## uniform hash function

for all \(i,\ell\), \(Pr[h(i)=\ell]=\frac{1}{m}\)

## 2-universal hash function

for all \(i,j\), \(Pr[h(i)=h(j)]=\frac{1}{m}\)

## pairwise independent hash function

for all \(i_1,i_2,\ell_1,\ell_2\), \(Pr[h(i)=\ell_1, h(j)=\ell_2]=Pr[h(i)=\ell_1]* Pr[h(j)=\ell_2]\)

## Example

\(h(x)= [(ax+b)% p ] % m\) is a 2-universal hash function