Cryptographic hash function

cryptographic Hash function $h(M)$

• must be deterministic given same message $M$
• $h(M)\ne h(M^{\prime })$ even if $M$ and $M^{\prime }$ very similar
• $h$ is intractable to invert, i.e., find $h^{-1}$ (trapdoors)
• $h$ collision resistant, i.e., intractable to find messages $M,M^{\prime }$ such that $M\ne M^{\prime }$ and $h(M)=h(M^{\prime })$, i.e., different messages that that produce same hash