I need a full and clear answer - intro to crypto course

2. (20 points) Modes of operation and error during transit. Alice and Bob have a shared AES key. Alice wants to send a plaintext of 500 bits long to Bob, using their AES key as a means to confidentially get this plaintext message across. Assume that the plaintext message m is encrypted using AES in ECB, CBC, OFB or CTR mode, assume that CBC and OFB have random IV and CTR a diversifier. 10 pt (a) What is the length of the ciphertext? Distinguish between different modes. i. ECB; ii. CBC; iii. OFB; iv. CTR. Assume that the corresponding ciphertext C gets disturbed in transfer to Bob. The bit m 200 is therefore flipped, yielding C' as the bit string that Bob receives. Bob decrypts the message to obtain m'. In this exercise, you should assume that whenever one input bit is flipped, the output of AES differs in half of the bits. 10 pt (b) In which bits does m' differ from m? Also give the number of bits where m' differs from m. Distinguish between different modes. i. ECB; ii. CBC; iii. OFB; iv. CTR