Cloud computing technology has rapidly evolved over the last decade, offering an alternative way to store and work with large amounts of data. However data security remains an important issue particularly when using a public cloud service provider. The recent area of homomorphic cryptography allows computation on encrypted data, which would allow users to ensure data privacy on the cloud and increase the potential market for cloud computing. This paper reviewed the development of homomorphic

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... ryption. It summarized two kinds of typical fully homomorphic encryption scheme, and analyzed the design method of fully homomorphic encryption algorithm. It also introduced the applications of the homomorphic encryption to the protection of the data confidentiality in cloud computing and to other fields. It pointed out the key problems of fully homomorphic encryption that needed to be researched at present. It can provide reference for further study of homomorphic encryption.