In cloud computing, a third party hosts a client's data, which raises privacy and security concerns. To maintain privacy, data should be encrypted by cryptographic techniques. However, encrypting the data makes it unsuitable for indexing and fast processing, as data needs to be decrypted to plain text before it can be further processed. Homomorphic encryption helps to overcome this shortcoming by allowing users to perform operations on encrypted data without decryption. Many academics have attempted to address the issue of data security, but none have addressed the issue of data privacy in cloud computing as thoroughly as this study has. This paper discusses the challenges involved in maintaining the privacy of cloud-based data and the techniques used to address these challenges. It was identified that homomorphic encryption is the best solution of all. This work also identified and compared the various homomorphic encryption schemes which are capable of ensuring the privacy of data in cloud storage and ways to implement them through libraries.