The　rapid　development　of　the　Industrial　Internet　of　Things　(IIoT)　has　led　to　an　explosion　of　industrial　data.　Due　to　computing　and　storage　capacity　limitations,　IIoT　devices　often　outsource　the　collected　data　to　remote　cloud　servers.　Unfortunately,　cloud　storage　and　cloud　sharing　services　are　not　as　reliable　as　they　claim　to　be.　Existing　schemes　aim　to　check　data　integrity　in　the　cloud　through　cloud　auditing.　However,　they　suffer　from　a　number　of　security　and　privacy　vulnerabilities.　The　challenge　of　designing　a　secure　storage　auditing　framework　for　industrial　IoT　comes　from　two　aspects:　1)　lack　of　physical　protection　of　data　owner　IIoT　devices;　2)　privacy　issues　due　to　auditing　of　sensitive　shared　data.　Inspired　by　the　aforementioned　challenges,　we　design　the　secure　storage　audit　framework　to　support　flexible　cloud　data　sharing　in　IIoT:　S2A-P2FS.　The　first　contribution　in　our　work　is　the　Polynomial　Prefix　Message　Authentication　Code(P2MAC)　design.　We　design　an　innovative　P2MAC　data　structure　as　a　label,　which　can　simultaneously　achieve　efficient　data　verification　in　cloud　data　storage　and　privacy　protection　in　flexible　cloud　data　sharing　for　cloud　auditing.　The　second　contribution　is　the　design　of　a　unique　Physical　Unclonable　Function(PUF)　for　IIoT.　Harsh　industrial　conditions　hinder　the　stable　operation　of　PUFs.　To　protect　the　trustness　of　IIoT　data　owners,　we　propose　a　robust　PUF-based　physical　protection　mechanism　for　IIoT　devices.　The　key　point　is　that　the　required　key　is　not　stored　in　the　memory　of　IIoT　but　hidden　within　its　physical　structure.　A　security　analysis　was　conducted　to　demonstrate　the　robustness　of　S2A-P2FS　against　known　vulnerabilities.　A　prototype　was　implemented　in　a　real-world　IIoT　scenario.　Experimental　results　indicate　that,　compared　to　state-of-the-art　schemes,　S2A-P2FS　achieves　over　a　3x　speedup　in　computational　time　and　requires　only　67.5%　of　the　communication　cost.　©　2002-2012　All　rights　reserved.