Spatial　keyword　queries　have　attracted　much　attention　over　the　past　decade　due　to　the　popularity　of　location-based　services　and　social　networks,　which　brings　great　economic　benefits.　Geo-textual　data　are　encrypted-and-delegated　to　public　clouds　for　efficient　management　and　utilization　while　preventing　potential　data　leakage.　However,　it　is　still　challenging　to　solve　secure　range　spatial　keyword　queries　on　encrypted　data　since　existing　works　are　either　vulnerable　or　inefficient.　In　this　paper,　a　secure　hybrid　index　is　built　to　implement　efficient　filtering,　by　embedding　nodes＇　paths　in　a　novel　symmetrical　kd-tree　into　inverted　indexes　and　employing　only　lightweight　cryptographic　techniques.　A　concrete　scheme　RASK　is　constructed　on　the　secure　index　by　utilizing　only　a　little　storage　and　computing　resources　of　clients.　Furthermore,　RASK+　is　proposed　based　on　secure　virtual　technology　by　migrating　all　storage　burdens　from　clients　to　public　clouds.　Both　schemes　are　theoretically　proved　to　be　indistinguishable　under　adaptive　chosen　keyword　attacks　(IND-CKA2).　Through　experimental　evaluations　on　three　real　datasets　within　consistent　environments,　both　schemes　reduce　the　response　time　by　about　50%-80%　compared　to　state-of-the-art　solutions　(i.e.,　SKSE,　LSKQ,　etc.).　The　storage　overheads　for　the　cloud　are　also　reduced　by　about　0.5-2　orders　of　magnitude.　IEEE