 Solution

In Diffie-Hellman key exchange, Alice and Bob publicly agree on a cyclic group $G=⟨g⟩$ in which the discrete logarithm problem is believed hard. Alice chooses a secret $a$ and sends $A=g^a$; Bob chooses a secret $b$ and sends $B=g^b$. They independently computeThusis their shared key. A passive eavesdropper sees $g,g^a,g^b$ but is believed unable to compute $g^{ab}$ efficiently; this is the computational Diffie--Hellman assumption. The basic protocol does not authenticate the participants and is therefore vulnerable to a man-in-the-middle attack unless the exchanged values are authenticated.