Problem 2- Error propagation in block cipher modes (12 marks) Error propagation is often an important consideration when choosing a mode of operation in prac- tice. In this problem, you will analyze the error propagation properties of an arbitrary block cipher in various such modes; note that these properties are independent of the cipher used. a. Suppose Alice wants to send a sequence of message blocks Mo, M1, M2,... to Bob, encrypted to ciphertext blocks Co, C1, C2, ... using some fixed key K. Assume that an error occurs during transmission of a particular block of ciphertext Ci. Justifying all your answers, explain which plaintext blocks are affected after Bob decrypts this (faulty) ciphertext block C, when the cipher is used in (i) (2 marks) ECB mode? (ii) (2 marks) CBC mode? (iii) (2 marks) OFB mode? (iv) (2 marks) CFB mode with one register? (v) (2 marks) CTR mode? b. (2 marks) Suppose now that an error occurs in a particular plaintext block M before Alice encrypts it and sends the corresponding ciphertext C to Bob. Upon decryption of Ci, which plaintext blocks M, are affected when using the cipher in CBC mode