A Restatement of Theorems and Full Proofs

In this section, we will restate our main results and give full proofs. We will show that our problem setup is a special case of that considered in Theorem 3; then, we can apply that result as a black box. Without loss of generality, assume U = [ s] . The result now follows from Theorem 3.Theorem 21 We prove Theorem 5 in two parts. We first show that although the adversary doesn't know (Theorem 6) We will proceed by contradiction.