3. (4 points) (This problem follows the notation for Diffie-Hellman in section 4.2). Alice and Bob wish to use the Diffie-Hellman Key Exchange to exchange a secret key. They choose the prime p = 31 and the primitive root g = 12. Then Alice chooses secret integer a = 2520 and Bob chooses secret integer b = 99. Alice then computes A = 12"20 (mod 31) = 1 (mod 31), so she sends Bob A = 1. Of course, this means that Bob's key is kg = 1 (mod 31) = 1 (mod 31). That is (for better or for worse) the secret key is the number 1. If Bob computes B = 1299 (mod 31), he gets B = 15, which he sends to Alice. Use successive squaring to verify that, in fact, Alice's secret key is KA = 1