In　this　paper,　we　propose　a　framework　for　lightning-fast　privacy-preserving　outsourced　computation　framework　in　the　cloud,　which　we　refer　to　as　LightCom.　Using　LightCom,　a　user　can　securely　achieve　the　outsource　data　storage　and　fast,　secure　data　processing　in　a　single　cloud　server　different　from　the　existing　multi-server　outsourced　computation　model.　Specifically,　we　first　present　a　general　secure　computation　framework　for　LightCom　under　the　cloud　server　equipped　with　multiple　Trusted　Processing　Units　(TPUs),　which　face　the　side-channel　attack.　Under　the　LightCom,　we　design　two　specified　fast　processing　toolkits,　which　allow　the　user　to　achieve　the　commonly-used　secure　integer　computation　and　secure　floating-point　computation　against　the　side-channel　information　leakage　of　TPUs,　respectively.　Furthermore,　our　LightCom　can　also　guarantee　access　pattern　protection　during　the　data　processing　and　achieve　private　user　information　retrieve　after　the　computation.　We　prove　that　the　proposed　LightCom　can　successfully　achieve　the　goal　of　single　cloud　outsourced　data　processing　to　avoid　the　extra　computation　server　and　trusted　computation　server,　and　demonstrate　the　utility　and　the　efficiency　of　LightCom　using　simulations.　©　2020,　The　Author(s).