Question

1. Consider a cipher with three keys, three plaintexts, and four ciphertexts, given by: C2 CA C C C3 C2 C4 C3 Ci m1 | 12 | 13 ki k2 ks Suppose all keys are equally likely, and the messages have probability P(mı) = 1/5, P(m2) 2/5, P(m3) = 2/5. (a) What is the probability of each ciphertext? (b) Compute P(q|m), Pq|m2), P(q|m3). Can you tell if the ciphertext has perfect secrecy from this calculation? (c) Compute P(ca|mı), P(c3|mı), P(ca|mı). Can we combine this with the previous answer to tell if the cipher has perfect secrecy? (d) Compute Pk1c3), P(ka|C3), P(k3|C3).

Answer 1

Answer:- Given that a) Pami) = ţ , Pcm) = , P(m3)- P(CI) = P(K2 mi) +P(13, m2) + P(K, , M3) -(-)+6->)(**) - 5 similarly P(cz)= pik,,mi) +PCK2, m3) .6**)+(++) P(63) = 4 15 P(Cu) - 5 b) PCalm.) = P(c, and mo) P(m) P(K), m.) p(mi) - Gx5) 5 - اما 3 similarly pcilme) = P(img) = since pasim) - PCalm): Plc,im) - PCC) It can be infered that ciphertext cr has perfect secrecy 3 P(C21m) = PCCz|mi) = ģ P(culm,)=0

since P (Calm) + PCC) we can not combine this tell if the cipher has perfect secrecy. PCENC3) = 0 PCk2lg) = PCkx, mm P(63) 3x مالی ( 9 05 P(glcs) : P(cam) X 3 - PCC) 니 IS