Answers for questions 1a, 6 and 8. ASAP

21. We know a message authentication code (MAC) is for the purpose of ensuring data integrity. If we use a hash to generate a tag as follows: 0 = h(k) m h(m), and m, o will be sent along. Would this be a secure MAC? briefly explain. Q6: A blockcipher normally can be considered as a pseudorandom permutation, i.e. E : {0,1}+2 + {0,1128, when encrypting a picture m, say with n = 105 blocks (each with 128 bits, total about 1.5 megabytes), and we use an ECB mode, i.e., C1 = E(k, m),..., On = E(k, mn). It is very common that the picture has many identical blocks, e.g., m = m2 = ..., = mk, explain why ECB mode will reveal this pattern; and why other modes such as counter mode will not? A counter mode encryption generates ciphertext as C1 = E(k,1) mi, cz = E(k, 2) m2, ..., n = E(k, n mn and here 1,2,3,..., n are all treated as a 128-bit binary string, assuming n