Two parties, A and B$,$ agree to securely communicate using a shared secret key, K$,$ exchanged with the help of Diffie$-$Hellman key exchange method. Both A and B$,$ choose a prime number p$,$ its primitive root g$,$ and a hash function H$.$ User A chooses a random number a and computes M$1=$ ga mod p$.$ For authentication purpose, A chooses a nonce N$1,$ and sends M$,$ and N$,$ to B$.$ While receiving M$,$ and N$1,$ B computes M$2=$ gb mod p by choosing b as the random number. It also computes the hash of N$,$ as H$($N$)$ and sends M$2,$ H$($N$),$ and its own nonce Na to A$.$ Upon receiving M$2,$ H$($N$),$ and NB$,$ A verifies the received hash H$($N$)$ and computes the key as K $=($M$)$ mod p$.$ It also computes the hash of Ng as H$($Na$)$ and sends it to B$.$ Similarly, B computes the key as K $=($M$)$ mod p and verifies the received hash H$($Na$).$ Consider an adversary, E$,$ which intercepts all communication between A and B$,$ and knows the parameters p and g$.$ If E does not have any information about the hash function H$,$ describe with proper reasoning whether it would be possible for E to get the secret key K and to establish the man$-$in$-$the$-$middle attack? Support your answer with clear and justified reasoning.