# Proving a hash function family is weakly universal

$H$ is a family of weakly universal hash functions if for two elements $x,y$:

$$P(h(x) = h(y)) \le \frac1m,$$

where $m$ is the size of the domain, and $h$ is chosen at random from $H$.

Given a hash family, how could one prove that it is weakly universal. I understand how to prove it isn't (proof by counter-example) but I cannot find any examples for when it is.

I apologise if this is a duplicate of another question. I was not able to find any examples online specifically for weakly universal hash functions.

• – Yuval Filmus May 13 '18 at 12:36
• You prove it by proving that the inequality above holds. Without knowing any specifics about what particular hash function you are dealing with, it's hard to say much more. – D.W. May 13 '18 at 14:48