In　cloud　computing,　cloud　users　can　upload　their　data　to　cloud　storage　server　in　order　to　save　local　storage　and　access　their　data　from　anywhere.　However,　cloud　storage　service　also　brings　serious　security　issues.　Cloud　users　should　be　convinced　of　the　correctness　of　their　data　stored　remotely　in　the　cloud.　Thus,　a　reliable　auditing　scheme　is　desired　to　help　cloud　users　check　the　integrity　of　their　remote　data.　In　this　paper,　we　first　propose　an　efficient　cloud　auditing　scheme　for　multi-cloud　storage　systems,　which　can　also　preserve　the　privacy.　Then,　we　extend　our　auditing　scheme　to　support　dynamic　auditing　and　batch　auditing　for　both　multiple　cloud　users　and　multiple　cloud　service　providers　(CSPs),　which　makes　the　scheme　more　practical　and　efficient.　Security　analysis　shows　that　our　auditing　scheme　is　provably　secure.　Our　experiments　indicate　that　our　solution　is　efficient　and　significantly　relieves　the　computation　burden　of　both　third　party　auditor　(TPA)　and　CSP.　©　2016　SERSC.