Analysis of a man-in-the-middle attack on the Diffie-Hellman key exchange protocol

The ability to distribute cryptographic keys securely has been a challenge for centuries. The Diffie-Hellman key exchange protocol was the first practical solution to the key exchange dilemma. The Diffie-Hellman protocol allows two parties to exchange a secret key over unsecured communication channels without meeting in advance. The secret key can then be used in a symmetric encryption application, and the two parties can communicate securely. However, if the key exchange takes place in certain mathematical environments, the exchange becomes vulnerable to a specific man-in-the-middle attack, first observed by Vanstone [1]. We explore this man-in-the-middle attack, analyze countermeasures against the attack, and extend the attack to the multi-party setting.