Comparison-based computations over fully homomorphic encrypted data

The possibility of outsourcing computation to the cloud offers businesses and individuals substantial cost-savings, flexibility, and availability of compute resources, but potentially sacrifices privacy. Homomorphic encryption can help address this problem by allowing the user to upload encrypted data to the cloud, on which the cloud can then operate without having the secret key. The cloud can return encrypted outputs of computations to the user without decrypting the data, thus providing data hosting and services without compromising privacy. This paper contribution is two-fold. First, it presents a survey into the subject of fully homomorphic encryption and highlights scenarios where homomorphic encryption could be an appropriate solution. Secondly, we focus on the modeling of number comparison in terms of homomorphic encryption. This approach is then used for applications such as the maximum value from a vector or the sorting problem.