Storage and management in cloud services are of growing importance due to their cost-effective approaches in using large shared resources. However, with public access to the information in clouds, security is a very important issue. Confidentiality of data can be preserved by encrypting critical data before storing it in the cloud. However, bringing the data back and processing after decryption also leads to an overhead and outweighs the advantage of cloud computing. Homomorphic encryption which allows operations directly on the encrypted data is a solution to reduce this overhead. However, operations defined over fully homomorphic domain are very limited. With the advent of cloud computing, we intend to revisit age old problems of searching and sorting on fully homomorphic data. This research aims to propose the first approach to perform sorting on encrypted data. Our work further analyzes the performance of such operations and proposes different techniques to accelerate the sorting process. Further, we investigate feasibility of search operation on encrypted data in cloud. However there are several practical limitations of applying the fully homomorphic encryption (FHE) scheme to solve real life problems. Finally, our aim is to design the hardware for such FHE based operations with efficient FHE addition and multiplication blocks.