Benefiting　from　the　fast　development　of　human-carried　mobile　devices,　crowd　sensing　has　become　an　emerging　paradigm　to　sense　and　collect　data.　However,　reliability　of　sensory　data　provided　by　participating　users　is　still　a　major　concern.　To　address　this　reliability　challenge,　truth　discovery　is　an　effective　technology　to　improve　data　accuracy,　and　has　garnered　significant　attention.　Nevertheless,　many　of　state　of　art　works　in　truth　discovery,　either　failed　to　address　the　protection　of　participants’　privacy　or　incurred　tremendous　overhead　on　the　user　side.　In　this　paper,　we　first　propose　a　privacy-preserving　truth　discovery　scheme,　named　PPTDS-I,　which　is　implemented　on　two　non-colluding　cloud　platforms.　By　capitalizing　on　properties　of　modular　arithmetic,　this　scheme　is　able　to　protect　both　users’　sensory　data　and　reliability　information,　and　simultaneously　achieve　high　efficiency　and　fault-tolerance.　Additionally,　for　the　scenarios　with　resource　constrained　devices,　an　efficient　truth　discovery　scheme,　named　PPTDS-II,　is　presented.　It　can　not　only　protect　users’　sensory　data,　but　also　avoids　user　participation　in　the　iterative　truth　discovery　procedure.　Detailed　security　analysis　shows　that　the　proposed　schemes　are　secure　under　a　comprehensive　threat　model.　Furthermore,　extensive　experimental　analysis　has　been　conducted,　which　proves　the　efficiency　of　the　proposed　schemes.　©　2019　Elsevier　Inc.