Cryptographic hash function

A cryptographic hash function maps input of any length to a fixed-size digest in a way that is fast to compute and infeasible to reverse. Three properties define it: preimage resistance (a digest cannot be traced back to an input), second preimage resistance (a given input cannot be matched by a second, different input), and collision resistance (no two colliding inputs can be found at all).

#Standard functions

The SHA-2 family (FIPS 180-4) and the SHA-3 family (FIPS 202) are the NIST-standardized general-purpose hashes; SHA-256 and SHA-384 dominate deployed protocols.

#Quantum impact

Grover's search (Grover's algorithm) gives at most a quadratic speedup, so the theoretical preimage margin of SHA-256 drops from 2^256 to about 2^128 quantum operations. Collision resistance is governed by the classical birthday bound (2^128 for SHA-256), and known quantum collision algorithms need so much memory that they offer little practical advantage. Hash functions with adequate output size are therefore treated as post-quantum safe, which is why Merkle tree constructions and hash-based signatures count among the most conservative post-quantum choices.