4. Defining Perfect Security from Ciphertexts (15 points). An upstart in the field of cryptography has proposed a new definition for perfect security of private-key encryption schemes. According to this new definition, a private-key encryption scheme (Gen, Enc, Dec) is perfectly secure, il, for all a priori distribution M over the message space, and any two cipher-texts c and d, we have the following identity. P[C=d] =P[C=d] Show that the definition in the class does not imply this new definition. Remark. You need to construct a private-key encryption scheme that is secure according to the definition we learned in the class. However, this scheme does not satisfy the new definition. 4. Defining Perfect Security from Ciphertexts (15 points). An upstart in the field of cryptography has proposed a new definition for perfect security of private-key encryption schemes. According to this new definition, a private-key encryption scheme (Gen, Enc, Dec) is perfectly secure, il, for all a priori distribution M over the message space, and any two cipher-texts c and d, we have the following identity. P[C=d] =P[C=d] Show that the definition in the class does not imply this new definition. Remark. You need to construct a private-key encryption scheme that is secure according to the definition we learned in the class. However, this scheme does not satisfy the new definition