They have chosen the curve E : y2 = x3 + 34x + 12, the field F79, and the point P = (2, 1).

4. Now Alice and Bob communicate using an Elliptic Curve ElGamal scheme. They use the same curve and point as in the previous problem. (a) Alice chooses a private key na = 17. What is her public key? (b) Suppose Bob's public key is QB = (31, 38). Alice wishes to send the message M = (68, 49) using the ephemeral key k = 4. What ciphertext does Alice send? (c) Alice receives the ciphertext (C1,C2) = ((25, 76), (59, 4)) from Bob. What mes- sage does she decrypt