• Based on slide 9, complete the computation of probability of "PrP (a|3),PrP (b|3),PrP (a|4),PrP (a|4)."
• Is the Shift Cipher perfectly secret? Using the probability to prove it.
• When using the one-time pad with the key k = 0^?, we have Enc_k (m) = k ? m = m and the message is sent in the clear! It has therefore been suggested to modify the one-time pad by only encrypting with k? 0^?. Is this modified scheme still perfectly secret? Explain.

Probability Example . Conditional Distributed Probability of Pro (m/c) a b 1 1 . Prp (a/1) = Pp(a)PK(K1) Pp = 1/4 Pp = 3/4 42 =1 Pc(1) k 2 (PR = 1/2) .0 . Prp (b/1) = Pp(b)PK(K1) = = 0 k2 2 3 Pc(1) Co | (PR = 1/4) 1 1 . Prp (a/2) = = Pp(a) PK(K2) = 4 4 = 1/7 K3 4 Pc(2) 7 16 (PK = 1/4) 3 1 . Prp (b/2) = Pp(b) PK(K1) 4 2 =6/7 Pc(1) = 1/8 Pc(2) 7 16 Pc(2) =3/8 + 1/16 = 7/16 PC(3) = 3/16 + 1/16 = 1/4 PC(4) = 3/16