Error propagation is often an important consideration when choosing a mode of operation in practice. 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 M0,M1,M2, to Bob, encrypted to ciphertext blocks C0,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 Ci 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 Mi before Alice encrypts it and sends the corresponding ciphertext Ci to Bob. Upon decryption of Ci, which plaintext blocks Mj are affected when using the cipher in CBC mode? Hint: Think about this carefully; it's easy to make a conceptual mistake here