Cryptographic Hash Function

cryptography

Definition

Cryptographic Hash Function

A cryptographic hash function is a hash function satisfying additional properties required for security applications:

• One-way: easy to compute the hash for a given input, infeasible to compute an input that maps to a given hash value
• Uniformity: the probability of obtaining a particular $L$-bit output for a random input should be $2^{-L}$
• Diffusion: each bit of the input message should affect as many output bits as possible
• Weak collision resistance: given a message $m$ and a hash function $h$, it is infeasible to find another message $m^{\prime }$ such that $h(m)=h(m^{\prime })$
• Strong collision resistance: given a hash function $h$, it is infeasible to find two different messages $m,m^{\prime }$ such that $h(m)=h(m^{\prime })$
• Near-collision resistance: given a hash function $h$, it is infeasible to find two different messages $m,m^{\prime }$ such that their hashes $h(m),h(m^{\prime })$ differ only in a few bits