The　Industrial　Internet　of　Things　(IIoT),　through　the　extensive　deployment　of　devices　for　sensing,　transmitting,　and　analyzing　production　states,　can　provide　users　with　more　comprehensive　services　and　enhance　production　and　manufacturing　efficiency.　However,　most　IIoT　devices　are　limited　by　software　and　hardware　resources,　and　existing　mature　security　mechanisms　are　no　longer　suitable　due　to　high-computing　and　communication　costs.　This　weakness　makes　these　devices　highly　susceptible　to　illegal　attacks,　such　as　counterfeiting,　leading　to　a　decline　in　service　quality　of　IIoT.　Therefore,　to　ensure　the　secure　and　efficient　verification　of　the　legitimacy　of　numerous　IIoT　devices,　scholars　have　employed　numerous　viable　solutions.　However,　many　existing　solutions　have　difficulty　achieving　a　balance　between　the　limited　resources　and　security　requirements　of　IIoT,　resulting　in　certain　shortcomings.　To　address　this,　we　first　propose　a　lightweight　certificateless　signature　scheme　without　pairing,　which　can　achieve　unforgeability　and　reduce　computation　pressure　by　batch　verification　for　multiple　signatures.　Furthermore,　we　propose　a　lightweight　certificateless　mutual　authentication　scheme　(LCLMA-BS)　for　the　IIoT.　LCLMA-BS　is　capable　of　conducting　key　agreement　for　both　authentication　parties　and　batch　authentication　for　multiple　participants.　Moreover,　through　analysis　and　proof,　LCLMA-BS　is　shown　to　have　various　security　properties,　such　as　perfect　forward　and　backward　security　and　known　session-specific　temporary　information　security.　Finally,　the　simulation　results　indicate　that　our　signature　and　LCLMA-BS　exhibit　higher　computational　efficiency　and　communication　efficiency,　demonstrating　better　suitability　for　the　IIoT.