Edge　computing　server　deployed　at　the　edge　of　the　network　has　promoted　the　development　of　the　Internet　of　Things　(IoT)　but　also　brings　some　security　problems.　Traditional　IoT　security　solutions　have　not　met　the　requirements　of　the　current　rapid　growth　of　equipment,　real-time　and　lightweight.　Therefore,　the　development　of　new　authentication　and　key　agreement　is　becoming　an　important　means　to　solve　the　security　problems　of　the　IoT.　To　address　this　challenge,　we　propose　an　authentication　framework　for　the　edge　computing-enabled　IoT　environment.　This　framework　aims　to　facilitate　the　establishment　of　secure　communication　among　devices　and　between　devices　and　edge　servers.　This　authentication　framework　achieves　secure　communication　and　identity　verification　among　edge　computing-enabled　IoT　devices　and　between　devices　and　edge　servers　by　incorporating　a　portion　of　the　local　private　key　during　registration　and　leveraging　a　distributed　blockchain　network.　Formal　and　informal　security　analyses　of　the　proposed　protocol　show　that　the　protocol　effectively　responds　to　numerous　security　threats　while　satisfying　various　security　attributes.　In　addition,　the　study　provides　a　comprehensive　assessment　of　the　computational　and　transmission　overheads　associated　with　the　protocol.　The　results　show　that　the　protocol＇s　commendable　performance　in　terms　of　both　computational　efficiency　and　transmission　cost-effectiveness.