In　2005,　Sui　et　al.　proposed　two　separable　and　anonymous　ID-based　key　issuing　protocols,　and　claimed　the　key-escrow　problem　has　been　solved　in　their　second　protocol.　However,　in　this　paper,　we　point　out　that　Sui　et　al＇s　second　protocol　dose　not　solve　the　key　escrow　problem　either　by　presenting　impersonation　attack.　Further,　we　present　an　improvement　to　resolve　such　problems,　in　which　KGC1　(or　KGC2)　confirms　a　user＇s　identity　by　a　short　signature　signed　by　the　user＇s　password　key.　©　2008　IEEE.