We want to select from a set of hash functions H with reasonable certainty that the above property is true.

Thus, the number of functions f in H such that h(x) = h(y) for
x,y U must satisfy

**Definition:** A universal collection of hash functions H
contains exactly hash functions such that h(x) = h(y)
for x,y U.

where key x = is decomposed into r+1 bytes

a = , each chosen randomly from {0, 1, .., m-1}.

is a universal collection of hash functions.

Thus, we want to randomly select ``a'' each time.