A Privacy-Friendly Loyalty System Based on Discrete Logarithms over Elliptic Curves

Abstract. Systems for the support of customer relationship management are be-coming increasingly attractive for vendors. Loyalty systems provide an interest-ing possibility for vendors in customer relationship management. This holds for both real world and online vendors. However, beside some potential benefits of a loyalty system, customers may also fear an invasion into their privacy, and may thus refuse to participate in such programs. In this paper, we present a privacy-friendly loyalty system to be used by online vendors to issue loyalty points. The system prevents vendors from exploiting data for the creation of customer profiles by providing unconditional unlinkability of loyalty points with regard to purchases. In the proposed system, we apply the difficulty for the computa-tion of discrete logarithms in a group of prime order to construct a secure and privacy-friendly counter. More precisely, all computations are carried out over special cryptographic groups based on elliptic curves where the decisional Diffie-Hellman problems can be solved easily while the computational Diffie-Hellman is believed to be hard.