How to distinguish on-line dictionary attacks and password mis-typing in two-factor authentication

Authenticated Key Exchange (AKE) protocol is one of the ways for establishing secure channels between two parties where they authenticate each other and share a common session key. In particular, some AKE protocols using passwords and high-entropy secrets (i.e., two-factor AKE) are preferable since they provide stronger authentication than one-factor authentication. However, existing two-factor AKE protocols never equip ability to distinguish on-line dictionary attacks from other events, such as client´s password mis-typing and communication errors. This problem submerges a critical symptom of high-entropy-secret-leakage (since without it adversaries cannot perform the on-line dictionary attacks) or it forces the users inconvenience by letting them change their passwords frequently to reset the entropy of it that might be guessed partially by the on-line dictionary attacks. In this paper, we propose two general methods to distinguish online dictionary attacks (performed by an attacker) from other harmless events in the two-factor AKE protocols.