Efficiently　mining　frequent　itemsets　and　association　rules　on　the　encrypted　outsourced　data　remains　a　great　challenge　for　the　time-consuming　ciphertext　computations.　Nowadays,　it　has　been　not　well　addressed　for　privacy-preserving　frequent　itemsets　and　association　rule　mining　schemes　with　mining　efficiency,　dataset,　and　query　confidentiality　simultaneously.　In　this　paper,　we　investigate　the　study　of　privacy　issues　on　frequent　itemset　mining　and　association　rule　mining　on　outsourced　data　in　a　two-cloud　model,　where　the　data　are　encrypted　and　outsourced　by　multiple　owners　holding　different　public　keys.　We　develop　several　secure　computation　protocols　based　on　additively　homomorphic　cryptosystem　and　additive　secret　sharing,　which　enable　the　clouds　could　securely　mine　the　frequent　itemsets　and　association　rules.　Furthermore,　we　also　design　two　kinds　of　frequent　itemset　and　association　rule　query　service,　i.e.,　service　customers　query　the　cloud-mined　results,　and　service　customers　query　with　their　own　decided　threshold.　The　proposed　scheme　not　only　supports　the　mining　process　on　the　data　encrypted　by　multiple　public　keys　without　compromising　the　security　of　the　datasets,　query　data　and　query　results,　but　also　offline　users.　In　addition,　the　experimental　results　show　that　our　query　scheme　is　much　more　efficient　than　the　state-of-the-art　work.