In　the　cloud-assisted　industrial　Internet　of　Things　(IIoT),　since　the　cloud　server　is　not　always　trusted,　the　leakage　of　data　privacy　becomes　a　critical　problem.　Dynamic　symmetric　searchable　encryption　(DSSE)　allows　for　the　secure　retrieval　of　outsourced　data　stored　on　cloud　servers　while　ensuring　data　privacy.　Forward　privacy　and　backward　privacy　are　necessary　security　requirements　for　DSSE.　However,　most　existing　schemes　either　trade　the　server＇s　large　storage　overhead　for　forward　privacy　or　trade　efficiency/overhead　for　weak　backward　privacy.　These　schemes　cannot　fully　meet　the　security　requirements　of　cloud-assisted　IIoT　systems.　We　propose　a　fast　and　firmly　secure　SSE　scheme　called　Veruna　to　address　these　limitations.　To　this　end,　we　design　a　new　state　chain　structure,　which　can　not　only　ensure　forward　privacy　with　less　storage　overhead　of　the　server　but　also　achieve　strong　backward　privacy　with　only　a　few　cryptographic　operations　in　the　server.　Security　analysis　proves　that　our　scheme　possesses　forward　privacy　and　Type-II　backward　privacy.　Compared　with　many　state-of-the-art　schemes,　our　scheme　has　an　advantage　in　search　and　update　performance.　The　high　efficiency　and　robust　security　make　Veruna　an　ideal　scheme　for　deployment　in　cloud-assisted　IIoT　systems.