Cryptographic hash function

A cryptographic hash function has the additional properties:

• It is one-way (preimage resistant) Given $y$, it is hard to compute an $x$ where $h(x)=y$.

And is usually either:

• 2nd-preimage resistant

  2nd-preimage resistant: it is computationally infeasible to find a second input that has the same output as any specified input, i.e. given $x$ to find an $x^{\prime }\ne x$ such that $h(x)=h(x^{\prime })$

  Link to original

• Collision resistant

  Collision resistant: it is difficult to find two distinct inputs $x,x^{\prime }$ where $h(x)=h(x^{\prime })$

  Link to original