Q1 Consider a cryptosystem with plaintext symbol set P a,b, c, ciphertext symbol set C 1,2,3,4,5), key set K (ki,k2, k3, k). Suppose P and K have probability distributions (p(a)p(b)-2/5,p(c)-1/5) anod (p(ki) = p(ks) = 1/3, p(k2-2/9, p(ka) = 1/9). The relatioship between (P, K) and (C) is given by the follow- ing table, wherein, for instance, eks (b)-5 k11 3 5 k2 2 4 3 ks 4 52 k4 2 4 a) Determine the probability distribution of the ciphertext symbols. b) Determine pcly 1 and p(x-bly-4) where X and Y are the random variables associated with and C, respectively c) Compute H(P), H(K), and H(KIC); logarithm function is considered on base 2; log3 1.58,log5-2.32, log7 = 2.81 ,log11-3.46. d) compute H(PC) e) Prove that in any cryptosystem we have H(P) H(K) H(P,C) +H(KIP,c) f) Does relation H(KIP, c) 0 hold for any cryptosystem? Q1 Consider a cryptosystem with plaintext symbol set P a,b, c, ciphertext symbol set C 1,2,3,4,5), key set K (ki,k2, k3, k). Suppose P and K have probability distributions (p(a)p(b)-2/5,p(c)-1/5) anod (p(ki) = p(ks) = 1/3, p(k2-2/9, p(ka) = 1/9). The relatioship between (P, K) and (C) is given by the follow- ing table, wherein, for instance, eks (b)-5 k11 3 5 k2 2 4 3 ks 4 52 k4 2 4 a) Determine the probability distribution of the ciphertext symbols. b) Determine pcly 1 and p(x-bly-4) where X and Y are the random variables associated with and C, respectively c) Compute H(P), H(K), and H(KIC); logarithm function is considered on base 2; log3 1.58,log5-2.32, log7 = 2.81 ,log11-3.46. d) compute H(PC) e) Prove that in any cryptosystem we have H(P) H(K) H(P,C) +H(KIP,c) f) Does relation H(KIP, c) 0 hold for any cryptosystem