Efficient Verifiable Computation of Linear and Quadratic Functions over Encrypted Data

In data outsourcing, a client stores a large amount of data on an untrusted server; subsequently, the client can request the server to compute a function on any subset of the data. This setting naturally leads to two security requirements: confidentiality of input data, and authenticity of computations. Existing approaches that satisfy both requirements simultaneously are built on fully homomorphic encryption, which involves expensive computation on the server and client and hence is impractical. In this paper, we propose two verifiable homomorphic encryption schemes that do not rely on fully homomorphic encryption. The first is a simple and efficient scheme for linear functions. The second scheme supports the class of multivariate quadratic functions, by combining the Paillier cryptosystem with a new homomorphic message authentication code (MAC) scheme. Through formal security analysis, we show that the schemes are semantically secure and unforgeable.