We　give　an　arbitrated　signature　protocol　of　classical　messages　over　a　collective　amplitude　damping　channel.　We　analyze　its　security　and　prove　that　it　is　secure　over　such　a　noisy　quantum　channel　even　if　the　arbitrator　is　compromised.　The　involvement　of　the　arbitrator　is　also　an　appealing　advantage　in　the　implementation　of　a　practical　quantum　distributed　communication　network.　(C)　2010　Elsevier　B.V.　All　rights　reserved.