A 2 -wise Secure MAC The problem in this section asks you to analyze the following simple MAC construction. Parameters: Let p be a large prime. The message space of this MAC will be ZpZp, and so we will implicitly parse our messages msg =(msg(1),msg(2)) as pairs. - Gen(): Draw a,b,cZp and set k=(a,b,c). - Sign (msg,k) : Parse msg=(msg(1),msg(2))ZpZp and k=(a,b,c)Zp3. Output = amsgl(1)+bmsg(2)+cZp. - Verify (msg,,k) : Parse msg=(msg(1), msg (2))ZpZp,Zp and kZp3. Output 1 if =amsg(1)+bmsg(2)+c; output 0 otherwise. Problem 4. Do both of the following. (a) Prove correctness. (b) Prove that for any adversary A (even inefficient adversaries), the probability that A can win the 2 -wise MAC forgery game for the above system is at most 1/p