The　first　lattice-based　verifier-local　revocation　group　signature　(GS-VLR)　was　introduced　by　Langlois　et　al.　in　2014,　and　subsequently,　a　full　and　corrected　version　was　proposed　by　Ling　et　al.　in　2018.　However,　zero-knowledge　proofs　in　both　schemes　are　within　a　structure　of　Bonsai　Tree,　and　thus　have　bit-sizes　of　the　group　public-key　and　member　secret-key　proportional　to　log　N,　where　N　is　the　group　size.　On　the　other　hand,　the　revocation　tokens　in　both　schemes　are　related　to　the　member　secret-key　and　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,　the　zero-knowledge　proofs　in　lattice-based　GS-VLR　schemes　are　not　that　secure　and　efficient.　In　this　work,　we　firstly　utilize　a　compact　and　scalable　identity-encoding　technique　which　only　needs　a　constant　number　of　public　matrices　to　encode　the　member’s　identity　information　and　it　saves　a　O(log　N)　factor　in　both　bit-sizes　for　the　group　public-key　and　member　secret-key.　Secondly,　separating　from　the　member　secret-key,　we　generate　revocation　token　within　some　public　matrix　and　a　short　Gaussian　vector,　and　thus　obtain　the　strongest　security,　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　proof　protocol　for　a　fully　anonymous　lattice-based　GS-VLR　scheme　enjoying　the　above　three　advantages　is　proposed.　©　Springer　Nature　Switzerland　AG　2020.