Loyalty program is a marketing effort by the merchant to keep customers loyal to their stores. It tries to keep track of the purchasing-behavior of a customer by recording customer's purchase information, including his credit card number, as a key identifier to the customer. While it may benefit the customer, the drawback is that the privacy of the customer is intruded. If the customer is using an anonymous payment system such as electronic cash I digital coins, his privacy is protected, but he will not get any benefit from the loyalty program which tries to record his payment information. This paper suggests several solutions to solve merchant's need to gather statistical data from customer's purchasing behavior versus customer's need for privacy. Among the solutions, we present the idea of blindly signed pseudo digital certificates, which satisfies our requirement for a loyalty program scheme with an anonymous payment system.
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