Efficient Homomorphic Encryption on Integer Vectors and Its Applications

Abstract—Homomorphic encryption, aimed at enabling com-putation in the encrypted domain, is becoming important to a wide and growing range of applications, from cloud computing to distributed sensing. In recent years, a number of approaches to fully (or nearly fully) homomorphic encryption have been proposed, but to date the space and time complexity of the associated schemes has precluded their use in practice. In this work, we demonstrate that more practical homomorphic encryption schemes are possible when we require that not all encrypted computations be supported, but rather only those of interest to the target application. More specifically, we develop a homomorphic encryption scheme operating directly on integer vectors that supports three operations of fundamental interest in signal processing applications: addition, linear transformation, and weighted inner products. Moreover, when used in combina-tion, these primatives allow us to efficiently and securely compute arbitrary polynomials. Some practically relevant examples of the computations supported by this framework are described, including feature extraction, recognition, classification, and data aggregation. I