We prove $\Omega (n^2)$ complexity \emph{lower bound} for the general model of \emph{randomized computation trees} solving the \emph{Knapsack Problem}, and more generally \emph{Restricted Integer Programming}. This is the \emph{first nontrivial} lower bound proven for this model of computation. The method of the proof depends crucially on the new technique for proving lower bounds on the \emph{border complexity} of a polynomial which could be of independent interest.