Due　to　the　lack　of　capability　of　solving　computationally　hard　problems　and　the　lack　of　high　processing　power　by　one　single　entity.　Swarm　robotics　emerge,　a　group　of　individual　robotics　shares　their　processing　resources　to　solve　a　complicated　problem.　Authentication　schemes　within　the　peer　robotics　are　necessary,　especially　when　the　swarm　robotics　is　sent　out　for　different　tasks.　In　this　study,　an　authentication　and　key　establishment　scheme　specially　designed　for　peer-to-peer　networks　is　proposed.　The　proposed　scheme　enables　authentication　between　two　registered　peer　entities　directly　without　the　help　of　a　trusted　server,　after　authentication,　two　peer　robotics　can　build　a　secure　two-way　communication　channel　in　a　public　environment.　Security　analysis　shows　that　this　scheme　is　secure,　compared　to　related　works　the　proposed　scheme　has　more　security　features.　In　addition,　our　experiment　results　show　the　proposed　scheme　is　efficient　compared　to　related　works.　©　2022　ACM.