Cryptographic Hashing

Another kind of useful function is the cryptographic hash function:

• like any hash function $h(m)$, these map arbitrary-size data to fixed-width integers, in uniformly distributed fashion
• A hash function $h$ is cryptographic if given an output $h(m)$ it is computationally infeasible to discover $m$ or any $m^{\prime }$ where $h(m^{\prime })=h(m)$.
• Example algorithms are MD5 (broken), SHA-1 (broken), SHA-2 (still secure)
• Useful for authentication of software (file hashes) and implementing passwords.