Abstract: Based on CPK,two safe one-round group key transfer protocols are presented,which are both authenticated using two factors namely a password and a smart card.The temporary keys are protected by the Chinese Remainder Theorem(CRT) in the first protocol,which is provably secure under the CDH assumption.In the second protocol,the temporary keys are generated by the combination of the elements of the secret random number matrix(SRM).The secure renewal process of the SRM is also given.Both protocols have lower computation costs,so they have higher potential applications.