A coupon represents the right to claim some service which is typically offered by vendors. In practice, issuing bundled multi-coupons is more efficient than issuing single coupons separately. The diversity of interests of the parties involved in a coupon system demands additional security properties beyond the common requirements (e.g., unforgeability). Customers wish to preserve their privacy when using the multi-coupon bundle and to prevent vendors from profiling. Vendors are interested in establishing a long-term customer relationship and not to subsidise one-time customers, since coupons are cheaper than the regular price. We propose a secure multi-coupon system that allows users to redeem a predefined number of single coupons from the same multi-coupon. The system provides unlinkability and also hides the number of remaining coupons of a multi-coupon from the vendor. A method used in the coupon system might be of independent interest. It proves knowledge of a signature on a message tuple of which a single message can be revealed while the remaining elements of the tuple, the index of the revealed message, as well as the signature remain hidden.
