Investigation of the Method of Authenticated Key Exchange

This thesis work investigates the method of authenticated key exchange, a key exchange protocol where communicating parties generate and exchange secret session keys for the purpose of authentication. We focused attention on the Efficient Two-Server Password-Only Authenticated Key Exchange by Xun Yi, San Ling, and Huaxiong Wang, the most recent authenticated key exchange protocol. The protocol uses two-server scenario to offer a symmetric solution for authenticated key exchange protocol in the password-only model. Before authentication process, the client chooses a password and computes password authenticator such that the password cannot be revealed from the authenticator to anyone, except the two servers conspired and sends to the two servers through a secure channel. The protocol generates shared session keys by each communicating party such that, in the result of their computations, parties arrive at a common session key. In our investigation, we discovered a problem with the protocol that will cause its failure and render it inefficient in general scenario. The problem is that the protocol does not take into account congruency of the exponents modulo Euler’s totient function, resulting in the parties arriving at different session keys at the end of computations, which we proved and illustrated by numerical counter-example. We provided a modification to the protocol by proposing that in choosing parameters whose inverses are involved in computations, care must be taken to ensure that their multiplicative inverses modulo Euler’s totient function exist. We provided a proof for the modification and a numerical example to illustrate the correctness of this modification and confirmed that the protocol works efficiently. With the proposed modification, it is certain the protocol will function without any failure. Keywords: Authenticated key exchange protocol, two-server architecture, password-only authentication, Diffie-Hellman, ElGamal encryption scheme