Exercise 1: Alice and Bob want to set up a symmetric cryptographic channel using the Diffie-Hellman key exchange protocol. Alice chooses p = 457 and needs to find a generator of Z. How would you test if g is a generator of Z;? How many exponents a > 1 do you need to test at most to prove that a given g is a generator of Z457? Hint: The order ordG(g) of any element ge G must divide the order of the finite group G. [5 marks]