1. [Pseudorandom ciphertext security] For a cipher (E,D) defined over (K,M,C), assume that C = {0,1}". Let us define an attack game between an adversary A and the challenger as follows. The adversary select a message me M and sends it to the challenger, who computes: ber(0,1), KERK, 60+ Ek,m), Gr{0,1}", C+Cb, and sends the ciphertext c to the adversary, who then computes and outputs a bit b'. We define A's advantage to be Pr[b=b']-1/2), and we say that the cipher (E, D) is pseudorandom ciphertext secure, if this advantage is negligible for all efficient adversaries. Task: Show that if a cipher is pseudorandom ciphertext secure, then it is semantically secure. 1. [Pseudorandom ciphertext security] For a cipher (E,D) defined over (K,M,C), assume that C = {0,1}". Let us define an attack game between an adversary A and the challenger as follows. The adversary select a message me M and sends it to the challenger, who computes: ber(0,1), KERK, 60+ Ek,m), Gr{0,1}", C+Cb, and sends the ciphertext c to the adversary, who then computes and outputs a bit b'. We define A's advantage to be Pr[b=b']-1/2), and we say that the cipher (E, D) is pseudorandom ciphertext secure, if this advantage is negligible for all efficient adversaries. Task: Show that if a cipher is pseudorandom ciphertext secure, then it is semantically secure