Frequent itemsets mining and association rules mining are among the top used algorithms in the area of data mining. Secure outsourcing of data mining tasks to the third-party cloud is an effective option for data owners. However, due to the untrust cloud and the distrust between data owners, the traditional algorithms which only work over plaintext should be re-considered to take security and privacy concerns into account. For example, each data owner may not be willing to disclose their own private data to others during the cooperative data mining process. The previous solutions are either not sufficiently secure or not efficient. Therefore, we propose a Secure and Efficient Data Mining Outsourcing (SecEDMO) scheme for secure outsourcing of frequent itemsets mining and association rules mining over the joint database (i.e., database aggregated from multiple data owners) in the paradigm of cloud computing. Based on our customized lightweight symmetric homomorphic encryption algorithm and a secure comparison algorithm, SecEDMO can ensure strong privacy protection and low data mining latency simultaneously. Moreover, the well-designed virtual transaction insertion algorithm can hide the information of the original database while still preserving the cloud's ability to perform data mining over the obfuscated data. By evaluation of a numerical experiment and theoretical comparisons, the correctness, security, and efficiency of SecEDMO are confirmed.