Based　on　the　three　earlier　MAC　(Message　Authentication　Code)　construction　approaches,　we　propose　and　analyze　some　variants　of　NMAC.　We　propose　some　key　recovery　attacks　to　these　NMAC　variants,　for　example,　we　can　recover　the　equivalent　inner　key　of　NMAC　in　about　O(2n/2)　MAC　operations,　in　a　related　key　setting.　We　propose　NMAC-E,　a　variant　of　NMAC　with　secret　envelop,　to　achieve　more　process　efficiency　and　no　loss　of　security,　which　needs　only　one　call　to　the　underlying　hash　function,　instead　of　two　invocations　in　HMAC.