With　the　development　of　the　Internet　of　Things　technology　and　the　advent　of　the　5G　era,　cloud　computing　is　difficult　to　meet　the　requirements　of　low　latency,　high　reliability,　and　data　security　for　various　application　services.　The　fog　computing　model　newly　proposed　by　researchers　in　recent　years　can　increase　the　task　processing　and　data　analysis　capabilities　of　network　edge　devices,　so　it　can　reduce　the　computing　load　of　cloud　computing　devices　and　improve　the　efficiency　of　data　operations.　Although　fog　computing　can　largely　solve　existing　cloud　computing　problems,　secure　access　and　privacy　protection　are　still　a　very　important　and　urgent　problem　to　be　solved.　Aiming　at　the　problem　of　selecting　a　relay　node　to　generate　a　security　key　under　the　fog　computing　model　under　the　fog　computing　model,　this　paper　proposes　a　secure　relay　node　selection　method　based　on　game　theory.　In　this　paper,　a　fog　computing　model　based　on　social　relationships　is　constructed.　Under　this　model,　a　secure　relay　node　selection　method　based　on　game　theory　is　designed　to　realize　the　selection　of　relay　nodes　when　a　communication　link　generates　a　security　key.　Finally,　this　paper　analyzes　the　selection　efficiency　from　the　two　dimensions　of　total　equipment　and　dynamic　changes　of　terminal　equipment.　Simulation　results　show　that　the　method　proposed　in　this　paper　can　quickly　select　secure　relay　nodes　in　the　social　connection-based　fog　computing　model.　©　2020,　Springer　Nature　Switzerland　AG.