Notation: Given a modulus n, o, denotes the affine map Hax+b (mod n). 4 Question 1 [25 marks). (a) Give two Vigenre keys which combine to the key SXNUMLUSVBXF such that one of the keys has length 4 (the other key can have any length you like). (b) We say that two affine ciphers on the English alphabet commute if it does not matter in which order we apply them, otherwise we say that they do not commute. Find an affine cipher that commutes with ra and another affine cipher that does not commute with 04.1. (c) The following text has been encrypted using an affine cipher the English 011 alphabet: 15) PJADQ RDMBW 17] We know that the first and the last letters of the plaintext are w and n, respectively. Decrypt the text. Show your working (d) A cipher text is obtained by applying a Vigenre cipher followed by an affine cipher. Does the first step in Kasiski's method give the correct key length? Justify your answer. (e) Can we use the following table for a stream cipher on the alphabet {a,b,c,d)? If the answer is yes, explain why. If the answer is no, justify your answer by giving an example of what can go wrong. (5) a b c d a a bbd bb c d a cd ab dd a b c