Scalar Product Lattice Computation for Efficient Privacy-preserving Systems

Privacy-preserving applications allow users to perform on-line daily actions without leaking sensitive information. Privacy-preserving scalar product is one of the critical algorithms in many private applications. The state-of-the-art privacy-preserving scalar product schemes use either computationally intensive homomorphic (public-key) encryption techniques such as Paillier encryption to achieve strong security (i.e., 128-bit) or random masking technique to achieve high efficiency for low security. In this paper, lattice structures have been exploited to develop an efficient privacy-preserving system. The proposed scheme is not only efficient in computation as compared to the state-of-the-art but also provides high degree of security against quantum attacks. Rigorous security and privacy analyses of the proposed scheme have been provided along with a concrete set of parameters to achieve 128-bit and 256-bit security. Performance analysis shows that the scheme is at least five orders faster than the Paillier schemes and at least twice as faster than the existing randomisation technique at 128-bit security.