Attribute-based　multi-keyword　search　(ABMKS)　facilitates　searching　with　fine-grained　access　control　over　outsourced　ciphertexts.　However,　two　critical　issues　impede　wide　application　of　ABMKS.　Firstly,　the　majority　of　ABMKS　schemes　have　suffered　huge　computation　and　communication　costs　in　the　process　of　ciphertexts　matching　and　transmission.　Secondly,　the　contents　of　data　file　containing　sensitive　information　are　encrypted　as　a　whole,　and　data　users　with　varying　roles　should　have　different　access　rights　to　the　ciphertext　returned　by　cloud,　thereby　preventing　sensitive　information　in　data　files　from　being　leaked　to　semi-trusted　data　users.　In　this　paper,　we　tackle　the　issue　of　content　access　rights　by　introducing　sensitive　information　hiding,　a　novel　concept　in　the　field　of　attribute-based　keyword　search.　Specifically,　we　propose　a　practical　multi-keyword　search　scheme　with　sensitive　information　hiding　by　integrating　a　modified　blindness　filtering　technique　into　ciphertext　policy　attribute-based　encryption　under　the　multi-keyword　search　model.　To　minimize　communication　costs　in　the　ciphertext　transmission　process,　we　utilize　a　super-increasing　sequence　to　aggregate　multiple　blinding　data　blocks　into　a　single　ciphertext.　The　ciphertext　can　be　recovered　by　using　a　recursive　algorithm.　Security　analysis　proves　that　our　scheme　is　provably　secure　within　the　random　oracle　model,　it　guarantees　keyword　secrecy　and　selective　security　against　chosen-keyword　attacks.　Performance　evaluations　demonstrate　that　our　scheme　surpasses　state-of-the-art　ABMKS　schemes,　making　it　highly　suitable　for　cloud　storage　systems.　©　The　Author(s),　under　exclusive　license　to　Springer　Nature　Switzerland　AG　2024.