Wireless　Body　Area　Network　(WBAN)　is　a　highly　promising　technology　enabling　health　providers　to　remotely　monitor　vital　parameters　of　patients　via　tiny　wearable　and　implantable　sensors.　In　a　WBAN,　medical　data　is　collected　by　several　tiny　sensors　and　usually　transmitted　to　a　server-side　(e.g.,　a　cloud　service　provider)　for　long-term　storage　and　online/offline　processing.　However,　as　the　health　data　includes　several　sensitive　information,　providing　confidentiality　and　fine-grained　access　control　is　necessary　to　preserve　the　privacy　of　patients.　In　this　paper,　we　design　an　attribute-based　encryption　(ABE)　scheme　with　lightweight　encryption　and　decryption　mechanisms.　Our　scheme　enables　tiny　sensors　to　encrypt　the　collected　data　under　an　access　control　policy　by　performing　very　few　computational　operations.　Also,　the　computational　overhead　on　the　users　in　the　decryption　phase　is　lightweight,　and　most　of　the　operations　are　performed　by　the　cloud　server.　In　comparison　with　some　excellent　ABE　schemes,　our　encryption　mechanism　is　more　than　100　times　faster,　and　the　communication　overhead　in　our　scheme　decreases　significantly.　We　provide　the　security　definition　for　the　new　primitive　and　prove　its　security　in　the　standard　model　and　under　the　hardness　assumption　of　the　decisional　bilinear　Diffie-Hellman　(DBDH)　problem.　©　2019　by　the　authors.　Licensee　MDPI,　Basel,　Switzerland.