Mobile　edge　computing　(MEC)　provides　computing　and　data　storage　capabilities　within　the　range　of　the　wireless　access　network　close　to　the　users,　which　is　driving　the　need　for　new　type　of　security　technologies.　Faced　with　rapid　traffic　growth　and　increasing　user　experience　requirements,　the　existing　security　schemes　can　no　longer　meet　the　new　requirements　of　real　time　and　lightweight.　New　solutions　that　do　not　require　complex　calculations,　such　as　identity-based　cryptography,　attract　great　attention　from　researchers.　To　meet　these　demands,　we　design　a　new　authentication　architecture　for　MEC　environment,　which　provides　secure　and　efficient　communication.　Based　on　this　authentication　architecture,　an　anonymous　identity-based　scheme　is　proposed　for　lightweight　devices.　In　the　meantime,　user　anonymity　is　also　fully　protected.　The　proposed　scheme　is　proved　to　be　secure　under　a　specific　security　model.　In　addition,　we　describe　the　security　properties　our　scheme　meets.　The　comparisons　of　time　consumption　and　communicational　cost　are　given　at　the　end　of　the　article,　to　demonstrate　that　our　scheme　performs　prior　to　several　previous　schemes.