A hash function is a mathematical function that takes an input (or "message") of arbitrary size and produces a fixed-size string of bytes, typically a number, which is called the hash value, hash code, or digest. The primary purpose of a hash function is to efficiently map data of arbitrary size to data of fixed size, which can then be used for various applications such as data retrieval, cryptography, and data integrity verification.
Key Properties of Hash Functions
Deterministic: The same input will always produce the same output.
Fixed Output Size: Regardless of the input size, the output (hash value) is always of a fixed length.
Efficiency: The hash function should be quick to compute.
Preimage Resistance: It should be computationally infeasible to reverse the hash function, i.e., to find the original input given only the hash value.
Second Preimage Resistance: Given an input and its hash, it should be difficult to find another input with the same hash.
Collision Resistance: It should be difficult to find two different inputs that produce the same hash value.
Uniform Distribution: The hash values should be uniformly distributed to minimize collisions.
Types of Hash Functions
Cryptographic Hash Functions: These are designed to be secure and resistant to various attacks. Examples include SHA-256 and MD5. They are used in applications like digital signatures, password hashing, and data integrity checks[3][6][9].
Non-Cryptographic Hash Functions: These are used for purposes like data indexing and checksums. Examples include the Fowler-Noll-Vo (FNV) hash and MurmurHash[4].
Perfect Hash Functions: These produce no collisions for a specific set of inputs and are used in applications like data lookup and data compression[4].
Universal Hash Functions: These produce uniformly distributed hash values across various inputs to prevent collisions and ensure efficiency[4].
Applications of Hash Functions
Data Storage and Retrieval: Hash functions are used in hash tables to quickly l...
