With the emergence of big data and the continued growth in cloud computing applications, serious security and privacy concerns emerged. Consequently, several researchers and cybersecurity experts have embarked on a quest to extend data encryption to big data systems and cloud computing applications. As most cloud users turn to using public cloud services, confidentiality becomes and even more complicated issue. Cloud clients storing their data on a public cloud always seek solutions to confidentiality problem. Homomorphic encryption emerged as a possible solution where client's data is encrypted on the cloud in a way that allows some search and manipulation operations without proper decryption. In this paper, we present a systematic review of research paper published in the field of homomorphic encryption. This paper uses PRISMA checklist alongside some items of Cochrane's Quality Assessment to review studies retrieved from various resources. It was highly noticeable in the reviewed papers that security in big data and cloud computing has received most attention. Most papers suggested the use of homomorphic encryption although the thematic analysis has identified other potential concerns. Regarding the quality of the articles, 38% of the articles failed to meet three checklist items, including explicit statement of research objectives, procedure recognition and sources of funding used in the study. The review also presented compendium textual analysis of di erent homomorphic encryption algorithms, application areas, and areas of future developments. Results of the evaluation through PRISMA and the Cochrane tool showed that a majority of research articles discussed the potential use and application of Homomorphic Encryption as a solution to the growing demands of big data and absence of security and privacy mechanisms therein. This was evident from 26 of the total 59 articles that met the inclusion criteria. The term Homomorphic Encryption appeared 1802 times in the word cloud derived from the selected articles, which speaks of its potential to ensure security and privacy, while also preserving the CIA triad in the context of big data and cloud computing.