Cloud computing which provides computation and storage resources in a pay-per-usage manner has emerged as the most popular computation model nowadays. Under the new paradigm, users are able to request computation resources dynamically in real-time to accommodate their workload requirements. The flexible resource allocation feature endows cloud computing services with the capability to offer affordable and efficient computation services. However, moving data and applications into the cloud exposes a privacy leakage risk of the user data. As the growing awareness of data privacy, more and more users begin to choose proactive protection for their data in the cloud through data encryption. One major problem of data encryption is that it hinders many necessary data utilization functions since most of the functions cannot be directly applied to the encrypted data. The problem could potentially jeopardize the popularity of the cloud computing, therefore, achieving efficient data utilization over encrypted data while preserving user data privacy is an important research problem in cloud computing. The focus of this dissertation is to design secure and efficient schemes to address essential data utilization functions over encrypted data in cloud computing. To this end, we studied three problems in this research area. The first problem that is studied in this dissertation is fuzzy multi-keyword search over encrypted data. As fuzzy search is one of the most useful and essential data utilization functions in our daily life, we propose a novel design that incorporates Bloom filter and Locality-Sensitive Hashing to fulfill the security and function requirements of the problem. Secondly, we propose a secure index which is based on the most popular index structure, i.e., the inverted index. Our innovative design provides privacy protection over the secure index, the user query as well as the search pattern and the search result. Also, users can verify the correctness of the search results to ensure the proper computation is performed by the cloud. Finally, we focus ourselves on the privacy-sensitive data application in cloud computing, i.e., genetic testings over DNA sequences. To provide secure and efficient genetic testings in the cloud, we utilize Predicate Encryption and design a bilinear pairing based secure sequence matching scheme to achieve strong privacy guarantee while fulfilling the functionality requirement efficiently. In all of the three research thrusts, we present thorough theoretical security analysis and extensive simulation studies to evaluate the performance of the proposed schemes. The results demonstrate that the proposed schemes can effectively and efficiently address the challenging problems in practice. / Ph. D.