With　the　rapid　development　of　cloud　computing　and　Internet　of　Things　(IoT),　smart　health　(s-health)　is　anticipated　to　enhance　healthcare　quality　significantly.　However,　data　integrity,　user　anonymity,　and　authentication　concerns　have　not　been　adequately　addressed　in　s-health.　Remote　data　integrity　checking　(RDIC)　and　digital　signature　schemes　have　great　potential　to　address　these　requirements.　Nevertheless,　the　direct　adoption　of　these　schemes　suffers　from　two　flaws.　First,　they　incur　prohibitively　high　computation　and　communication　overhead.　Second,　they　leak　sensitive　health　information　about　patients　and　do　not　provide　complete　anonymity.　To　address　these　issues,　we　introduce　A(3)B-RDV,　an　aggregate　anonymous　attribute-based　remote　data　verification　scheme.　In　A(3)B-RDV,　the　integrity　of　an　arbitrary　number　of　cloud　data　files　can　be　verified　at　once　without　downloading　the　whole　data,　thereby　saving　communication　and　computation　resources.　Moreover,　in　A(3)B-RDV,　data　owners　can　be　authenticated　by　performing　highly　efficient　operations.　Also,　A(3)B-RDV　provides　complete　anonymity　and　supports　dishonest-user　traceability.　We　provide　security　definitions　for　A(3)B-RDV　and　prove　its　security　under　the　hardness　assumption　of　the　bilinear　Diffie-Hellman　(BDH)　problem.　Performance　comparisons　and　experimental　results　indicate　that　A(3)B-RDV　is　more　efficient　and　expressive　than　state-of-the-art　approaches.