# Bad data for hash function

Is it possible to choose such a nontrivial set of queries so that the amortized running time for a hash table with a public key and a function like $$(a_{N − 1}k^{N − 1} +... + A_{1}k + a_0) (mod \: p)$$ for $$N = 2$$ is $$\Omega(\sqrt{n})$$, where $$n$$ is the total number of keys in the table (as a last resort, at least $$\Omega(\log n)$$)?

• Where do the $a_i$'s lie, what is the domain of the hash function? Where does the public key come in? Is the hash chosen at random? Those details are crucial to being able to give a meaningful answer. Dec 1 '20 at 14:53