Blockchain　technology,　known　for　its　decentralized　and　immutable　nature,　serves　as　the　foundation　for　various　applications.　As　a　prominent　application　of　blockchain,　decentralized　storage　is　powered　by　blockchain　technology　and　is　expected　to　provide　a　reliable　and　cost-effective　alternative　to　traditional　centralized　storage.　A　major　challenge　in　blockchain-powered　decentralized　storage　is　how　to　guarantee　the　quality　of　storage　services　in　decentralized　storage　nodes　(DSNs).　Storage　auditing　can　ensure　the　integrity　and　security　of　the　stored　data.　Unfortunately,　it　incurs　additional　computational　costs　for　data　owners　and　extra　storage　overheads　for　DSNs,　which　thereby　cannot　be　directly　applied　to　decentralized　storage　networks　consisting　of　nodes　with　various　computation　and　storage　capacity.　In　this　article,　we　overcome　these　problems　and　minimize　additional　burdens　in　storage　auditing.　We　propose　EDCOMA,　a　computation　and　storage　efficient　auditing　scheme　for　blockchain-based　decentralized　storage,　in　which　a　double　compression　method　is　designed　to　compress　data　authenticators　using　both　data　and　polynomial　commitment.　To　prevent　replay　attacks　on　double　compression　launched　by　DSNs,　we　introduce　zero　knowledge　proof　and　design　a　compression　arithmetic　circuit　to　guarantee　the　execution　of　compression　operations　in　DSNs.　We　analyze　the　security　of　EDCOMA　under　the　random　oracle　model　and　conduct　extensive　experiments　to　evaluate　the　performance　of　EDCOMA.　Experimental　results　affirm　that　EDCOMA　outperforms　state-of-the-art　approaches　in　both　computational　and　storage　efficiency.