The　first　lattice-based　group　signature　scheme　with　verifier-local　revocation　(GS-VLR)　was　introduced　by　Langlois　et　al.　in　PKC　2014,　and　subsequently,　a　full　and　corrected　version　was　designed　by　Ling　et　al.　in　TCS　2018.　However,　zero-knowledge　proofs　in　both　schemes　are　within　a　structure　of　Bonsai　Tree,　and　have　bit-sizes　of　the　group　public-key　and　the　member　secret-key　proportional　to,　where　N　is　the　group　size.　On　the　other　hand,　the　revocation　tokens　in　both　schemes　are　related　to　some　public　matrix　and　the　group　member　secret-key,　and　thus　only　obtain　a　weaker　security,　selfless-anonymity.　For　the　tracing　algorithms　in　both　schemes,　they　just　run　in　the　linear　time　of　N.　Therefore,　for　a　large　group,　zero-knowledge　proofs　in　lattice-based　GS-VLR　schemes　are　not　that　secure　and　efficient.　In　this　work,　we　firstly　utilize　an　efficient　and　compact　identity-encoding　technique　which　only　needs　a　constant　number　of　public　matrices　to　encode　the　member’s　identity　information　and　it　saves　a　factor　in　both　bit-sizes　for　the　group　public-key　and　the　group　member　secret-key.　Secondly,　separating　from　the　member　secret-key,　we　generate　revocation　token　within　some　secret　Gaussian　vector　and　thus　obtain　a　stronger　security,　almost-full　anonymity.　Moreover,　the　explicit　traceability,　to　trace　the　signer’s　identity　in　a　constant　time,　independent　of　N,　for　the　tracing　authority　is　also　satisfied.　In　particular,　a　new　Stern-type　statistical　zero-knowledge　proofs　protocol　for　an　improved　lattice-based　GS-VLR　scheme　enjoying　the　above　three　advantages　is　proposed.　©　2019,　Springer　Nature　Singapore　Pte　Ltd.