Connected　autonomous　vehicles　(CAVs)　employ　the　point　cloud　data　captured　by　LiDAR　to　enhance　the　capability　of　object　recognition　and　detection.　Edge　computing　with　its　inherent　advantages　can　help　CAVs　alleviate　resource　constraints　and　enable　faster　situational　awareness　and　data　processing.　However,　the　point　cloud　data　contains　private　information,　such　as　vehicle　identity,　location　and　trajectory,　directly　uploading　the　raw　point　cloud　to　the　edge　nodes　or　other　vehicle　will　lead　to　serious　privacy　leakage.　To　the　best　of　our　knowledge,　we　are　the　first　to　try　to　tackle　this　challenge　and　propose　a　privacy-preserving　object　detection　framework　over　random　point　cloud　shares　for　CAVs　(referred　to　SecPCV),　aiming　to　guarantee　the　privacy　of　both　point　cloud　and　object　detection　results.　In　SecPCV,　CAVs　split　point　cloud　into　two　random　shares　based　on　additive　secret　sharing　(ASS)　and　upload　them　to　two　competing　edge　nodes,　respectively,　which　greatly　compress　the　computational　load　of　CAVs.　Without　changing　the　object　detection　network　in　plaintext　environment,　the　edge　nodes　can　cooperatively　and　securely　extract,　regress,　and　classify　over　point　cloud　shares.　Theoretical　analysis　ensure　the　efficiency　and　security　of　the　SecPCV　framework.　Experimental　results　with　the　real　KITTI　point　cloud　dataset　indicate　that　SecPCV　can　achieve　the　consistent　object　detection　accuracy　as　that　in　plaintext　environment,　and　provide　a　feasible　solution　for　CAVs　secure　sharing　of　point　cloud　data.