All the information is given, Kindly give the correct answer.

(a) Consider the following Hash function: H:{0,1}64{0,1}8X{0,1}64,suchX=(x0,x1,,x7),eachxiisabyteH(X)=(x0+x1++x7) Provide a possible pre-image of the hashed value of H(X)=00000000 [5 marks] (b) Explain, using a numerical example, whether or not the above Hash function is collision resistant? [5 marks] (c) Explain, with the aid of an illustrative diagram, the working principles of a Hash function based on the Merkle-Damgard Scheme. [5 marks] (d) Alice and Bob wish to communicate over an insecure link and have agreed to use the AES encryption algorithm with a key length of 128 bits. However, they need to agree on a cryptographic mode of operation. ECBC,ECTR are two possible implementations of the AES algorithm in the cipher block chaining and counter modes, respectively, in both cases assuming the standard AES block of 128 bits. Which of the above two modes do you recommend in order to reduce the number of times the key needs to be changed? Explain and justify your answer. For your chosen mode, calculate, with full explanation, the maximum number of bits that can be transmitted over this link using the same encryption key such that the advantage of an adversary capable of carrying out a chosen plaintext attack does not exceed 240. It is assumed that the advantage of the adversary over AES is 245 in the case of one time key use