(a) Which of the following encryption methods is more secure? (i) A Vigenre cipher on the English alphabet with a key that is of the same length as the plaintext. (ii) A Vigenre cipher on the binary alphabet {0,1} with a key that is of the same length as the plaintext. Justify your answer. (b) The following is the output sequence of a 5-bit shift register. 4 10010110011111000 [7] 17 Determine the shift register. Show your working. (e) Prove that r + x2 +1 is irreducible over Z/2Z. (d) How many primitive 8-bit shift registers are there? Show your calculations. [7]