Cloud-based　data　storage　service　has　drawn　increasing　interests　from　both　academic　and　industry　in　the　recent　years　due　to　its　efficient　and　low　cost　management.　Since　it　provides　services　in　an　open　network,　it　is　urgent　for　service　providers　to　make　use　of　secure　data　storage　and　sharing　mechanism　to　ensure　data　confidentiality　and　service　user　privacy.　To　protect　sensitive　data　from　being　compromised,　the　most　widely　used　method　is　encryption.　However,　simply　encrypting　data　(e.g.,　via　AES)　cannot　fully　address　the　practical　need　of　data　management.　Besides,　an　effective　access　control　over　download　request　also　needs　to　be　considered　so　that　Economic　Denial　of　Sustainability　(EDoS)　attacks　cannot　be　launched　to　hinder　users　from　enjoying　service.　In　this　article,　we　consider　the　dual　access　control,　in　the　context　of　cloud-based　storage,　in　the　sense　that　we　design　a　control　mechanism　over　both　data　access　and　download　request　without　loss　of　security　and　efficiency.　Two　dual　access　control　systems　are　designed　in　this　article,　where　each　of　them　is　for　a　distinct　designed　setting.　The　security　and　experimental　analysis　for　the　systems　are　also　presented.