• Fold bytes of every four characters into an integer: not secure
• CRC32: not secure
• MD5: not efficient, not secure
• SHA2: stable, uniform, not efficient, secure