“…, P s ) by using only the shared secret password k. It means that the Client authentication response f (k, realm, P c , s, β, α, P s )} in step (3) and the Server authentication response f (k, realm, P s , s, α, β, P c )} in step (4) just only defend on the password k. Unlike Wu et al's NAKE protocol, in order to overcome the off-line password guessing attacks in the improved NAKE protocol, since the Client authentication response f (k, DH k , realm, P c , s, β, α, P s )} in step (3) and the Server authentication response f (k, DH k , realm, P s , s, α, β, P c ) in step (4) To secure the DenningSacco attacks, we change the session key sk = xyP with sk = f (xyP ) by using secure one-way hash function in our improved NAKE protocol. Then, although an attacker obtains the shared session key sk = f (xyP ), he/she cannot obtain the Client's secret password k from the Client authentication response f (k, DH k , realm, P c , s, β, α, P s )} in step (3) and the Server authentication response f (k, DH k , realm, P s , s, α, β, P c ) in step (4) because f (·) is a secure one-way hash function by Definition 4.…”