Ciphertext-Policy　Attribute-Based　Keyword　Search　(CP-ABKS)　schemes　support　both　fine-grained　access　control　and　keyword-based　ciphertext　retrieval,　which　make　these　schemes　attractive　for　resource-constrained　users　(i.e.,　mobile　or　wearable　devices,　sensor　nodes,　etc.)　to　store,　share　and　search　encrypted　data　in　the　public　cloud.　However,　ciphertext　length　and　decryption　overhead　in　the　existing　CP-ABKS　schemes　grow　with　the　complexity　of　access　policies　or　the　number　of　data　users＇　attributes.　Moreover,　such　schemes　generally　do　not　consider　the　practical　multi-owner　setting　(e.g.,　each　file　needs　to　be　signed　by　multiple　data　owners　before　being　uploaded　to　the　cloud　server)　or　prevent　malicious　cloud　servers　from　returning　incorrect　search　results.　To　overcome　these　limitations,　in　this　paper　we　first　design　an　optimized　Verifiable　Fine-grained　Keyword　Search　scheme　in　the　static　Multi-owner　setting　(termed　as　basic　VFKSM),　which　achieves　short　ciphertext　length,　fast　ciphertext　transformation,　accelerated　search　process,　and　authentic　search　result　verification.　Then,　we　extend　the　basic　VFKSM　to　support　multi-keyword　search　and　multi-owner　update　(also　called　as　extended　VFKSM).　Finally,　we　prove　that　the　basic　(or　extended)　VFKSM　resists　the　Chosen-Keyword　Attack　(CKA)　and　external　Keyword-Guessing　Attack　(KGA).　We　also　evaluate　the　performance　of　these　schemes　using　various　public　datasets.