In　the　Internet　of　Things,　based　on　the　collaboration　of　sensing　nodes,　sensing　data　are　collected　and　transmitted.　The　collaboration　of　sensing　nodes　also　plays　an　important　role　in　the　safeguard　of　the　Internet　of　Things.　Owing　to　the　limited　ability　of　the　single　sensing　node,　the　threshold　authentication　based　on　the　collaboration　of　sensing　nodes　can　improve　the　trust　of　security　authentication　of　sensing　nodes.　The　current　threshold　authentication　schemes　may　require　high-computational　complexity,　and　more　importantly,　most　of　them　are　instantiated　by　membership　authentication.　It＇s　challenging　to　apply　the　current　state　of　the　arts　to　the　case　where　sensing　nodes　with　various　weights　join　together　to　fulfill　a　relatively　lightweight　authentication.　In　this　paper,　we　first　design　a　communication　key　distribution　scheme　for　sensing　networks　based　on　a　symmetric　operator.　Using　the　permutation　function,　the　scheme　is　able　to　generate　characteristic　sequences　to　improve　the　efficiency　of　key　distribution　in　sensing　networks.　In　addition,　we　propose　a　threshold　authentication　scheme　based　on　weights,　in　which　the　higher　weight　represents　the　more　important　role　in　authentication.　Our　authentication　scheme　only　requires　lightweight　operations,　so　that,　it　is　extremely　friendly　to　the　IoT　nodes　with　restricted　computation　power.　The　security　analysis　and　the　case　verification　demonstrate　that　our　novel　authentication　protects　IoT　nodes　without　yielding　significantly　computational　burden　to　the　nodes.