As　a　new　revocation　mechanism　for　identity-based　encryption　(IBE),　server-aided　revocable　IBE　(SR-IBE),　firstly　proposed　by　Qin　et　al.　in　2015,　achieves　remarkable　advantages　over　previous　identity　revocation　techniques.　In　this　primitive,　almost　all　of　workloads　on　the　users　(i.e.,　receivers)　side　can　be　delegated　to　an　untrusted　server　which　does　not　possess　any　secret　information,　and　the　users　can　compute　short-term　decryption　keys　alone　at　any　time　period　without　having　to　communicate　with　either　the　private　key　generator　(PKG)　or　server.　In　2016,　Nguyen　et　al.　creatively　presented　the　first　lattice-based　SR-IBE　by　adopting　a　＇double　encryption＇　mechanism　to　enable　smooth　interactions　between　the　sender　and　the　server,　as　well　as　between　the　server　and　the　receiver,　while　ensuring　the　confidentiality　of　encrypted　messages.　In　this　paper,　inspired　by　recent　work　on　a　new　treatment　of　the　identity　space　and　the　time　period　space,　we　simplify　the　first　construction　of　lattice-based　SR-IBE　provided　by　Nguyen　et　al.,　and　remove　some　items　from　the　public　parameters　and　the　master　secret　key.　In　particular,　our　scheme　is　more　efficient　by　reducing　the　workloads　of　PKG,　the　server,　the　sender　and　the　receivers,　simultaneously.　At　the　heart　of　our　new　design　is　a　tool　called　＇leveled　ciphertexts＇　that　enables　constant　ciphertexts　and　simplified　encryptions,　not　linear　in　the　length　of　user　identities　and　without　a　burdensome　double　encryption　technique,　which　serves　as　a　more　effective　solution　to　the　challenge　in　turning　the　pairing-based　instantiation　of　SR-IBE　into　the　world　of　lattice-based　cryptography,　and　based　on　the　hardness　of　learning　with　errors　(LWE)　problem,　we　prove　that　our　new　scheme　is　selectively　secure　in　the　standard　model.　©　2022,　The　Author(s),　under　exclusive　license　to　Springer　Nature　Switzerland　AG.