2. Suppose an encryption function is given by the following table, where the plaintext messages are {a, b, c, d} and cipher text messages are {1, 2, 3, 4} using keys {k1, k2, k3} . a. Compute the marginal probability of the cipher text messages. b. Compute the conditional probabilities Pr {Plain = p | Cipher = c} for all plaintexts p and cipher texts c. c. Compute the following quantities: H (P), H (K), H(C), H (K | C), and H (P | C) (20 points) Solution a) p(1)=3/12,p(2)=3/12,p(3)=4/12,p(4)=2/12 b) p(a|1)=0,p(a|2)=0,p(a|3)=2/3,p(a|4)=1/3 p(b|1)=1/3,p(b|2)=0,p(b|3)=1/3,p(b|4)=1/3 p(c|1)=1/3,p(c|2)=1/3,p(c|3)=1/3,p(c|4)=0 p(d|1)=1/3,p(d|2)=2/3,p(d|3)=0,p(d|4)=0 c) h(p)=ln(4) h(k)=ln(3) h(c)=ln(4) h(p|c)=(4/3)ln(2/27) h(k|c)=5/2(ln(1/2)) + 2*ln(1/6) .