Consider the following key-exchange protocol: Common input: The security parameter 1^n. (a) Alice runs g(1^n) to obtain (G, q, g). (b) Alice chooses x_1, x_2 rightarrow Z_q and sends alpha = x_1 + x_2 to Bob. (c) Bob chooses x_3 leftarrow Z_q and sends h_2 = g^x3 to Alice. (d) Alice sends h_3 = g^x_2 middot x_3 to Bob. (e) Alice outputs h_2^x1. Bob outputs (g^alpha)^x3 middot (h_3)^-1. 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)