A strongly unsplittable multi-coupon system with off-line verification and selectively-revocable anonymity

This paper firstly reports a security flaw and a way to fix it detected in a multi-coupon system presented by Liu et al. in a paper published in 2017. That proposal provides selectively-revocable anonymity in the sense that the anonymity of customers is guaranteed unless they act dishonestly by redeeming a multi-coupon more times than allowed. Nevertheless, that system lacks two important security properties of multi-coupons: unlinkability and unsplittability. After that, we propose a novel multi-coupon construction which takes Brands off-line e-coin system as a building block. In this way, the multi-coupon system inherits the selective-revocability property of the mentioned e-coin system without the need to develop new ad-hoc cryptography. Furthermore, the proposed system is also proven to be unlinkable and strongly unsplittable. Its design makes use of a novel extension of the RSA blind signature protocol which endows it with conditional secret recovery.