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With the flourish of applications based on the Internet of Things (IoT), privacy issues have been attracting a lot of attentions. Although the concept of privacy homomorphism was proposed along with the birth of the well-known RSA cryptosystems, cryptographers over the world have spent about three decades for finding the first implementation of the so-called fully homomorphic encryption (FHE). Despite of, currently known FHE schemes, including the original Gentry's scheme and many subsequent improvements as well as the other alternatives, are not appropriate for IoT-oriented applications because most of them suffer from the problems of inefficient key size and noisy restraining. In addition, for providing fully support to IoT-oriented applications, symmetric fully homomorphic encryptions are also highly desirable. This survey presents an analysis on the challenges of designing secure and practical FHE for IoT …