Cryptography question: answer completely and carefully with full working out for a thumbs up.

Exercise 1: a) What is the key space K for the multiplicative cipher on an alphabet with 33 characters (e.g. Russian)? Justify your answer by studying the multiplicative group of integers modulo 33, (Z33,-). b) Alice tries to improve the security of the 26-character multiplicative cipher by applying two rounds of the cipher with the same key k. Show that the resulting cryptosystem is even less secure than the original cipher (Hint: Study the key space). Exercise 1: a) What is the key space K for the multiplicative cipher on an alphabet with 33 characters (e.g. Russian)? Justify your answer by studying the multiplicative group of integers modulo 33, (Z33,-). b) Alice tries to improve the security of the 26-character multiplicative cipher by applying two rounds of the cipher with the same key k. Show that the resulting cryptosystem is even less secure than the original cipher (Hint: Study the key space)