Cryptanalysis of tran-pang-deng verifiable homomorphic encryption

Abstract

Tran, Pang and Deng (AsiaCCS’16) proposed two verifiable computation schemes on outsourced encrypted data in the cloud computing scenario. One of them enables the delegation of linear functions and the other is constructed for multivariate quadratic polynomials. In the quadratic function case, it was claimed that their scheme is the first to guarantee both confidentiality of input data and authenticity of computations without using fully homomorphic encryption (FHE). In this paper we present a cryptanalysis which shows that their scheme cannot guarantee confidentiality of input data. We start with a technical lemma on pseudorandom functions that have a range of Abelian group and then provides a simple attack which allows the adversary to successfully break the scheme with probability close to 1.