Industrial　Internet　platforms　(IIP)　can　provide　many　intelligent　services　based　on　the　industrial　big　data　stored　in　clouds.　However,　the　vulnerability　of　cloud　storage　can　cause　data　corruption,　demanding　verifying　its　integrity.　Unfortunately,　existing　cloud　storage　verification　approaches　cannot　be　directly　applied　to　IIP,　since　they　pose　heavy　computational　burdens　on　the　edge　side.　In　this　work,　we　propose　an　efficient　and　dynamic　storage　verification　scheme　Edasvic　for　cloud　storage　in　the　IIP.　We　adopt　the　polynomial　commitment　to　build　an　efficient　homomorphic　authenticator,　and　further　design　an　authenticator　accumulator,　which　can　be　efficiently　generated　with　limited　computational　overheads.　In　addition,　we　integrate　the　dynamic　information　into　the　authenticator　accumulator　to　support　data　dynamics.　The　security　of　Edasvic　is　analyzed　under　the　random　oracle　model.　We　conduct　extensive　experiments　to　evaluate　the　performance　of　Edasvic　and　compare　it　with　the　state-of-the-art　approaches.　Experimental　results　affirm　that　Edasvic　is　superior　to　existing　solutions　in　terms　of　computational　efficiency.