Consider the following key-exchange protocol: (a) Alice chooses uniform k, r in {0, 1}^n, and sends s := k xor r to Bob. (b) Bob chooses uniform t in {0, 1}^n, and sends u := s xor t to Alice. (c) Alice computes w := u xor r and sends w to Bob. (d) Alice outputs k and Bob outputs w xor t. Show that Alice and Bob output the same key. Analyze the security of the scheme (i.e., either prove its security or show a concrete attack).