With　enhanced　functionalities　and　capabilities,　wireless　mesh　networks　are　used　for　emergency　services　to　improve　the　efficiency　of　public　safety　communication　to　prevent　or　respond　to　incidents　that　harm　or　endanger　persons　or　property.　This　special　field　communication　brings　new　security　challenges.　In　this　paper,　we　propose　a　key　agreement　scheme　special　for　public　safety　mesh　networks　based　on　station-to-station　protocol　and　extend　the　scheme　to　the　key　agreement　with　voting　receiver　using　directed　signature　which　can　be　verified　only　by　the　signature　receiver.　Also　we　import　the　expectancy-value　theory　in　cognitive　psychology　to　the　analysis　of　key　authentication.　The　results　of　analysis　show　that　our　schemes　can　provide　resistance　to　unknown　key-share　attacks　by　little　computational　cost　in　comparison　to　the　station-to-station　protocol.　©　2010　IEEE.