Investigating the method of authenticated key exchange protocol

Abstract

This research paper focused on investigating the method of authenticated key exchange, a protocol where communicating parties generate and exchange secret session keys for authentication. We examined the Two-Server Password-Only Authenticated Key Exchange  by Xun Yi, San Ling, and Huaxiong Wang, a two-server password-only authenticated key exchange protocol. In the protocol, each  communicating party generates a shared key such that in the result of their computations, they arrive at the same session key. This  analysis was deemed very relevant because failure to arrive at a shared session key is a chief design weakness in any cryptosystem. We  employed numerical examples to assist in proving the efficiency of the protocol. In our computations with randomly selected numerical  values as suggested by the protocol, it failed to arrive at a common session key. It was discovered that this failure was a result of not  considering the congruency of the powers modulo Euler’s totient function while selecting parameters at random for the computations.  We, therefore, proposed that the parameters whose inverse is involved in the computation should be chosen such that its multiplicative  inverse modulo Euler’s totient function exists instead of selecting them at random. In another numerical example, we employed this  restriction in selecting parameters for computations and it resulted in a more secure and efficient protocol.