4. We consider a DHKE protocol over a Galois fields GF(2^m). Up to now, we have been using groups but it is possible (and simple) to use GF for DHKE. Here, the generator is a polynomial (denoted as g(x)) and we have an irreducible polynomial instead of our public prime p (denoted as p(x)). (a) In our example here, all arithmetic is done in GF(2^5) with p(x) = x^5 +x^2 +1 as an irreducible field polynomial. (b) The primitive element for the Diffie-Hellman scheme is g(x) = x^2. The private keys are a = 3 and b = 12. What is the session shared key KAB? Hint: Derive the public key of Alice (A) by using the generator and her private key (A=g(x)^a mod p(x) in GF(2^5)). Do not forget to reduce using p(x). Bob can now find the session key Kas through another exponentiation. Do not forget to reduce. ||