With　the　widespread　growth　of　cloud　computing　technology,　cloud　software　services　are　ubiquitous　these　days.　Using　this　technology,　software　providers　can　sell　their　products　through　cloud　computing　environments　in　the　pay-as-you-use　fashion.　However,　performing　secure　and　accurate　calculations　in　cloud　computing　environments　has　become　extremely　challenging.　As　the　data　to　be　processed　by　cloud　software　might　be　highly　sensitive,　its　confidentiality　needs　to　be　taken　care　of　before　transferring　the　data　to　the　cloud　server.　Also,　in　addition　to　the　data　confidentiality,　the　security　of　algorithms　employed　in　the　software　is　of　vital　importance,　and　thus　software　owners　may　be　worried　about　revealing　their　algorithms　through　the　cloud　server.　Homomorphic　cryptosystems　can　provide　confidentiality　for　data　to　be　processed　online.　However,　the　confidentiality　of　algorithms　is　still　an　open　problem.　To　address　this　issue,　we　put　forward　a　privacy-preserving　joint　data　and　function　homomorphic　encryption　(JDF-HE)　mechanism.　Our　JDF-HE　can　provide　confidentiality　for　both　algorithms　and　data,　thereby　being　suitable　for　cloud　software　services.　We　prove　the　security　of　JDF-HE　and　analyze　its　performance　by　evaluating　its　actual　execution　overhead.　Our　performance　and　security　analysis　demonstrate　that　JDF-HE　is　secure　and　suitable　for　real-time　applications.　©　2014　IEEE.