Wearable　computing　has　shown　tremendous　potential　to　revolutionize　and　uplift　the　standard　of　our　lives.　However,　researchers　and　field　experts　have　often　noted　several　privacy　and　security　vulnerabilities　in　the　field　of　wearable　computing.　In　order　to　tackle　these　problems,　various　schemes　have　been　proposed　in　the　literature　to　improve　the　efficiency　of　authentication　and　key　establishment　procedure.　However,　the　existing　schemes　have　relatively　high　computation　and　communication　overheads　and　are　not　resilient　to　various　potential　security　attacks,　which　reduces　their　significance　for　applicability　in　constrained　wearable　devices.　In　this　work,　we　propose　an　efficient　and　anonymous　authenticated　key　exchange　scheme　for　wearable　computing　(EAKE-WC),　which　performs　mutual　authentication　between　the　user　and　the　wearable　device,　and　between　the　cloud　server　and　the　user.　It　also　establishes　secret　session　keys　for　each　session　to　secure　communication　among　the　communicating　entities.　Additionally,　the　proposed　EAKE-WC　scheme　is　designed　using　authenticated　encryption　with　associated　data　(AEAD)　primitives　like　ASCON,　bitwise　XOR,　and　hash　functions.　Our　results　from　the　security　analysis　depict　compliance　of　the　proposed　EAKE-WC　with　wearable　computing＇s　security　criteria.　In　addition,　we　also　demonstrate　through　a　comprehensive　comparative　analysis　that　the　proposed　scheme,　EAKE-WC,　outperforms　the　existing　benchmark　schemes　in　various　key　performance　areas,　including　lower　communication　and　computational　overheads,　enhanced　security,　and　added　functionality.