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This is the age of communication and data sharing, which requires safe and secure transactions. Cryptography is the science associated with maintenance and analysis of security, allowing accesses to authorized data. Nowadays, almost data information are stored and processed by third parties, especially on the cloud. Cloud computing is a wide and diverse phenomena. Users are allowed to store large amounts of data on storage cloud for future use. This leads to a lot of problems about data confidentiality, privacy, integrity and authenticity that must have a solution. For most cloud service providers, they store data in plaintext format before uploading to the cloud. Users need to use their own cryptography algorithms for securing their private data. Nevertheless, for each process of computation on encrypted data in the cloud, the data must be first downloaded to the client side and then be decrypted for computing. After being processed, clients have to re-encrypt the data and re-upload data to the cloud. This time-consuming procedure makes the computation more complex and out-weighs the strength of using cloud computing. And decrypting data before processing makes data confidentiality and privacy defeated. Although data is encrypted for storing, it continuously faces a lot of threats. Homomorphic encryption (HE) is a new technology of cryptography which can help solve above problem. It provides the ability of storing and processing data privately and securely without decrypting it first. Cloud computing is a new application, where HE is predicted to express its power for providing us desired security solutions. Therefore, the goals of this project are researching homomorphic encryption and then applying homomorphic encryption to guarantee the confidentiality and privacy of data stored in cloud.