Compare and contrast the various key exchange protocols used in end-to-end encrypted systems, assessing their relative strengths and weaknesses.

Key exchange protocols are fundamental to end-to-end encrypted (E2EE) systems, enabling parties to securely establish shared secret keys over insecure channels. These protocols differ in their mechanisms, security properties, and efficiency. Some common protocols are Diffie-Hellman (DH), Elliptic Curve Diffie-Hellman (ECDH), and the Signal Protocol's Extended Triple Diffie-Hellman (X3DH). Let's compare and contrast these. First, the classic Diffie-Hellman (DH) key exchange protocol was one of the earliest widely adopted methods. In DH, two parties, let's say Alice and Bob, agree on a publicly known large prime number 'p' and a generator 'g'. Alice chooses a random private key 'a', and computes her public key 'A = g^a mod p'. Similarly, Bob chooses 'b' and computes 'B = g^b mod p'. They exchange their public keys. Then, Alice calculates the shared secret as 'B^a mod p' and Bob as 'A^b mod p'. The result is the same shared secret without ever transmitting the secret itself. The primary strength of DH is its relative simplicity and mathematical elegance. It was revolutionary because it demonstrated that a shared secret could be created over a public medium. The main weakness of basic DH is its vulnerability to man-in-the-middle (MitM) attacks. If an attacker intercepts the public keys and replaces them with their own, they can establish separate shared keys with both parties and decrypt the traffic. DH itself doesn't offer authentication, so it needs additional mechanisms such as digital signatures or pre-shared secrets to be secure in real-world scenarios. Another potential weakness is the use of....