XTR　is　a　novel　public　key　system　based　on　a　method　to　represent　elements　of　a　subgroup　of　a　multiplicative　group　of　a　finite　field.　It　integrates　most　of　the　advantages　of　RSA　and　ECC　without　any　of　their　limitations.　Compared　with　RSA,　XTR　keys　are　much　smaller　than　RSA　keys　of　equivalent　security;　compared　with　ECC,　parameters　and　key　selections　for　XTR　are　much　faster　than　ECC.　Many　researchers　focus　on　XTR　and　much　research　work　has　been　developed　since　it　was　proposed.　An　identity　based　digital　signature　algorithm　and　an　identity　based　blind　signature　algorithm　of　XTR　system　are　proposed　in　the　paper.　The　security　is　equivalent　to　solving　discrete　logarithm　problem　of　XTR　group　and　the　two　signature　algorithms　provide　a　wider　application　domain.　Finally,　we　prove　the　security　of　the　signature　algorithms　and　analysis　the　efficiency.　Its　implementation　takes　a　good　reference　for　E-Government　and　E-Business.　©　2008　IEEE.