Scalar Product Lattice Computation for Efficient Privacy-Preserving Systems

Yogachandran Rahulamathavan, Safak Dogan, Xiyu Shi, Rongxing Lu, Muttukrishnan Rajarajan, Ahmet M. Kondoz

Abstract: Privacy-preserving (PP) applications allow users to perform online daily actions without leaking sensitive information. The PP scalar product (PPSP) is one of the critical algorithms in many private applications. The state-of-the-art PPSP schemes use either computationally intensive homomorphic (public-key) encryption techniques, such as the Paillier encryption to achieve strong security (i.e., 128 b) or random masking technique to achieve high efficiency for low security. In this article, lattice structures have been exploited to develop an efficient PP system. The proposed scheme is not only efficient in computation as compared to the state-of-the-art but also provides a 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-b and 256-b 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 randomization technique at 128-b security. Also the proposed scheme requires six-time fewer data compared to the Paillier and randomization-based schemes for communications.