Cloud　storage　becomes　a　new　trend　that　more　and　more　users　move　their　data　to　cloud　storage　servers　(CSSs).　To　ensure　the　security　of　cloud　storage,　many　cloud　auditing　schemes　are　proposed　to　check　the　integrity　of　users＇　cloud　data.　However,　most　of　them　are　based　on　public　key　infrastructure,　which　leads　to　complex　certificates　management　and　verification.　Besides,　most　existing　auditing　schemes　are　inefficient　when　user　uploads　a　large　amount　of　data　or　a　third　party　auditor　(TPA)　performs　auditing　for　multiple　users＇　data　on　different　CSSs.　To　overcome　these　problems,　in　this　paper,　we　propose　an　efficient　and　secure　auditing　scheme　based　on　identity-based　cryptography.　To　relieve　user＇s　computation　burden,　we　introduce　a　proxy,　which　is　delegated　to　generate　and　upload　homomorphic　verifiable　tags　for　user.　We　extend　our　auditing　scheme　to　support　auditing　for　dynamic　data　operations.　We　further　extend　it　to　support　batch　auditing　in　multiple　users　and　multiple　CSSs　setting,　which　is　practical　and　efficient　in　large　scale　cloud　storage　system.　Extensive　security　analysis　shows　that　our　scheme　is　provably　secure　in　random　oracle　model.　Performance　analysis　demonstrates　that　our　scheme　is　highly　efficient,　especially　reducing　the　computation　cost　of　proxy　and　TPA.